Computational Fluid Dynamics

Also known as CFD

Follow this topic Ask about this topic

Momentum

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

Jul 13Week of Sep 28

Latest papers 165

Oct 7, 2026physics.flu-dyn

Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields

Rapid and accurate prediction of urban wind and temperature fields is important for urban microclimate design and climate adaptation. Large-eddy simulation (LES) effectively resolves these instantaneous fields, but its application is limited in iterative design of urban microclimate applications due to high computational cost. Existing regressive data-driven models offers quick outputs, but they produce only deterministic point predictions that inherently fail to represent turbulent stochasticity. This paper adopts a novel generative framework of Conditional Flow Matching (CFM) that uses building geometry and mean flow as guidance to generate plausible three-dimensional instantaneous velocity and temperature fields for urban microclimate in seconds. To overcome the GPU memory bottleneck of pixel space 3D generation, the model operates in parallel on overlapping pixel space through a shared-noise initialization that preserves high spatial continuity of flow structure across the entire domain. Against reference LES data, the CFM surrogate can rapidly and accurately restore the first-order statistics with Normalized Root Mean Square Error (NRMSE) of 2.99% for wind and 1.77% for temperature, second-order turbulence metrics with NRMSE of 7.17% for wind and 8.84% for temperature, turbulent kinetic energy with NRMSE of 7%, probability density function and vertical profiles in representative locations. Wind engineering application of local gust prediction demonstrate that the speed and accuracy of CFM, supporting the use of generative AI for making turbulence-aware resilient urban design and climate adaptation more computationally feasible.

Peng Liu, Shaoxiang Qin, Theodore Potsis +3

Concordia University, Centre for Zero Energy Building Studies, Department of Building, Civil and Environmental Engineering, Montreal H3G 1M8, Canada · McGill University, School of Computer Science, Montreal, H3A 0E9, Canada

Computational Fluid Dynamics Conditional Flow Matching PDE Surrogate Modeling

Oct 7, 2026cs.LG

Cross-Domain Pretraining for Steady-State Neural CFD Surrogates

Neural surrogates for computational fluid dynamics (CFD) have the potential to greatly enhance engineering innovation through accelerating simulation. However, the primary limitation for neural surrogates is the lack of generalization to geometries and applications beyond the training set, which is significant given the diversity of engineering scenarios. Currently, this is addressed by generating a new dataset for a specific application; however, this requires running costly numerical solvers. In this work, we take a step toward addressing this by studying neural surrogates trained across different geometries, boundary conditions, and fidelities. We find that cross-domain pretraining improves zero- and few-shot performance on held-out datasets relative to both training from scratch and transferring from domain-specific experts. In particular, finetuning a pretrained, cross-domain model can achieve 2-3x lower errors at the same sample size and use 8x fewer samples to achieve the same error, compared to training from scratch. This benefit is architecture agnostic and improves with model size and pretraining dataset diversity. Furthermore, we study how and why cross-domain pretraining works in CFD surrogates, and find that simply pooling steady-state datasets is both sufficient and effective. Given the high cost of generating CFD data, leveraging existing datasets through cross-domain pretraining will likely be a valuable strategy as future surrogates expand to tackle new problems and use cases.

Anthony Zhou, Amir Barati Farimani, Shirley Ho +1

Carnegie Mellon University · New York University · Polymathic AI +4

Cross-Domain Generalization PDE Surrogate Modeling Computational Fluid Dynamics

Oct 7, 2026cs.LG

PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media

Multiphase flow in porous microstructures is central to CO

_2

storage, fuel-cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.

