Computational Fluid Dynamics

Also known as CFD

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23 papers in the last four weeks, up 667% on the four weeks before. 0.2% of all new papers.

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Latest papers 165

Aug 8, 2026physics.flu-dyn

Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of

\|\nablaφ\|

from unity. A previous two-dimensional study identified this weight as the dominant hyperparameter and found its optimum shifts by four orders of magnitude between rigid-body and deforming flows, but left open whether these principles transfer to three dimensions and whether single-seed results survive run-to-run variability. We answer both by repeating the weight selection across four 3D benchmarks (translating sphere, rotating sphere, slotted sphere, reversed vortex), sweeping six weights with three seeds at full training budget under a pre-registered selection rule. The ordering transfers: the selected weight tracks how far the exact solution departs from the signed-distance property, spanning four decades from

10^{-1}

where it holds exactly to

10^{-5}

where the interface is stretched. Values transfer only benchmark by benchmark; two of four carry over unchanged and two do not, so inheritance must be verified. The multi-seed protocol reveals that at small weights the seed-to-seed standard deviation equals the error itself, and the regulariser reduces it by more than an order of magnitude, buying reproducibility as well as accuracy. We benchmark against a fifth-order WENO solver on identical grids and error measures; the classical scheme is more accurate on all four problems, by two orders of magnitude on smooth rigid advection, with a margin that narrows with geometric difficulty and is smaller in volume conservation than in the field norm. Finally, we show that the relative

L_2

error cannot certify the preservation of thin features, and report a feature-restricted measure that can.

Muhammad Akbar Khan

Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

Neural PDE Solvers Physics-Informed ML Computational Fluid Dynamics

Aug 8, 2026physics.flu-dyn

Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

Jeeeun Lee, Denis Korolev, Miro Duhovic +1

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 34141, Republic of Korea · Weierstrass-Institute for Applied Analysis and Stochastics, Anton-Wilhelm-Amo-Str. 39, Berlin, 10117, Germany · Leibniz-Institut für Verbundwerkstoffe GmbH, Erwin-Schrödinger-Str. 58, Kaiserslautern, 67663, Germany

Neural PDE Solvers Physics-Informed ML Computational Fluid Dynamics

Aug 7, 2026cs.LG

Neural Operators for Immersed-Boundary Soft Swimmers Locomotion

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid--structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

Mohammad Sadegh Eshaghi, Yizheng Wang, Navid Valizadeh +2

Chair of Computational Science and Simulation Technology, Institute of Photonics, Department of Mathematics and Physics, Leibniz University Hannover, Germany · Department of Engineering Mechanics, Tsinghua University, Beijing, China · Institute of Structural Mechanics, Bauhaus-Universität Weimar, Germany

PDE Surrogate Modeling Robot Locomotion Physics-Based Simulation Neural Operators Computational Fluid Dynamics

Aug 7, 2026cs.LG

Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning

Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive. Recent advances, such as Diffusion Graph Networks (DGNs), have combined diffusion models with graph neural networks to sample equilibrium states directly from unstructured meshes, enabling distributional accuracy even from short simulations. However, graph-based diffusion approaches suffer from hand-crafted architectural constraints, limited receptive fields in message passing, and costly multi-scale designs, which restrict scalability to larger and more complex domains. We propose Fluid-DiT, a Graph-Free Diffusion Transformer that replaces graph message passing with attention-based denoising, eliminating explicit graph design while preserving the ability to model distributions of chaotic flows. Our framework introduces a latent-space formulation that disentangles geometric fidelity from distributional learning, reducing high-frequency artifacts and accelerating sampling. By leveraging the transformer's global receptive field, Fluid-DiT naturally captures both local flow structures and long-range correlations without requiring hierarchical graph coarsening. On canonical benchmarks including laminar cylinder wakes, ellipse-flow systems, and turbulent 3D wing experiments, Fluid-DiT consistently outperforms graph-based diffusion baselines in both sample quality and distributional accuracy, achieving higher

R^2

correlations and lower Wasserstein distances. Moreover, it generalizes robustly from short, incomplete trajectories to unseen Reynolds numbers and geometries, demonstrating strong scalability.

