Daily Papers

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, truncated domains, which introduce non-negligible errors and limit applicability in real-world scenarios. In this study, we propose a novel framework utilizing Physics-Informed Neural Networks (PINNs) to solve the full nonlinear compressible potential equation in an unbounded (infinite) domain. We address the unbounded-domain and convergence challenges inherent in standard PINNs by incorporating a coordinate transformation and embedding physical asymptotic constraints directly into the network architecture. Furthermore, we employ a Multi-Stage PINN (MS-PINN) approach to iteratively minimize residuals, achieving solution accuracy approaching machine precision. We validate this framework by simulating flow over circular and elliptical geometries, comparing our results against traditional finite-domain and linearized solutions. Our findings quantify the noticeable discrepancies introduced by domain truncation and linearization, particularly at higher Mach numbers, and demonstrate that this new framework is a robust, high-fidelity tool for computational fluid dynamics.

The objective of this study is to develop a fully compressible magnetohydrodynamic solver for fast simulations of the global dynamo of the Sun using unstructured grids and GPUs. Accurate modeling of the Sun's convective layers is vital to predicting the Sun's behavior, including the solar dynamo and sunspot cycles. Currently, there are many efficient codes capable of conducting these large simulations; however, many assume an anealastic density distribution. The anelastic assumption is capable of producing accurate results for low mach numbers; however, it fails in regions with a higher mach number and a fully compressible flow must be considered. To avoid these issues, Wang et al. [1] created a Compressible High-ORder Unstructured Spectral difference (CHORUS) code for simulating fluid dynamics inside stars and planets. CHORUS++ augmented the CHORUS code to adopt a higher degree of polynomials by using cubed-sphere meshing and transfinite mapping to perform simulations on unstructured grids [2]. Recently, CHORUS++ was further developed for parallel magnetohydrodynamic (MHD) solutions on GPUs at Clarkson University. In this study the solar benchmark problems presented by Chen et al. [2] are extended to unsteady solar dynamo problems, with two different density scale heights. The CHORUS-MHD code is further accelerated by multiple GPUs and used to successfully solve these solar dynamo benchmark problems. [1] Wang, J., Liang, C., and Miesch, M. S., "A Compressible High-Order Unstructured Spectral Difference Code for Stratified Convection in Rotating Spherical Shells," Journal of Computational Physics, Vol. 290, 2015, pp. 90-111. [2] Chen, K., Liang, C., and Wan, M., "Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids," Physics of Fluids, Vol. 35, 2023, p. 086120.

This paper presents a neural surrogate approach for improving the accuracy of natural convection problems simulated with a Boussinesq flow model (incompressible flow with heat transfer). Our approach, based on Fourier neural operators, uses training data consisting of matched pairs of simulations run under the computationally cheaper yet less accurate Boussinesq flow model and a more computationally expensive and more accurate compressible flow model. In both cases, we implement our parallelized simulation codes based on an implicit monolithic mixed finite element method (FEM) approach using the open-source FEniCSx framework. Our implementations are validated against a commercial software package, COMSOL, as well as standard test problems from the literature. We include a careful discussion and analysis of data set generation and present learning results in two and three spatial dimensions. Using compressible flow results as high-fidelity reference solutions, our learning approach, with a single model evaluation per simulation, substantially improves the per-channel accuracy of Boussinesq predictions, with structural similarity (SSIM) close to unity across all flow variables and test distributions and corresponding mean-squared error reductions of one to nearly three orders of magnitude. All code and data is released as open-source.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf

The widespread use of neural surrogates in automotive aerodynamics, enabled by datasets such as DrivAerML and DrivAerNet++, has primarily focused on bluff-body flows with large wakes. Extending these methods to aerospace, particularly in the transonic regime, remains challenging due to the high level of non-linearity of compressible flows and 3D effects such as wingtip vortices. Existing aerospace datasets predominantly focus on 2D airfoils, neglecting these critical 3D phenomena. To address this gap, we present a new dataset of CFD simulations for 3D wings in the transonic regime. The dataset comprises volumetric and surface-level fields for around 30,000 samples with unique geometry and inflow conditions. This allows computation of lift and drag coefficients, providing a foundation for data-driven aerodynamic optimization of the drag-lift Pareto front. We evaluate several state-of-the-art neural surrogates on our dataset, including Transolver and AB-UPT, focusing on their out-of-distribution (OOD) generalization over geometry and inflow variations. AB-UPT demonstrates strong performance for transonic flowfields and reproduces physically consistent drag-lift Pareto fronts even for unseen wing configurations. Our results demonstrate that AB-UPT can approximate drag-lift Pareto fronts for unseen geometries, highlighting its potential as an efficient and effective tool for rapid aerodynamic design exploration. To facilitate future research, we open-source our dataset at https://huggingface.co/datasets/EmmiAI/Emmi-Wing.

In this paper, we study multidimensional perturbations of radially symmetric rarefactive flows for the compressible Euler equations. No assumptions on the smallness of the background are imposed. We derive lower bounds on both the classical lifespan and stability timespan of the perturbed solution. These lower bounds are demonstrated to tend to infinity as the size of the perturbation approaches zero. Furthermore, owing to the rarefactive nature of the background, the resulting estimate is shown to be substantially longer than the corresponding estimate for a general classical background with bounded first derivatives.

In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative formulations of the same system, are evolved simultaneously. Since nonconservative schemes are known to produce nonphysical weak solutions near discontinuities, we exploit the difference between these two solutions to construct a smoothness indicator (SI). In smooth regions, the difference between the conservative and nonconservative solutions is of the same order as the truncation error of the underlying discretization, whereas in nonsmooth regions, it is {cal O}(1). We apply this idea to the Euler equations of gas dynamics and define the SI using differences in the momentum and pressure variables. This choice allows us to further distinguish neighborhoods of contact discontinuities from other nonsmooth parts of the computed solution. The resulting classification is used to adaptively select numerical discretizations. In the vicinities of contact discontinuities, we employ the low-dissipation central-upwind numerical flux and a second-order piecewise linear reconstruction with the slopes computed using an overcompressive SBM limiter. Elsewhere, we use an alternative weighted essentially non-oscillatory (A-WENO) framework with the central-upwind finite-volume numerical fluxes and either unlimited (in smooth regions) or Ai-WENO-Z (in the nonsmooth regions away from contact discontinuities) fifth-order interpolation. Numerical results for the one- and two-dimensional compressible Euler equations show that the proposed adaptive method improves both the computational efficiency and resolution of complex flow features compared with the non-adaptive fifth-order A-WENO scheme.