Chunyang Wang, Mingrui Zhang, Yuyan Zhang +5

Imperial College London · Stanford University · EarthFlow AI, Inc. +1

Neural Surrogate Modeling Computational Fluid Dynamics

Oct 5, 2026cs.CV

End-to-End Autonomous Recursive Arborescence Deformable Flow and Non-Linear Hemodynamics for Patient-Specific Coronary Centerline Extraction

Extracting patient-specific vascular trees from volumetric medical images is fundamental to computational angiography and non-invasive hemodynamic assessment. Conventional voxel segmentation models often sever delicate bifurcations, while heuristic Euclidean Minimum Spanning Trees introduce non-anatomical shortcuts. Moreover, linear Poiseuille flow neglects quadratic kinetic dissipation across arterial narrowings, underestimating ischemia. We formulate an end-to-end framework decoupling continuous geometric arborescence generation from non-linear hemodynamics. First, an autonomous 3D Ostium Landmark Localization Head with dual-sinus query channels and spherical-gated refinement eliminates centerline seeding dependency, achieving cohort mean localization error of 7.63 mm (7.43 mm LCA, 7.83 mm RCA; 71.4% <= 8.0 mm) from raw contrast context. Second, a Spatially-Grounded Deformable Step Flow Architecture queries continuous 3D feature pyramids via trilinear sampling, sequentially generating trajectories with anchor boundary enforcement (X(0) = P_start). Third, a Top-Down Recursive Arborescence State Machine detects bifurcation peaks via Tree-NMS and parameterizes predecessor parent pointers (p_k < k), guaranteeing single connected acyclic tree topology (beta_0 = 1, beta_1 = 0) with differentiable step termination. Fourth, an iterative Picard non-linear Kirchhoff solver with Young-Tsai / Gould quadratic dissipation enforces machine-precision mass conservation (residual 5.82e-11 mL/s). Across 14 development patients under standardized in-silico stenosis stress testing (Q_0 = 4.0 mL/s), linear Poiseuille flow misclassifies 75% diameter lesions as non-ischemic (FFR > 0.80) in 14/14 cases, whereas our non-linear solver captures functional ischemia (FFR = 0.5864, lesion disparity 32.89 mmHg, p = 6.10e-5) with 3.66x collateral shunting. Test set firewall isolation was maintained.

Zeyu Jia, Xin Ming

School of Biomedical Engineering and Technology, Tianjin Medical University, Tianjin 300070, China

Coronary Angiography Computational Fluid Dynamics

Oct 4, 2026cs.LG

Advectra: Asymmetric Latent Transport for Non-Stationary Physics

Many latent neural operators represent input and output fields in a stationary latent chart. In particular, common latent routing mechanisms use fixed or shared assignment weights for feature projection and reconstruction, limiting their ability to model transport-dominated systems where coherent structures move relative to fixed coordinate frames. We propose Advectra, a transport-aware latent operator that introduces a regularized kinematic coordinate map to decouple source and target coordinate systems. This yields an approximately co-moving latent reference frame and enables asymmetric feature aggregation and reconstruction. Combined with a geometry-aware ordering mechanism for state-space models, Advectra captures advective dynamics while maintaining stable global interactions. Advectra achieves the best performance among evaluated geometry-constrained and form-free baselines on advection-dominated benchmarks, including passive scalar transport in Navier--Stokes flows and Rayleigh--Taylor instability, while demonstrating strong generalization on real-world engineering tasks. These results highlight the benefit of explicit moving-frame structure in neural operators for non-stationary physics.

Nodens Koren, Thomas Hofmann, Georgios Kissas

Department of Computer Science ETH Zürich Zürich, Switzerland · Swiss Data Science Center ETH Zürich Zürich, Switzerland

PDE Operator Learning Neural Operators Computational Fluid Dynamics

Sep 30, 2026cs.LG

Do Better Scores Mean Better Physics? Physics-Grounded Explanations for Sim2Real Neural Operators

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.