Shentong Mo, Guolin Ke

CMU · DP Tech

Diffusion Transformer Generative Modeling Diffusion Models Computational Fluid Dynamics

Aug 4, 2026physics.flu-dyn

TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

Yilong Dai, Yiming Sun, Yiheng Chen +4

University of Alabama Tuscaloosa, USA · University of Pittsburgh Pittsburgh, USA

Forecasting Benchmarks Scientific ML Computational Fluid Dynamics

Aug 2, 2026cs.CE

Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation

Pure Lagrangian neural simulators offer geometric flexibility and exact advection, making them well-suited for modeling moving domains and free surfaces. However, the absence of a fixed global reference frame introduces two severe limitations: a spatial bottleneck, in which model capacity is wasted on uniform regions because the dense particle neighborhoods required for stable gradients are applied indiscriminately, and rapid temporal drift, caused by purely local message passing that lacks a global anchor. Inspired by classical hybrid numerical solvers, we propose a Hybrid Lagrangian-Eulerian neural simulator that augments Lagrangian dynamics with an Eulerian representation. To address the spatial bottleneck, we introduce adaptive downsampling that eliminates kinematic redundancy, preserving micro-scale details on particles while aggregating compressed features onto Eulerian nodes to resolve large-scale dynamics. To counter temporal drift, we employ a cross-attention mechanism that queries these Eulerian features, using the fixed grid as a stable spatial anchor to correct trajectory deviations at every timestep. Comprehensive experiments show that this hierarchical, cross-attended design substantially suppresses error accumulation, establishing a new state-of-the-art for accuracy and rollout stability in Lagrangian fluid simulation.

Ruoyan Li, Wei Wang, Yizhou Sun

University of California, Los Angeles

Neural PDE Solvers Computational Fluid Dynamics

Jul 29, 2026math.NA

Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem

We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break problem. Neither reduced model requires time integration: both learn a direct parameter-to-solution map from space, time, and dam-break parameters to the physical state, with the PINN providing predictions at arbitrary times and the TROM reconstructing solutions at the stored snapshot times. In addition, we demonstrate that it is essential to introduce shock-aware collocation to improve the robustness of the PINN model.

Anton Myshak, Md Rezwan Bin Mizan, Ilya Timofeyev

Dept. of Mathematics, University of Houston, Houston, TX 77204

PDE Surrogate Modeling Reduced-Order Modeling Physics-Informed ML Computational Fluid Dynamics

Jul 26, 2026math.NA

No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

We test whether an architecture that succeeds on a simple flow regime also succeeds on a richer one, with each trained separately on each regime. We explore two transient flows under time-varying boundary conditions: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), central to semiconductor manufacturing, and the two-dimensional Kármán vortex street (KVS). Eight surrogate models on one shared pipeline differ in whether they learn the full field or a latent representation, and in whether they predict in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the cumulative wall shear stress to 2.7% relative error. On the wake, a latent autoregressive DeepONet retains 90% of the shedding power that direct and one-shot models damp to almost zero. The treatment of time decides the outcome. The self-sustained wake calls for autoregressive feedback and the boundary-driven film for a direct map. Pointwise RMSE hides the damped oscillation on the wake, compresses the sixfold lead on the film's process target, and picks the damped model under wake extrapolation. The evaluation scores five physical questions. Trained surrogates answer queries 10^3 to 10^4 times faster than the finite-element solver and pay off from the first query beyond the training set on the film and from the third on the wake. Neither the winning architecture nor its validation holds across regimes. The choice of surrogate should follow the dynamical character of the target flow, and its validation should resolve the failure modes.

Georg Winkler, Martin Stoll

Department of Mathematics, Chemnitz University of Technology, 09111, Chemnitz, Germany

Neural Surrogate Modeling PDE Surrogate Modeling Neural Operators Computational Fluid Dynamics Autoregressive Modeling

Jul 24, 2026physics.flu-dyn

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna {https://github.com/tumaer/Neptuna}, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

Harish Ramachandran, Björn Kimpel, Thomas Paula +3

Technical University of Munich

Neural Surrogate Modeling PDE Surrogate Modeling Computational Fluid Dynamics

Jul 23, 2026physics.flu-dyn

Explainable quantum-compressed machine learning for complex fluid flows

Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from

524{,}288

trainable parameters to no more than

8

. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.