This is the second part of the two-paper sequence, which aims to present a comprehensive study for current-vortex sheets with or without surface tension in ideal compressible magnetohydrodynamics (MHD). The results of this paper are two-fold: First, we establish the zero-surface-tension limit of compressible current-vortex sheets under certain stability conditions on the free interface; Second, when the two-phase flows are isentropic and the density functions converge to the same constant as Mach number goes to zero, we can drop the boundedness assumption (with respect to Mach number) on high-order time derivatives by combining the paradifferential approach applied to the evolution equation of the free interface, the structure of wave equations for the total pressure and the anisotropic Sobolev spaces with suitable weights of Mach number. To our knowledge, this is the first result that rigorously justifies the incompressible limit of free-surface MHD flows. Moreover, we actually present a robust framework for the low Mach number limit of vortex-sheet problems, which was never established in any previous works.

It is well known that the compressible Euler equations with planar shock initial data may admit infinitely many entropy weak solutions, as shown by Chiodaroli, De Lellis and Kreml [Comm. Pure Appl. Math. (2015)]. In this paper, we introduce a suitable notion of global-in-time weak solutions to the two-dimensional (2D) compressible Navier-Stokes equations with density-dependent viscosities in R times T. Within this solution framework, we establish the first vanishing viscosity limit selection criterion for the physically relevant planar shock solution to the 2D compressible Euler equations. More precisely, we prove the uniqueness and stability of the 2D Euler planar shock solution within a class of inviscid limits of Navier-Stokes solutions emanating from near-planar initial data while the shock direction perturbation can be arbitrarily large. Starting from the relative κ-entropy for 2D compressible Navier-Stokes equations in T^2 by Bresch, Noble and Vila [ESAIM Proc. Surveys (2017)], we first establish the relative frac12-entropy between 2D weak solution of compressible Navier-Stokes equations in R times T and one-dimensional (1D) strong solution for averaged initial data in R. Then we achieve the desired vanishing viscosity limit selection criterion by successfully bridging the fundamental structural gap between 2D Eulerian formulation of the original Navier-Stokes system in the relative frac12-entropy and 1D vanishing viscosity limit to a shock solution of Euler equations in Lagrangian coordinates by Kang and Vasseur [Invent. Math. (2021)]. The framework developed herein can be applied to the three-dimensional limit selection criterion in R times T^2, as well as to more complex planar Riemann solutions and interacting wave patterns.

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of κ-entropy, we rigorously justify the convergence of weak solutions toward the generalized anelastic system in a three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we establish a similar convergence result in the whole space, relying essentially on dispersive estimates for acoustic waves. Compared with the work of Fanelli and Zatorska [Commun. Math. Phys., 400 (2023), pp. 1463-1506], our analysis is conducted for the standard isentropic pressure law, thereby eliminating the need for the cold pressure term that played a crucial role in the previous approach. To the best of our knowledge, this is the first rigorous singular limit result for the compressible Navier-Stokes equations with degenerate viscosity that requires no additional regularization of the system.

We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range 1<γleq5{3}. The perturbed solutions develop an asymptotically self-similar implosion in finite time. Our result allows perturbations with small, nonzero constant pressure in the quiescent region ahead of the shock. The proof combines weighted L^infty estimates along characteristics with a computer-assisted proof of stability inequalities for the Guderley profile.

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

We study the initial--boundary value problem for the one-dimensional full compressible Navier--Stokes system whose viscosity and heat conductivity are given by μ(θ)=μθ^α and κ(θ)=κθ^β, respectively. The initial density is nonnegative and is allowed to vanish. For α>2 and β>2α+4, we prove the existence of a global strong solution for arbitrarily large compatible H^2 data, provided that the prescribed boundary temperature is sufficiently high relative to their size. No velocity or temperature perturbation is required to shrink as the boundary temperature tends to infinity. A shifted initial-layer weight and an exact symmetrization of the two material-derivative equations separate the fast thermal mode from the momentum mode. The resulting estimates are uniform with respect to the positive lower bound used in the approximation and therefore survive the limit to genuine vacuum. The proof further combines a relative-entropy identity centered at the conserved mean density, the physical effective viscous flux, a Zlotnik-type estimate along particle trajectories, and finite-time transport estimates for the density derivatives. The density remains uniformly bounded and the temperature stays uniformly comparable with the prescribed boundary temperature. After the initial layer we establish vacuum-compatible exponential relaxation: the density converges to its conserved mean in every finite L^p, the velocity and temperature perturbation decay in H^1, and the weighted material-derivative energy decays at rate cbarθ^{1-α}.

We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve, particularly conservation laws whose physically relevant solutions contain shocks and discontinuities. FV methods are widely used for their mathematical properties: convergence to entropy solutions, flow conservation, or total variation diminishing, but often lack accuracy and flexibility in complex settings. Neural Finite Volume addresses these limitations by learning update rules over extended spatial and temporal stencils while preserving conservation structure. It supports both supervised training on solution data (NFV) and unsupervised training via weak-form residual loss (UNFV). Applied to first-order conservation laws, (U)NFV achieves up to 10x lower error than Godunov's method, outperforms ENO/WENO, and rivals discontinuous Galerkin solvers with far less complexity. On traffic modeling problems, both from PDEs and from experimental highway data, (U)NFV captures nonlinear wave dynamics with significantly higher fidelity and scalability than traditional FV approaches.

We study the Cauchy problem for the one-dimensional isothermal compressible Navier--Stokes system with the van der Waals equation of state, and analyze the well-posedness and asymptotic stability of steady-state phase-transition solutions at subcritical temperatures. Working in Lagrangian coordinates, we use variational techniques to construct piecewise smooth steady-state solutions corresponding to two-phase equilibrium states under finite-mass perturbations. Introducing artificial-viscosity regularization, we first establish existence of the global minimizer of the regularized variational problem, unique within each fixed symmetry class; passing to the vanishing artificial-viscosity limit then yields a physically admissible steady-state solution with two phase interfaces. For initial perturbations that are small with respect to energy, piecewise-gradient, total-variation, and integral norms but may exhibit large pointwise jumps across phase boundaries, we derive uniform a priori bounds for weak solutions near the two-phase equilibrium profile. We further prove that these global weak solutions converge to the steady-state two-phase equilibrium in L^infty(R) as ttoinfty, thereby characterizing their large-time asymptotic behavior. Physically, finite mass perturbations break the uniqueness of the uniform steady state and generate infinitely many piecewise constant two-phase equilibria satisfying the Maxwell equal-area rule. Artificial viscosity acts as a selection principle that singles out the physically relevant two-interface steady-state configuration, and this two-phase equilibrium is asymptotically stable under small integral perturbations that allow large-amplitude discontinuities at phase interfaces.

We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity ρ^β, and pressure ρ^γ. For every β>1 and γ>1, we construct global finite-energy renormalized weak solutions from strictly positive bounded W^{1,q} densities, q>2, and arbitrary H^1 velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the β-power density potential yields weak--strong uniqueness against positive H^2 strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when γ>max{5-2β,β+1}. Writing m=intρ_0, the density perturbation is bounded in the scaled norm m^{(γ-3)/2}|ρ_0-m|_{H^2}, while the fixed H^2 velocity and magnetic norms need not be small. For sufficiently large m, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum 7/3, with the endpoint excluded. For β>2 the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on β. The strong theorem has no upper restriction on γ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to γ=3.

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

Simulating fluid flow around arbitrary shapes is key to solving various engineering problems. However, simulating flow physics across complex geometries remains numerically challenging and computationally resource-intensive, particularly when using conventional PDE solvers. Machine learning methods offer attractive opportunities to create fast and adaptable PDE solvers. However, benchmark datasets to measure the performance of such methods are scarce, especially for flow physics across complex geometries. We introduce FlowBench, a dataset for neural simulators with over 10K samples, which is currently larger than any publicly available flow physics dataset. FlowBench contains flow simulation data across complex geometries (parametric vs. non-parametric), spanning a range of flow conditions (Reynolds number and Grashoff number), capturing a diverse array of flow phenomena (steady vs. transient; forced vs. free convection), and for both 2D and 3D. FlowBench contains over 10K data samples, with each sample the outcome of a fully resolved, direct numerical simulation using a well-validated simulator framework designed for modeling transport phenomena in complex geometries. For each sample, we include velocity, pressure, and temperature field data at 3 different resolutions and several summary statistics features of engineering relevance (such as coefficients of lift and drag, and Nusselt numbers). %Additionally, we include masks and signed distance fields for each shape. We envision that FlowBench will enable evaluating the interplay between complex geometry, coupled flow phenomena, and data sufficiency on the performance of current, and future, neural PDE solvers. We enumerate several evaluation metrics to help rank order the performance of neural PDE solvers. We benchmark the performance of several baseline methods including FNO, CNO, WNO, and DeepONet.

Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy. Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/tum-pbs/SFBC.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (P-IGANO). We enforce the incompressible Navier Stokes equations in the free-flow region and a Darcy Forchheimer extension in the porous region within a unified loss and condition the networks on geometry and material parameters. Datasets are generated with OpenFOAM on 2D ducts containing porous obstacles and on 3D windbreak scenarios with tree canopies and buildings. We first verify the pipeline via the method of manufactured solutions, then assess generalization to unseen shapes, and for PI-GANO, to variable boundary conditions and parameter settings. The results show consistently low velocity and pressure errors in both seen and unseen cases, with accurate reproduction of the wake structures. Performance degrades primarily near sharp interfaces and in regions with large gradients. Overall, the study provides a first systematic evaluation of PIPN/PI-GANO for simultaneous through-and-around porous flows and shows their potential to accelerate design studies without retraining per geometry.

We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver, while maintaining excellent to reasonable accuracy.

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure--density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure--density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

Deep learning has emerged as a promising paradigm for spatio-temporal modeling of fluid dynamics. However, existing approaches often suffer from limited generalization to unseen flow conditions and typically require retraining when applied to new scenarios. In this paper, we present LLM4Fluid, a spatio-temporal prediction framework that leverages Large Language Models (LLMs) as generalizable neural solvers for fluid dynamics. The framework first compresses high-dimensional flow fields into a compact latent space via reduced-order modeling enhanced with a physics-informed disentanglement mechanism, effectively mitigating spatial feature entanglement while preserving essential flow structures. A pretrained LLM then serves as a temporal processor, autoregressively predicting the dynamics of physical sequences with time series prompts. To bridge the modality gap between prompts and physical sequences, which can otherwise degrade prediction accuracy, we propose a dedicated modality alignment strategy that resolves representational mismatch and stabilizes long-term prediction. Extensive experiments across diverse flow scenarios demonstrate that LLM4Fluid functions as a robust and generalizable neural solver without retraining, achieving state-of-the-art accuracy while exhibiting powerful zero-shot and in-context learning capabilities. Code and datasets are publicly available at https://github.com/qisongxiao/LLM4Fluid.

Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and memory demand required by CFD codes may become very high for flows of practical interest, such as in aerodynamic shape optimization. This expense is associated with the complexity of the fluid flow governing equations, which include non-linear partial derivative terms that are of difficult solution, leading to long computational times and limiting the number of hypotheses that can be tested during the process of iterative design. Therefore, we propose DeepCFD: a convolutional neural network (CNN) based model that efficiently approximates solutions for the problem of non-uniform steady laminar flows. The proposed model is able to learn complete solutions of the Navier-Stokes equations, for both velocity and pressure fields, directly from ground-truth data generated using a state-of-the-art CFD code. Using DeepCFD, we found a speedup of up to 3 orders of magnitude compared to the standard CFD approach at a cost of low error rates.