Xiao Xue, Maida Wang, Mingyang Gao +2

Centre for Computational Science, University College London, London, UK · Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities, Boltzmannstraße 1, 85748 Garching, Germany · Centre for Advanced Research Computing, University College London, London, UK

Neural Surrogate Modeling Interpretable ML Quantum Machine Learning Computational Fluid Dynamics

Jul 22, 2026physics.flu-dyn

Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields

Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.

Tianyu Li, Zhiwei Cao, Qingang Zhang +3

Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, Singapore. · School of Future Technology, Fuzhou University, Fuzhou, China. · College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore. +2

Neural Surrogate Modeling Graph Neural Networks PDE Solving Physics-Informed ML Physics-Informed GNNs Computational Fluid Dynamics

Jul 22, 2026physics.flu-dyn

Guarantees by Construction for Learned Finite Volume Schemes on Steady Supersonic Flow

A second order finite volume scheme rests on two local quantities: a gradient reconstructed in each cell, and a limiter which scales it down where the reconstruction would overshoot. Both are set by fixed formulas, and on coarse unstructured meshes a small network can supply better values. But a network is free to output anything, and the usual safeguard is a penalty in the training loss, which discourages inadmissible states without preventing them. We replace the penalty by a hard constraint. The network still sets both quantities, and every value it can produce lies inside safe bounds: its stencil weights cannot cancel a neighbour, and its limiter is capped by the local flow. The flux, the wall treatment and the time step are not learned and carry their own guarantees. Admissibility therefore holds for every value of the weights rather than as an outcome of training, and no negative density or pressure occurred in any computation reported here. Because the scheme is safe whatever the network does, we could ask what the network contributes. We test it on supersonic channel flow over an obstacle, including the forward facing step of Woodward and Colella. Learning lowers the error by 38% on an unseen geometry and 29% on an unseen obstacle topology, measured against the same scheme with the network switched off. The method aims at the accuracy of a fine mesh for the cost of a coarse one, and refining once improves the error fourfold while multiplying the run time by eight. Learning secures half of this improvement for a sixth of this time. All of this comes from one of the two quantities the network sets. The gradient reconstruction reproduces the full effect on its own, and the limiter accounts for about a tenth as much. This also explains why the gain fades beyond the Mach numbers the weights were trained on.

Denis Gueyffier

ONERA -- Institut Polytechnique de Paris · Direction Scientifique G´en´erale, ONERA · Institut Polytechnique de Paris, Palaiseau, France

Neural PDE Solvers Computational Fluid Dynamics

Jul 21, 2026cs.LG

Thermodynamics-Informed Input Reparameterization for Neural Prediction of Real-Fluid Thermodynamic Properties in Supercritical Combustion

Real-fluid thermodynamic property evaluation is a major computational cost in supercritical combustion simulations. In the enthalpy-based pressure-correction formulation, the closure evaluates temperature T, density

ρ

, and compressibility coefficient

ψ

from the solver state (h,p,Y) through enthalpy-temperature inversion and repeated real-fluid equation-of-state evaluations. Neural-network surrogates offer fixed-cost inference, but direct mapping from (h,p,Y) to

(T,ρ,ψ)

must capture the enthalpy-temperature relation and non-ideal equation-of-state response, resulting in a complex regression problem. This work introduces a thermodynamics-informed input reparameterization strategy, termed target-aligned input reparameterization (TAIR). TAIR replaces the raw enthalpy coordinate of each property network with a target-matched thermodynamic coordinate: the temperature network uses a temperature estimate obtained by inverting a constant-

c_p

ideal-gas mixture enthalpy approximation, whereas the density and compressibility networks use an ideal-gas density estimate. These algebraic transformations use only solver-available variables and species constants, guiding the networks to learn real-fluid departures from ideal-gas baselines rather than reconstructing the full closure from raw enthalpy. The method is assessed using supercritical methane-oxygen counterflow flame data against a raw-input baseline and target-inconsistent cross-reparameterization controls. TAIR reduces held-out RMSE by factors of about 1.5, 2.0, and 7.5 for T,

ρ

, and

ψ

, respectively. For an unseen strain-rate flame within the augmented thermodynamic envelope, the corresponding factors are 3.6, 14.5, and 6.0. The target-inconsistent controls perform worse, indicating that the gains arise from thermodynamically matched input design rather than generic preprocessing.