This paper investigates the stability of steady transonic shocks with constant states in rectangular nozzles under small three dimensional perturbations of the external force and the exit pressure. Mathematically, the problem can be formulated as a nonlinear free boundary problem for a hyperbolic-elliptic coupled PDE system. One of the key difficulties lies in the arbitrary location of the background shock, which may lead to multiple shock solutions for the same external force and exit pressure under perturbations, revealing the instability of the background shock. We reformulate the steady Euler equations in terms of deformation and vorticity to effectively decompose the hyperbolic and elliptic modes. Linearizing the reformulated system and the Rankine-Hugoniot conditions at background transonic shocks, we find that the class of nonzero horizontal external forces helps to uniquely determine the shock location, where the conservation of mass plays a critical role. A delicate iteration is developed to establish the existence and structural stability of transonic shock solutions. Our analysis shows that the stability mechanisms of steady transonic shocks in flat and divergent nozzles are quite different in many aspects.

Two-dimensional Kolmogorov flow is a common proving ground for the dynamical systems picture of turbulence. Hundreds of unstable periodic orbits have been found for this system across many Reynolds numbers and domain sizes, although the most well explored is Re=40 on a square 2πtimes 2π domain with a forcing wavenumber of k=4. Here I present a catalog of 8952 exact steady states of the flow in this canonical parameter regime. These solutions provide a fixed constellation informing the dynamics of both turbulence and transients.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

We introduce a dataset of approximately 10,000 Reynolds-Averaged Navier-Stokes (RANS) simulations of steady, incompressible, two-dimensional subsonic flow around downforce-generating NACA 4-digit airfoils, targeting aerodynamic regimes relevant to automotive and motorsport applications (openly available on https://huggingface.co/datasets/ratiolabs/downforce-airfoils). Using this resource, we study geometry-conditioned neural surrogates for fast flow prediction, comparing neural fields with neural ODEs, MLPs with graph-based models, and several spectral geometry-conditioning methods. We further propose Airfoil2Vec, an airfoil-specific spectral geometry encoder that combines the joint contour spectrum with separate spectral representations of camber and thickness, for predicting continuous pressure and velocity fields. We evaluate generalization through angle-of-attack interpolation, interpolation and extrapolation to unseen NACA 4-digit geometries, and generalization to unseen non-NACA airfoils. The resulting surrogate accurately captures aerodynamic quantities and qualitative flow features while providing orders-of-magnitude speedups over conventional computational fluid dynamics.

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

This paper constitutes Part III of a series investigating the excitation of non-modal perturbations in hypersonic blunt-nose boundary layers. Based on the numerical shock-fitting harmonic linearised Navier-Stokes (SF-HLNS) approach presented in Part I (Zhao & Dong, J. Fluid Mech. 2025, vol. 1013: A44) and the asymptotic analysis developed in Part II (Dong et al., J. Fluid Mech., under review), the present work focuses specifically on the influence of nose bluntness (Reynolds number R) and wall temperature T_w on receptivity efficiency through seven detailed case studies. Analysed via the three-step asymptotic model, the downstream perturbation amplitude is governed by two distinct factors: the stagnation vorticity perturbation, determined through shock-perturbation interaction and the slow-down convection mechanism, and the parabolic evolution of non-modal perturbations driven by the lift-up mechanism. Increasing R strongly amplifies the stagnation vorticity response, with only mild enhancement of the lift-up effect. In contrast, decreasing T_w strengthens the stagnation vorticity perturbation, but slightly weakens the lift-up effect; the net result is an overall intensification of the downstream perturbation amplitude with decreasing T_w. Furthermore, explicit scaling laws for receptivity efficiency with respect to R and T_w are established. This study completes the theoretical foundation for non-modal receptivity in hypersonic blunt boundary layers, and serves as a key step toward a physics-based transition prediction framework.

Urban microclimate, encompassing wind and temperature fields shaped by building geometry, strongly affects building energy use, pedestrian wind comfort, pollutant dispersion, the urban heat island, and public health. Conventional Computational Fluid Dynamics (CFD) is computationally prohibitive for rapid assessments, while many deep learning approaches require extensive training data and struggle with generalization to unseen configurations. In this work, we present the Fast Localized Urban Microclimate Emulator (FLUME), a rapid, data-efficient, and geometry-aware framework based on a Fourier neural operator for predicting three-dimensional wind and temperature fields. FLUME assumes that, under prescribed inflow and thermal forcing, much of the spatial variation of these mean fields is controlled by surrounding building geometry. The framework introduces a Multi-Directional Distance Feature (MDDF), which captures geometry over adaptive, visibility-defined spatial scales. By decomposing simulations of only 23 urban blocks into smaller 3D patches enriched with precomputed MDDF information, FLUME enables learning from limited CFD data. The model achieves mean absolute errors of 0.2 m/s for streamwise velocity and 0.19^{circ}C for temperature on unseen urban configurations. A deep ensemble provides a practical proxy for epistemic uncertainty, and conformal prediction transforms these estimates into calibrated prediction intervals. Ensemble spread is positively related to local prediction error, with greater uncertainty in roof-level shear layers, building wakes, and vertical velocity near the ground. These results indicate FLUME's potential for rapid scenario assessment in urban design and urban climate studies.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial differential equations (i.e., surrogate modeling). Although these neural networks may have lower accuracy than traditional numerical methods, they, once trained, are orders of magnitude faster at inference. Hence, one crucial feature is that these operators can generalize to unseen PDE parameters without expensive re-training.In this paper, we construct CFDBench, a benchmark tailored for evaluating the generalization ability of neural operators after training in computational fluid dynamics (CFD) problems. It features four classic CFD problems: lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. The data contains a total of 302K frames of velocity and pressure fields, involving 739 cases with different operating condition parameters, generated with numerical methods. We evaluate the effectiveness of popular neural operators including feed-forward networks, DeepONet, FNO, U-Net, etc. on CFDBnech by predicting flows with non-periodic boundary conditions, fluid properties, and flow domain shapes that are not seen during training. Appropriate modifications were made to apply popular deep neural networks to CFDBench and enable the accommodation of more changing inputs. Empirical results on CFDBench show many baseline models have errors as high as 300% in some problems, and severe error accumulation when performing autoregressive inference. CFDBench facilitates a more comprehensive comparison between different neural operators for CFD compared to existing benchmarks.

This paper studies the existence and asymptotic stability of traveling shock waves for the one-dimensional full compressible Navier--Stokes--Poisson equations, which model viscous heat-conducting ions in a self-consistent electrostatic field. We first prove the existence and uniqueness of a smooth shock profile of small amplitude by the center manifold theorem, and then establish its large-time asymptotic stability under suitably small smooth perturbations. The proof is based on an energy estimate for a specially constructed integrated system derived from the full compressible Navier--Stokes--Poisson equations. To carry out this estimate, we introduce suitable anti-derivative variables that incorporate the effects of the self-consistent electrostatic potential and heat conduction, thereby reformulating the original system as a dissipative integrated one. The subsequent energy estimates are completed by carefully handling the induced couplings.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

In this paper, we rigorously derive the fundamental PDEs of fluid mechanics, such as the compressible Euler and incompressible Navier-Stokes-Fourier equations, starting from the hard sphere particle systems undergoing elastic collisions. This resolves Hilbert's sixth problem, as it pertains to the program of deriving the fluid equations from Newton's laws by way of Boltzmann's kinetic theory. The proof relies on the derivation of Boltzmann's equation on 2D and 3D tori, which is an extension of our previous work (arXiv:2408.07818).

Deep Learning methods have seen a wide range of successful applications across different industries. Up until now, applications to physical simulations such as CFD (Computational Fluid Dynamics), have been limited to simple test-cases of minor industrial relevance. This paper demonstrates the development of a novel deep learning framework for real-time predictions of the impact of manufacturing and build variations on the overall performance of axial compressors in gas turbines, with a focus on tip clearance variations. The associated scatter in efficiency can significantly increase the CO2 emissions, thus being of great industrial and environmental relevance. The proposed C(NN)FD architecture achieves in real-time accuracy comparable to the CFD benchmark. Predicting the flow field and using it to calculate the corresponding overall performance renders the methodology generalisable, while filtering only relevant parts of the CFD solution makes the methodology scalable to industrial applications.

Numerical analysis of unconfined flow over an obstacle has always been challenging in computational fluid dynamics due to the truncation of the computational domain while replicating the real-life flows and the application of the boundary conditions. Confined flows studies have been well established and documented while unconfined flow studies are relatively challenging. Present work demonstrates the implementation of lattice Boltzmann method for unconfined flow over a circular cylinder for Re 100. The cylinder was placed at 10D upstream and 30D downstream and 10D from both the top and bottom walls. Different boundary conditions were implemented at the top and bottom walls to ensure unconfined flow. Drag and lift coefficients are also presented and were computed using the momentum exchange algorithm. Results are in complete agreement with the existing literature which demonstrate the capability of the solver.

Computational Fluid Dynamics (CFD) is an essential simulation tool in various engineering disciplines, but it often requires substantial domain expertise and manual configuration, creating barriers to entry. We present Foam-Agent, a multi-agent framework that automates complex OpenFOAM-based CFD simulation workflows from natural language inputs. Our innovation includes (1) a hierarchical multi-index retrieval system with specialized indices for different simulation aspects, (2) a dependency-aware file generation system that provides consistency management across configuration files, and (3) an iterative error correction mechanism that diagnoses and resolves simulation failures without human intervention. Through comprehensive evaluation on the dataset of 110 simulation tasks, Foam-Agent achieves an 83.6% success rate with Claude 3.5 Sonnet, significantly outperforming existing frameworks (55.5% for MetaOpenFOAM and 37.3% for OpenFOAM-GPT). Ablation studies demonstrate the critical contribution of each system component, with the specialized error correction mechanism providing a 36.4% performance improvement. Foam-Agent substantially lowers the CFD expertise threshold while maintaining modeling accuracy, demonstrating the potential of specialized multi-agent systems to democratize access to complex scientific simulation tools. The code is public at https://github.com/csml-rpi/Foam-Agent

Traditional experimental and numerical approaches for fluid dynamics problems often suffer from high computational cost, mesh sensitivity, and limited capability in capturing complex physical behaviors. Moreover, conventional physics-informed neural networks (PINNs) frequently struggle in chaotic and highly unsteady flow regimes. In this work, we propose PhysicsFormer, a fast and efficient transformer-based physics-informed framework that incorporates multi-head encoder-decoder cross-attention. Unlike multilayer perceptron-based PINNs, PhysicsFormer operates on sequential representations constructed from spatio-temporal data, enabling effective learning of long-range temporal dependencies and improved propagation of initial condition information. A data-embedding strategy is employed to convert spatio-temporal points into pseudo-sequences, while a dynamics-weighted loss function replaces the standard PINNs formulation. Owing to its parallel learning structure, PhysicsFormer demonstrates superior computational efficiency compared to existing transformer-based approaches. The framework is validated on Burgers' equation and flow reconstruction governed by the Navier-Stokes equations, achieving mean squared errors on the order of 10^{-6}. In addition, an inverse problem involving parameter identification in the two-dimensional incompressible Navier-Stokes equations is investigated. For clean data, PhysicsFormer achieves zero identification error for both λ_1 and λ_2; under 1% Gaussian noise, the errors are 0.07% for λ_1 and 0% for λ_2. These results demonstrate that PhysicsFormer provides a reliable and computationally efficient surrogate modeling framework for time-dependent fluid flow problems.

Large Language Models (LLMs) have demonstrated strong performance across general NLP tasks, but their utility in automating numerical experiments of complex physical system -- a critical and labor-intensive component -- remains underexplored. As the major workhorse of computational science over the past decades, Computational Fluid Dynamics (CFD) offers a uniquely challenging testbed for evaluating the scientific capabilities of LLMs. We introduce CFDLLMBench, a benchmark suite comprising three complementary components -- CFDQuery, CFDCodeBench, and FoamBench -- designed to holistically evaluate LLM performance across three key competencies: graduate-level CFD knowledge, numerical and physical reasoning of CFD, and context-dependent implementation of CFD workflows. Grounded in real-world CFD practices, our benchmark combines a detailed task taxonomy with a rigorous evaluation framework to deliver reproducible results and quantify LLM performance across code executability, solution accuracy, and numerical convergence behavior. CFDLLMBench establishes a solid foundation for the development and evaluation of LLM-driven automation of numerical experiments for complex physical systems. Code and data are available at https://github.com/NREL-Theseus/cfdllmbench/.