Haoze Zhang, Han Li, Ke Xiao +3

State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China · AI for Science Institute (AISI), Beijing 100080, China

Neural Surrogate Modeling Computational Fluid Dynamics

Jul 17, 2026cs.LG

Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls

Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight. For design, optimisation and certification, it is indispensable to quantify such unsteady aerodynamic effects. Industry-standard computational fluid dynamics methods, such as solving the unsteady Reynolds-averaged Navier-Stokes equations or the linearized frequency domain method, are either computationally expensive or restricted by assumptions like linearity. Once trained, machine learning methods are capable of computing non-linear relationships very fast, making them suitable as surrogate models. By autoregressively applying graph neural networks (GNNs), operating on a discretised spatial domain, spatio-temporal predictions can be made. However, autoregressive GNNs suffer from error accumulation leading to unstable rollouts over time. Here we show that combining GNNs with augmented Neural Ordinary Differential Equations yields temporally stable predictions of the surface forces on a pitching airfoil. We found that our approach, called GNODE, based on Graph Neural Ordinary Differential Equations, provides temporally more stable, spatially smoother, and overall more accurate results than an autoregressive GNN baseline. Tests are conducted on a dataset consisting of a simulations of a pitching airfoil, including transonic shocks, transient behaviour and dynamic non-linearities. Augmenting GNODEs with additional latent dimensions improves the expressivity and accuracy by capturing underlying history effects. The developed method demonstrates an approach that is suitable to model non-linear spatio-temporal systems with exogenous inputs.

Henrik Lange, Reik Thormann, Philipp Bekemeyer

German Aerospace Center (DLR), Lilienthalpl. 7, 38108 Brunswick, Germany · Airbus Operations, Airbus Allee 1, 28199 Bremen, Germany

Graph Neural Networks PDE Surrogate Modeling Spatiotemporal Forecasting Neural ODEs Computational Fluid Dynamics

Jul 16, 2026math.NA

Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables

We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particular, we employ a decoupled neural network architecture explicitly separating the subgrid corrections into two distinct components: a conservative Flux Potential network and an Eddy Viscosity network. We demonstrate that this reduced-order framework maintains high physical fidelity, accurately reproducing the energy spectrum, spatial and temporal correlation functions, and dynamical characteristics of the full-scale system. Furthermore, we show that our approach is robust and applicable to parameters outside the training regime.

Aijaz Nazir, Ilya Timofeyev

Dept. of Mathematics, University of Houston, Houston, TX 77204

Neural Surrogate Modeling PDE Solving Computational Fluid Dynamics

Jul 14, 2026physics.flu-dyn

Gradient-free learning of a closed-loop wall controller for turbulent drag reduction

Closed-loop wall control learnt by multi-agent reinforcement learning can lower skin-friction drag in turbulent channels, but these gradient-based policies are trained on small periodic boxes and exhibit reduced performance when carried over to a larger domain. We recently showed that such policies are also prone to saturated bang-bang actuations that collapse into standing streamwise waves whose scale is set by the computational box rather than by the near-wall cycle, and proposed architectural fixes that avoid these degeneracies. Here, we employ Evolution Strategy (ES) to optimise a recurrent closed-loop controller directly on a large turbulent channel at

\mathit{Re}_τ\simeq180

, evaluating policy performance over full flow episodes using an energy-aware criterion and processing candidate policies in parallel. To our knowledge, this is the first application of an evolution strategy to the control of a turbulent flow. The ES controller reduces the skin friction by about

26\%

, exceeding the gradient-based multi-agent controller of Cavallazzi et al. (2026), GRU-MARL, trained on a minimal box (

17\%

), and marginally exceeding classic opposition control (OC,

22\%

). A wall-normal decomposition of the friction, Reynolds-stress profiles and anisotropy invariants show that the ES and opposition-controlled flows follow separate trajectories through the buffer layer, reaching comparable drag reduction by different reorganisations of the near-wall turbulence. In particular, the ES actuation correlates predominantly with the streamwise velocity fluctuations rather than with the wall-normal velocity that classical OC targets.