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Computational Fluid Dynamics (CFD) is an essential simulation tool in engineering, yet its steep learning curve and complex manual setup create significant barriers. To address these challenges, we introduce Foam-Agent, a multi-agent framework that automates the entire end-to-end OpenFOAM workflow from a single natural language prompt. Our key innovations address critical gaps in existing systems: 1. An Comprehensive End-to-End Simulation Automation: Foam-Agent is the first system to manage the full simulation pipeline, including advanced pre-processing with a versatile Meshing Agent capable of handling external mesh files and generating new geometries via Gmsh, automatic generation of HPC submission scripts, and post-simulation visualization via ParaView. 2. Composable Service Architecture: Going beyond a monolithic agent, the framework uses Model Context Protocol (MCP) to expose its core functions as discrete, callable tools. This allows for flexible integration and use by other agentic systems, such as Claude-code, for more exploratory workflows. 3. High-Fidelity Configuration Generation: We achieve superior accuracy through a Hierarchical Multi-Index RAG for precise context retrieval and a dependency-aware generation process that ensures configuration consistency. Evaluated on a benchmark of 110 simulation tasks, Foam-Agent achieves an 88.2% success rate with Claude 3.5 Sonnet, significantly outperforming existing frameworks (55.5% for MetaOpenFOAM). Foam-Agent dramatically lowers the expertise barrier for CFD, demonstrating how specialized multi-agent systems can democratize complex scientific computing. The code is public at https://github.com/csml-rpi/Foam-Agent.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

This paper describes the first-ever open-source high-fidelity CFD dataset of a high-lift aircraft for the purpose of AI surrogate model development. The dataset is composed of 1800 samples, arising from 180 geometry variants and 10 angles of attack for the high-lift NASA Common Research Model (CRM) geometry, used within the AIAA High-Lift Prediction Workshop series. One of the novelties of this dataset is the use of a GPU-accelerated high-fidelity explicit, wall-modeled LES approach for each simulation, using solution-adapted grids between 300M and 500M cells. This ensures the greatest possible accuracy given known challenges in steady-state RANS approaches for these portions of the flight envelope. The entire dataset (geometries, time-averaged volume and surface variables and integral forces) are available, free of charge with a permissive open-source license (CC-BY-4.0). By making this data publicly available, we aim to accelerate the research and development of AI surrogate modeling within the aerospace industry.

Neural surrogates offer a promising route to accelerating computationally expensive simulations governed by partial differential equations across science and industry. Their practical deployment, however, is limited by unreliable predictions under out-of-distribution (OOD) conditions. We develop a solver-coupled surrogate-Newton framework that uses surrogate predictions as high-quality initial guesses for Newton-Krylov iterations, thereby combining rapid global flow-field prediction with high-accuracy numerical convergence at the terminal stage. On an OOD benchmark comprising geometries sampled from actual transonic airfoil optimization trajectories, the framework lowers the median residual L_2 ratio by over seven orders of magnitude while substantially reducing field and aerodynamic errors. In practical supercritical airfoil optimization, it improves online prediction reliability while achieving a 15.5-fold generation-level speedup over CFD. We further test the framework's extension to three dimensions using a flying-wing dataset. Together, these studies demonstrate the potential of surrogate-Newton coupling to deliver accurate, efficient and scalable steady CFD across industrial workflows.

High-fidelity scientific simulations are now producing unprecedented amounts of data, creating a storage and analysis bottleneck. A single simulation can generate tremendous data volumes, often forcing researchers to discard valuable information. A prime example of this is plasma turbulence described by the gyrokinetic equations: nonlinear, multiscale, and 5D in phase space. It constitutes one of the most computationally demanding frontiers of modern science, with runs taking weeks and yielding tens of terabytes of data dumps. The increasing storage demands underscore the importance of compression. However, reconstructed snapshots do not necessarily preserve essential physical quantities. We present a spatiotemporal evaluation pipeline, accounting for structural phenomena and multi-scale transient fluctuations to assess the degree of physical fidelity. Indeed, we find that various compression techniques lack preservation of both spatial mode structure and temporal turbulence characteristics. Therefore, we explore Physics-Informed Neural Compression (PINC), which incorporates physics-informed losses tailored to gyrokinetics and enables extreme compressions ratios of over 70,000x. Entropy coding on top of PINC further pushes it to 120,000x. This direction provides a viable and scalable solution to the prohibitive storage demands of gyrokinetics, enabling post-hoc analyses that were previously infeasible.

The advancement of high-performance computing has enabled the generation of large direct numerical simulation (DNS) datasets of turbulent flows, driving the need for efficient compression/decompression techniques that reduce storage demands while maintaining fidelity. Traditional methods, such as the discrete wavelet transform, cannot achieve compression ratios of 8 or higher for complex turbulent flows without introducing significant encoding/decoding errors. On the other hand, a super-resolution-based generative adversarial network (SR-GAN), called ZipGAN, can accurately reconstruct fine-scale features, preserving velocity gradients and structural details, even at a compression ratio of 512, thanks to the more efficient representation of the data in compact latent space. Additional benefits are ascribed to adversarial training. The high GAN training time is significantly reduced with a progressive transfer learning approach and, once trained, they can be applied independently of the Reynolds number. It is demonstrated that ZipGAN can enhance dataset temporal resolution without additional simulation overhead by generating high-quality intermediate fields from compressed snapshots. The ZipGAN discriminator can reliably evaluate the quality of decoded fields, ensuring fidelity even in the absence of original DNS fields. Hence, ZipGAN compression/decompression method presents a highly efficient and scalable alternative for large-scale DNS storage and transfer, offering substantial advantages over the DWT methods in terms of compression efficiency, reconstruction fidelity, and temporal resolution enhancement.

Air lubrication regimes were studied using simultaneous drag force measurements and multi-plane imaging to characterize the regimes and identify the governing mechanisms of drag reduction. A bubbly, transitional, and air layer regime are identified over a large range of freestream velocities (U_{infty}), air flow rates (Q_{air}), and Froude-depth numbers (Fr_d). For the lowest U_{infty}, drag reduction lags significantly behind the non-wetted area coverage at all cases and no simple correlation exists. Within the bubbly regime, a drag increase is found for low U_{infty} with large, slow-moving bubbles forming a single layer over the plate height. For higher velocities, bubbles become smaller and disperse vertically, while the drag starts decreasing. For higher Q_{air}, irrespective of U_{infty}, air patches start to form (transitional regime) and drag monotonically decreases, with the onset of the air layer regime at 60\% drag reduction. A new scaling of the associated critical Q_{air} is proposed, combining the air exit velocity, the liquid velocity close to the air layer and Fr_d. For a further increase of Q_{air} and low U_{infty}, a thicker and smoother air layer is formed with even lower drag; for higher U_{infty}, marginal differences are observed. The air layer morphology is significantly altered however, depending on Fr_d: for Fr_d>0.7, it is unbounded, extending beyond the current test section length, and for subcritical conditions (deep water regime, Fr_d<0.61) a closure is formed and the air layer transitions to a cavity of a specific length.

Heterogeneous high--performance computing architectures expose numerical algorithms to perturbations arising from the non--associativity of floating--point arithmetic. In Large--Eddy Simulation (LES), similar numerical effects may become relevant when they affect the filter--width entering the subgrid scale (SGS) model. This work investigates this mechanism for the least--squares (LSQ) based filter--width formulation, focusing on how floating--point effects are generated, transmitted, and coupled with the resolved flow. We show that, for fixed resolved kinematics, the LSQ filter--width is logarithmically non-expansive but not strictly contractive with respect to perturbations of the mesh metrics. Consequently, small disturbances may be transmitted with little attenuation through strongly directional filter-width responses. To mitigate this sensitivity, we introduce a scalar max--min compression of the directional mesh scales together with a bounded modulation based on the resolved velocity gradient. The resulting formulation reroutes floating--point perturbations through the filter-width operator, improving robustness while preserving the flow--dependent character of the original LSQ construction. The framework is assessed on heterogeneous CPU and GPU architectures for flow past a circular cylinder at Re=3900 and the Taylor--Green vortex at Re=1600. In the former, nearly one--to--one transmission of relative metric disturbances can become relevant when the transmitted perturbations interact with shear-layer transition. By contrast, on orthogonal Taylor--Green vortex grids, the accumulation pathway is structurally absent and no comparable macroscopic response develops. These results suggest floating--point sensitivity matters for LES filter--width formulations in heterogeneous computing environments.

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the multidimensional torus is analyzed. The equations describe the dynamics of population species with repulsive or attractive interactions. The numerical scheme is based on a generalized Scharfetter-Gummel discretization of the nonlocal flux term. For merely integrable kernel functions, the scheme preserves the positivity, total mass, and entropy structure. The existence of a discrete solution and its convergence to a solution to the continuous problem, as the mesh size tends to zero, are shown. A key difficulty is the degeneracy of the generalized Bernoulli function in the Scharfetter-Gummel approximation. This issue is overcome by proving a uniform estimate for the discrete Fisher information, which requires both the Boltzmann and Rao entropy inequalities. Numerical simulations illustrate the features of the scheme in one and two space dimensions.

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

Recent work in scientific machine learning (SciML) has focused on incorporating partial differential equation (PDE) information into the learning process. Much of this work has focused on relatively ``easy'' PDE operators (e.g., elliptic and parabolic), with less emphasis on relatively ``hard'' PDE operators (e.g., hyperbolic). Within numerical PDEs, the latter problem class requires control of a type of volume element or conservation constraint, which is known to be challenging. Delivering on the promise of SciML requires seamlessly incorporating both types of problems into the learning process. To address this issue, we propose ProbConserv, a framework for incorporating conservation constraints into a generic SciML architecture. To do so, ProbConserv combines the integral form of a conservation law with a Bayesian update. We provide a detailed analysis of ProbConserv on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs. ProbConserv is effective for easy GPME variants, performing well with state-of-the-art competitors; and for harder GPME variants it outperforms other approaches that do not guarantee volume conservation. ProbConserv seamlessly enforces physical conservation constraints, maintains probabilistic uncertainty quantification (UQ), and deals well with shocks and heteroscedasticities. In each case, it achieves superior predictive performance on downstream tasks.

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using paired computational-fluid-dynamics simulations and experimental particle-image-velocimetry measurements. A mean-preserving input intervention removes velocity fluctuations from selected regions of observed flow histories. Across four neural operators, removing fluctuations from the most energetic 10% of valid observed cells changes forecasts more than equal-area random removal. Because the masks are not matched for removed fluctuation energy, this contrast measures sensitivity, not independent evidence of physical importance. Separately, a CNO has lower velocity-field error but substantially higher two-component fluctuation-energy error than the reference on both analysis subsets. An output attenuation stress test also demonstrates disagreement between benchmark errors and domain-summed fluctuation energy. These single-benchmark results motivate reporting complementary physical diagnostics alongside aggregate prediction scores; they do not establish counterfactual physical correctness.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Physics-Informed machine learning models have recently emerged with some interesting and unique features that can be applied to reservoir engineering. In particular, physics-informed neural networks (PINN) leverage the fact that neural networks are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations. The transient diffusivity equation is a fundamental equation in reservoir engineering and the general solution to this equation forms the basis for Pressure Transient Analysis (PTA). The diffusivity equation is derived by combining three physical principles, the continuity equation, Darcy's equation, and the equation of state for a slightly compressible liquid. Obtaining general solutions to this equation is imperative to understand flow regimes in porous media. Analytical solutions of the transient diffusivity equation are usually hard to obtain due to the stiff nature of the equation caused by the steep gradients of the pressure near the well. In this work we apply physics-informed neural networks to the one and two dimensional diffusivity equation and demonstrate that decomposing the space domain into very few subdomains can overcome the stiffness problem of the equation. Additionally, we demonstrate that the inverse capabilities of PINNs can estimate missing physics such as permeability and distance from sealing boundary similar to buildup tests without shutting in the well.