Giorgio Maria Cavallazzi, Miguel Pérez Cuadrado, Alfredo Pinelli

Department of Engineering, City St. George’s, University of London, Northampton Square, EC1V 0HB, London, UK

Computational Fluid Dynamics

Jul 13, 2026cs.LG

A multi-scale feature enhanced graph neural network for fluid dynamics prediction in complex geometries

Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs. Deep neural networks have shown promise in improving simulation efficiency, especially graph neural networks (GNNs), which demonstrate great potential due to their flexibility with unstructured data. However, GNNs face challenges when dealing with tasks involving complex geometries and large-scale meshes. In this paper, we propose the Multi-scale Feature Enhanced Graph Neural Network (ME-GNN) to tackle these challenges. ME-GNN employs a graph neural network with a two-step message-passing mechanism to capture detailed local features effectively. Additionally, it integrates an Attention U-Net with uniform grid discretization, enabling the extraction of both fine and coarse features. The model also utilizes K-hop sampling to construct subgraphs, facilitating efficient training on large datasets while preserving detailed local features. We evaluated ME-GNN on three benchmark datasets and achieved state-of-the-art results: a relative L2 error of 0.0196 for the velocity field and 0.0556 for the surface pressure on ShapeNet-Car, a normalized mean squared error of 0.0033 for the flow field on AirfRANS, and a relative L2 error of 0.1416 for the surface pressure on DrivAerNet.

Li Xiao, Tianyu Li, Yiye Zou +2

Graph Neural Networks PDE Surrogate Modeling Multi-Scale Feature Fusion Computational Fluid Dynamics

Jul 13, 2026cs.LG

IG-GAN: A Generative Adversarial Network for Aerodynamic Data Generation Based on Intrinsic Geometry

Existing generative models learn data distributions in flat Euclidean space. However, most data in our real world are manifolds embedded in high dimensional Euclidean space. Therefore, we propose an intrinsic-geometry-based generative adversarial network (IG-GAN) for data generation in the field of aerodynamics. The generator of the IG-GAN represents aerodynamic data as a piecewise smooth manifold constructed by Bézier surfaces, and the generator tries to learn the coefficients of each Bézier surface to further combine multiple Bézier surfaces into a smooth manifold automatically. The discriminator in the IG-GAN is a radial-basis-function based discriminator (RBF-D). Experimental results show that IG-GAN achieves lower predicted Mean Squared Errors (MSEs) than those of three baselines. Specifically, on the Burgers' equation dataset, IG-GAN reduces the predicted MSE of velocity u by 97.41% compared with state of the art SSL-Transformer. Additionally, on the ONERA M6 aircraft dataset, IG-GAN reduces the overall MSE of nine aerodynamic coefficients by 82.95% compared with SSL-Transformer.

Ying Yan, Liwei Hu, Xiaoming Zhang

School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, 050091, China

Synthetic Data Generation Geometric Representation Learning Generative Adversarial Networks Computational Fluid Dynamics

Jul 10, 2026physics.flu-dyn

Entropy-Constrained Machine Learning with Residual Data Augmentation for Modeling Chemical Kinetics

We present a physics-constrained machine learning framework for accelerating the direct numerical simulation (DNS) of turbulent reacting flows. The model replaces the direct evaluation of detailed chemical source terms with a surrogate that predicts reaction rates from a reduced thermochemical state. To improve physical consistency, the second law of thermodynamics is incorporated as a training constraint by enforcing non-negative entropy generation, which restricts the evolution of the thermochemical state to physically admissible directions and improves stability during time integration. The approach is demonstrated on DNS of a two-dimensional planar lean premixed methane-air flame interacting with a turbulent flow field. The model reproduces detailed-chemistry results with high fidelity while achieving more than an order-of-magnitude reduction in computational cost. Furthermore, a residual-based synthetic data augmentation strategy enables parametric exploration by constructing new training data from the original dataset, allowing accurate simulation at new inlet conditions without additional detailed-chemistry CFD runs. These results demonstrate that thermodynamically constrained machine learning can provide reliable and computationally efficient surrogates for detailed chemistry in high-fidelity combustion simulations.