We present the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator for amortized incompressible density transport. Given a new source-target density pair, VIOT predicts a divergence-free velocity field and generates the full transport trajectory by feed-forward inference, replacing the hour-scale per-pair optimization used by adjoint fluid solvers and differentiable simulation baselines. The system consists of three components: a stream-function or vector-potential representation that enforces incompressibility by construction, a regularized incompressible transport objective that balances endpoint accuracy and flow smoothness, and a Fourier Neural Operator backbone that amortizes the solve across new pairs and grid resolutions. Together, these components make incompressible transport a reusable neural operator that facilitates various transport processes. Further, the generative capability extends beyond the training distribution, with VIOT producing incompressible transports for user-drawn source-target pairs in a real-time interactive system. We demonstrate VIOT on 2D and 3D density-transport benchmarks. Both 2D and 3D rollouts complete in seconds per pair, while per-instance baselines in our 2D comparisons optimize each new pair from scratch and require on the order of an hour, a roughly 10^4times online speedup.

In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and 2, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler fluids.

High-fidelity computational fluid dynamics (CFD) is widely used for thermal-fluid design, but repeated CFD solves remain expensive for design optimization, uncertainty analysis, and digital-twin workflows. Recently, our team has demonstrated that a proper orthogonal decomposition and neural-network (POD-NN) surrogate can predict two-dimensional thermal fields in an electronics-cooling cold plate with large inference speedups while preserving physically interpretable modal structure. Reproducing and extending such workflows, however, typically requires custom scripts for parameter sampling, Fluent automation, data extraction, reduced-order model construction, neural-network training, validation, and prediction. This paper introduces CFDTwin, an open-source Python package and optional desktop graphical user interface (GUI) that packages these steps into a reusable workflow for ANSYS Fluent simulations. CFDTwin allows users to define simulation inputs and output quantities, generate design-of-experiments samples, run and resume Fluent batch simulations, train POD-NN surrogate models for scalar, surface-field, and cell-zone outputs, inspect validation metrics, and evaluate trained models at new design points without re-running Fluent. The same workflow is exposed through a scriptable Python API and a GUI, supporting reproducible studies, user-facing model validation, and automated design exploration. CFDTwin extends the prior POD-NN modeling study from a case-specific research implementation to a reusable research-software platform for CFD surrogate modeling and digital-twin development.

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.

The rapid evolution of large language models (LLMs) is transforming artificial intelligence into autonomous research partners, yet a critical gap persists in complex scientific domains such as combustion modeling. Here, practical AI assistance requires the seamless integration of domain literature knowledge with robust execution capabilities for expertise-intensive tools such as computational fluid dynamics (CFD) codes. To bridge this gap, we introduce FlamePilot, an LLM agent designed to empower combustion modeling research through automated and self-corrective CFD workflows. FlamePilot differentiates itself through an architecture that leverages atomic tools to ensure the robust setup and execution of complex simulations in both OpenFOAM and extended frameworks such as DeepFlame. The system is also capable of learning from scientific articles, extracting key information to guide the simulation from initial setup to optimized results. Validation on a public benchmark shows FlamePilot achieved a perfect 1.0 executability score and a 0.438 success rate, surpassing the prior best reported agent scores of 0.625 and 0.250, respectively. Furthermore, a detailed case study on Moderate or Intense Low-oxygen Dilution (MILD) combustion simulation demonstrates its efficacy as a collaborative research copilot, where FlamePilot autonomously translated a research paper into a configured simulation, conducted the simulation, post-processed the results, proposed evidence-based refinements, and managed a multi-step parameter study to convergence under minimal human intervention. By adopting a transparent and interpretable paradigm, FlamePilot establishes a foundational framework for AI-empowered combustion modeling, fostering a collaborative partnership where the agent manages workflow orchestration, freeing the researcher for high-level analysis.

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of 2.70 times 10^{-4}, compared with 4.02 times 10^{-4} for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

The work focuses on gathering high-fidelity and low-fidelity numerical simulations data using Nektar++ (Solver based on Applied Mathematics) and XFOIL respectively. The utilization of the higher polynomial distribution in calculating the Coefficient of lift and drag has demonstrated superior accuracy and precision. Further, Co-kriging Data fusion and Adaptive sampling technique has been used to obtain the precise data predictions for the lift and drag within the confined domain without conducting the costly simulations on HPC clusters. This creates a methodology to quantifying uncertainty in computational fluid dynamics by minimizing the required number of samples. To minimize the reliability on high-fidelity numerical simulations in Uncertainty Quantification, a multi-fidelity strategy has been adopted. The effectiveness of the multi-fidelity deep neural network model has been validated through the approximation of benchmark functions across 1-, 32-, and 100-dimensional, encompassing both linear and nonlinear correlations. The surrogate modelling results showed that multi-fidelity deep neural network model has shown excellent approximation capabilities for the test functions and multi-fidelity deep neural network method has outperformed Co-kriging in effectiveness. In addition to that, multi-fidelity deep neural network model is utilized for the simulation of aleatory uncertainty propagation in 1-, 32-, and 100 dimensional function test, considering both uniform and Gaussian distributions for input uncertainties. The results have shown that multi-fidelity deep neural network model has efficiently predicted the probability density distributions of quantities of interest as well as the statistical moments with precision and accuracy. The Co-Kriging model has exhibited limitations when addressing 32-Dimension problems due to the limitation of memory capacity for storage and manipulation.

Machine Learning (ML) has the potential to revolutionise the field of automotive aerodynamics, enabling split-second flow predictions early in the design process. However, the lack of open-source training data for realistic road cars, using high-fidelity CFD methods, represents a barrier to their development. To address this, a high-fidelity open-source (CC-BY-SA) public dataset for automotive aerodynamics has been generated, based on 500 parametrically morphed variants of the widely-used DrivAer notchback generic vehicle. Mesh generation and scale-resolving CFD was executed using consistent and validated automatic workflows representative of the industrial state-of-the-art. Geometries and rich aerodynamic data are published in open-source formats. To our knowledge, this is the first large, public-domain dataset for complex automotive configurations generated using high-fidelity CFD.

In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data u_0in B^{s}_{p,r} and for some T>0, the solutions of the Navier--Stokes equations converge strongly in L^infty_TB^{s}_{p,r} to the Euler equations as the viscosity parameter tends to zero. We furthermore prove the failure of the uniform (with respect to the initial data) B^{s}_{p,r} convergence in the inviscid limit of a family of solutions of the Navier-Stokes equations towards a solution of the Euler equations.