Okezzi Ukorigho, Opeoluwa Owoyele

Department of Mechanical and Industrial Engineering Louisiana State University, Baton Rouge, LA 70810, USA

Surrogate Modeling PDE Surrogate Modeling Physics-Informed ML Computational Fluid Dynamics

Jul 10, 2026cs.RO

CORL-AUV: CFD Oriented Reinforcement Learning for Autonomous Underwater Vehicles

Precise control and positioning of autonomous underwater vehicles (AUVs) is critical for sampling, maintenance, and survey applications. Reinforcement learning (RL) offers rapid controller development while handling a range of deployment parameters via domain randomization (DR). However, DR is limited by the underlying simulation's capacity to model real physics such as drag, which is a large contributor to sim-to-real gaps. Computational fluid dynamics (CFD) provides high-fidelity drag models but has significant computational cost. Thus, in this paper we train surrogate approximations of CFD data of a given vehicle, providing drag estimates 700,000x faster than solving for drag at each time step with CFD within the RL training pipeline. We deploy a Proximal Policy Optimization (PPO) policy zero-shot on a 6-DOF AUV in which policy training is performed on these surrogate drag models (SDMs), providing analysis on zero-shot transfer, reward shaping sensitivity, and physical parameter perturbations. On 15 identical segments in the ocean, we observe median gains of 19% in mean tracking error and 31% in control effort compared to the equivalent inertia box model. Our SDM based RL controller better predicts zero-shot transfer and reaches the most waypoints across all three reward shaping choices that we evaluate. Finally, we add 0.907 kg to the vehicle perturbing the mass, center-of-mass, and center-of-buoyancy. The policy reaches 100% of waypoints only when the SDM drag model is used; the policy fails to reach any of the 15 waypoints when the other drag models are used.

Steven Roche, Milo Van Mooy, Nathan McGuire +3

MIT-WHOI Joint Program, MA 02543, USA · WHOI, MA 02543, USA · Massachusetts Institute of Technology, Cambridge, MA 02319, USA

RL Control RL for Robotics Surrogate Modeling Sim-to-Real Transfer Computational Fluid Dynamics

Jul 8, 2026cs.LG

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Rachna Ramesh, Kiet Bennema ten Brinke, Douwe Orij +2

Department of Mathematics and Computer Science, Eindhoven University of Technology · Department of Chemical Engineering and Chemistry, Eindhoven University of Technology

Generative Modeling Spherical Harmonics Trajectory Prediction Computational Fluid Dynamics

Jul 5, 2026cs.CV

CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws

We present CoFINN (Conservation Flux Informed Neural Networks), a physics-informed deep learning framework for predicting compressible flow fields governed by conservation laws. Unlike conventional data-driven convolutional neural networks (CNNs), which optimize only pixel-wise similarity metrics, CoFINN embeds finite-volume conservation physics directly into the training process. Unlike classical physics-informed methods which enforce differential-equation residuals at collocation points through automatic differentiation, CoFINN adopts a finite-volume perspective consistent with modern CFD methodology. CoFINN interprets CNN output fields as structured computational grids, where each pixel represents a finite-volume cell, and enforces conservation consistency through sophisticated numerical flux calculations. The framework is evaluated on transonic flow prediction around airfoils at (M=0.7, Re=6 * 10^6), including challenging conditions involving shock waves and high angles of attack. Results show that CoFINN improves aerodynamic force prediction accuracy, reducing drag prediction error by up to 34% at extreme angles of attack and by approximately 15% on average across the test set. Improvements are particularly significant in limited-data regimes, demonstrating that the conservation-based loss acts as an effective physical regularizer. The proposed approach maintains the computational efficiency advantages of CNN surrogates while significantly improving physical consistency and conservation behavior. The framework is architecture-agnostic and extensible to broader classes of conservation-law-governed physical systems.

Adnan Harun Doğan, Mert Deniz, Hande Alemdar +1

Dept. of Computer Engineering Middle East Technical University Ankara, Turkey · Dept. of Mechanical Engineering Middle East Technical University Ankara, Turkey

PDE Surrogate Modeling Physics-Informed ML Convolutional Neural Networks Computational Fluid Dynamics

Jul 3, 2026cs.MA

LOTUSim: Multi-Domain Simulator for Marine Robotics

Simulation is essential for maritime robotics, supporting operator training, mission rehearsal, and human-vehicle interaction in environments where real-world testing is costly or hazardous. Existing simulators focus primarily on autonomy systems and often lack human-in-the-loop interaction and realistic environmental physics. This paper introduces LOTUSim, an open-source, real-time maritime simulator supporting multi-user interaction across aerial, surface, and underwater robotic systems for coordinated naval-style operations. The first contribution of this work is enabling real-time interactive performance for users while ensuring scalability to large fleets operating within a shared interactive simulation environment. Validation demonstrates robust human-in-the-loop performance, maintaining strict real-time execution and high visual fidelity while scaling to large heterogeneous maritime drone swarms. The second contribution is a computationally efficient, Ekman-inspired layered, underwater current model that captures wind-driven, depth-dependent flow dynamics with sufficient physical fidelity for large-scale simulations. Validation against ocean reanalysis data demonstrates substantially improved accuracy compared to commonly used stochastic Gauss-Markov current models. These results confirm LOTUSim's suitability as a simulation platform for operatorin-the-loop maritime robotics research.

Cédric Buche, Juliette Grosset, Hélène Lechêne +4

CROSSING, IMT Atlantique · CROSSING IRL 2010, CNRS · IMT Atlantique +2

Multi-Robot Systems Robotics Simulation Human-in-the-Loop Evaluation Robotics Physics-Based Simulation Computational Fluid Dynamics

Jul 2, 2026cs.LG

Fourier Neural Operators for Rayleigh-Bénard Convection

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.

Chelsea Maria John, Thibaut Lunet, Sebastian Götschel +3

Jülich Supercomputing Centre, Jülich, Germany · Hamburg University of Technology, Hamburg, Germany

Fourier Neural Operator PDE Surrogate Modeling Computational Fluid Dynamics

Jun 30, 2026physics.ao-ph

Scaling Storm-Resolving Atmospheric AI Simulation to the Entire Planet

Kilometer-scale convection shapes precipitation extremes, tropical organization, and cloud feedbacks, but most global atmospheric models approximate these processes at 25-100 km resolution. Global storm-resolving physics models resolve convective systems explicitly, but at a cost -- roughly one MWh per simulated day on exascale supercomputers -- that limits long-duration simulation. We introduce STRATA (Storm-resolving Tile-based autoRegressive Atmosphere Transformer Architecture), the first autoregressive AI emulator for global storm-resolving atmospheric dynamics. STRATA is trained on the highest-resolution atmospheric dataset yet used for global AI emulation: 17 days of SCREAM physics-model output at 4.9-km resolution (~25 million grid cells) sampled every 10 minutes. Our central premise is that on 10-minute timescales atmospheric dynamics are predominantly local, so training on small spatial tiles trades scarce global temporal samples for abundant local spatial samples and enables global rollout via overlapping-tile blending. STRATA combines 3D patch embedding and local 3D neighborhood attention, a novel Stereographic Rotary Position Embedding (StereoRoPE) for grid-invariant encoding, and a pixel-space de-aliasing decoder that suppresses patch-scale rollout artifacts. An iso-FLOP scaling study reveals that km-scale emulation requires ~10x more FLOPs per grid point than coarse-resolution AI weather models, consistent with the higher information density of convective-scale dynamics. Trained on only 17 days of data, STRATA produces stable 24-hour global rollouts with realistic km-scale dynamics across diverse regimes, though large-scale biases develop with lead time. It achieves 48 simulation days per megawatt-hour -- about 50 times better energy efficiency than the SCREAM physics model -- and 741 simulated days per wall-clock day at 512 H100 GPUs. Code and dataset are publicly available.

Zeyuan Hu, Akshay Subramaniam, Noel Keen +9

NVIDIA · LBNL · PNNL +1

AI for Science Transformer Computational Fluid Dynamics Autoregressive Modeling

Jun 28, 2026physics.flu-dyn

Kriging and neural network models for pressure losses across perforated plates

In this paper, two novel data-driven models based on kriging and neural networks (NN) are proposed to predict pressure losses across perforated plates with circular perforations in turbulent flows. The models are developed using two sets of experimental data available in the literature. The predictive performance of the proposed models is assessed and compared against widely used empirical formulae. It is found that the proposed models consistently outperform existing empirical models for most perforated plate configurations contained in the experimental datasets. Besides, the predicted pressure losses generally show good agreement with experimental measurements, demonstrating that data-driven approaches based on kriging and NN provide a feasible framework for modelling pressure losses across perforated plates. Overall, both approaches are promising, despite being trained on a relatively limited amount of experimental data, owing to the scarcity of measurements reported in the literature. To demonstrate the applicability of the proposed models in numerical simulations, two-dimensional channel flows are simulated using the Reynolds-averaged Navier-Stokes (RANS) equations, in which the new pressure-loss models are implemented as a source term in the momentum equations. The RANS predictions are found to be in excellent agreement with the model predictions, confirming the suitability of the proposed approaches for practical computational fluid dynamics applications.

Shuai Li

Division of Fluid Dynamics, Department of Mechanical Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

Neural Surrogate Modeling Computational Fluid Dynamics

Jun 28, 2026stat.ML

Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamics

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this bidirectional flow can be used as a self-supervised consistency metric for uncertainty and error estimation, which enables the model to estimate test-time uncertainty and error without access to ground truth, by comparing how closely flowing forwards and backwards in time returns to the same predicted fields. We also demonstrate this methods's potential to serve as a non-invasive plasma diagnostic, and show how adaptive feedback can be used to make the model more robust based on sparse diagnostics or limited views/measurements.

Alexander Scheinker

Los Alamos National Laboratory, Los Alamos, NM, 87545.

Uncertainty Quantification Autoregressive Diffusion Latent Diffusion Models Diffusion Models Computational Fluid Dynamics

Jun 27, 2026cs.CE

Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

Samuel Ahnert, Esther Lagemann, H. Jane Bae +4

Department of Mechanical Engineering, University of Washington, Seattle, WA, USA · AI Institute in Dynamic Systems, University of Washington, Seattle, WA, USA · Lynn Booth and Kent Kresa Department of Aerospace, California Institute of Technology, Pasadena, CA, USA +2

Computational Fluid Dynamics

Jun 25, 2026cs.LG

Boundary condition fidelity for bottom-hole pressure and CO2 plume prediction in geological carbon storage

Accurate prediction of bottom-hole pressure (BHP) and CO2 plume migration is essential for safe geological carbon storage, yet practical simulations often rely on truncated domains where artificial boundaries distort pressure diffusion and CO2 saturation footprints. In this study, we evaluate how boundary-condition fidelity affects BHP and CO2 plume prediction by comparing ten reduced-domain boundary treatments against full-domain reference simulations in homogeneous and heterogeneous reservoirs. We test uniform pore-volume multipliers, transmissibility modifiers, corner-adjusted pore-volume corrections, layered corrections, and gradual modifiers using BHP RMSE, NRMSE, peak pressure deviation, and plume Intersection over Union (IoU) as performance metrics. Our results show that conserving corner pore volume is the most important requirement for truncated-domain modeling. We find that uniform treatments which neglect corner storage generate large pressure errors, with BHP RMSE of 362 to 382 psi in the homogeneous model and 250 to 304 psi in the heterogeneous model, and yield plume IoU values near 0.80 to 0.84, indicating roughly 16 to 20% of the combined plume area is misrepresented. Corner-adjusted scenarios substantially reduce pressure errors and raise plume IoU above 0.94, but we observe that transmissibility correction is not universally beneficial. In homogeneous reservoirs, uniform transmissibility adjustment improves pressure fidelity; in heterogeneous reservoirs, it can over-restrict flow across variable-permeability boundary faces, increasing BHP error and contracting the predicted plume. We find the gradual modifier with transmissibility correction provides the most consistent performance, achieving BHP NRMSE below 3.7% and plume IoU above 0.97 in both reservoir types.

Romal Ramadhan, Seyyed A. Hosseini, Larry W. Lake

Department of Earth and Planetary Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, TX 78712, USA · Bureau of Economic Geology, The University of Texas at Austin, 10611 Exploration Way, Austin, TX 78758, USA · Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA

Computational Fluid Dynamics

Jun 25, 2026cs.LG

Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste +4

ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain · Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain · Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB), 07122 Palma de Mallorca (Spain)

Multilayer Perceptrons Surrogate Modeling Kolmogorov-Arnold Networks Computational Fluid Dynamics