Somyajit Chakraborty, Xizhong Chen

State Key Laboratory of Synergistic Chem-Bio Synthesis, Department of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

Neural Surrogate Modeling Explainable Artificial Intelligence Neural Operators Computational Fluid Dynamics

Sep 30, 2026cs.LG

Physics-Informed Method of Group Data Handling: Adaptive Construction of Functional Representations with an Application to the Navier-Stokes Equations

Physics-informed computational methods usually optimize parameters within a functional representation whose structure is fixed in advance. This work proposes a Physics-Informed Method of Group Data Handling (PI-GMDH), in which representations of coupled physical fields are progressively constructed during solution. Candidate functional directions are evaluated through the first variation of the complete physical and observational objective, introduced in packages, and followed by block-coordinate damped Gauss-Newton coefficient optimization. The framework is demonstrated with tensor-product Chebyshev functions on the incompressible Navier-Stokes equations using a two-dimensional time-dependent Taylor-Green benchmark. Under the tested configuration, adaptive PI-GMDH reached validation and held-out test losses of 5.299e-19 and 5.296e-19 with 204, 201, and 175 active functions for u, v, and p. Complete degree-by-degree and all-terms PI-GMDH variants, together with selected PINN and KAN reference configurations, are used to examine the effect of structural construction policy. The results show that, for this controlled synthetic benchmark, selective progressive construction can provide a favorable combination of accuracy, representation size, and wall-clock time. The comparison is illustrative rather than a claim of universal superiority over alternative physics-informed approaches.

Mykhailo Minin

JSC KIEP, Kyiv, Ukraine

Neural PDE Solvers Physics-Informed ML Computational Fluid Dynamics

Sep 30, 2026cs.LG

Scale-Split Neural Operator for Memory- and Data-Efficient 3D Turbulence Prediction

Neural surrogates have emerged as fast alternatives to the numerical simulation of three-dimensional turbulence. However, training them at high resolution remains challenging, since the memory of full-field models grows with the resolution. In addition, full-resolution training data are expensive to simulate and store, and therefore scarce. We introduce ScaleSplit-NO (Scale-Split Neural Operator), which exploits the scale structure of turbulence with two neural operators: a Parent predicts the global coarse field at the next time step, and a Child predicts full-resolution local patches conditioned on this prediction. Neither model operates on the full-resolution field. The Child is pretrained alone and then attached to the Parent's coarse prediction through zero-initialized connections. On two complex high-resolution turbulence benchmarks, ScaleSplit-NO surpasses all competing baselines in both prediction accuracy and data efficiency. On the higher-resolution dataset JHTDB256 (

256^3

), its normalized mean squared error (NMSE) is 53% lower than that of the strongest baseline, and its training memory is 79% lower than that of the most memory-efficient baseline. We further demonstrate its effectiveness for urban wind prediction in a real district of Montreal on a

500\times150\times500

grid, reducing one-step NMSE by 65.8% relative to the baseline. Moreover, swapping in a Parent trained on additional coarse fields improves prediction without retraining the Child, providing further accuracy gains at a small storage cost.

Shaoxiang Qin, Yucheng Zhao, Zongyi Li +2

University of Tennessee, Knoxville · McGill University · New York University +1

PDE Surrogate Modeling Neural Operators Memory-Efficient Training Data-Efficient Learning Computational Fluid Dynamics

Sep 30, 2026stat.ML

Warm-starting PDE solvers with any-dimensional machine learning

Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the GNN transferability literature, we show mathematical conditions under which a partial differential equation (PDE) learning-based solver can be trained in small dimensions and directly applied to solve a higher dimensional PDE in a zero-shot fashion. These conditions are based on symmetries in both the partial differential equation and the initial data. When the equations satisfy the symmetries but the data does not, which is the case for many PDEs arising from physics, we show that our theory gives a principled way of warm-starting low-dimensional PDE solvers for higher dimensional PDEs. We apply this method on the heat equation, Burgers' equation, and the compressible Navier--Stokes equations, improving the performance in both zero-shot and typical training regimes on high dimensional data. For example, we train a surrogate model on 2D Navier--Stokes data and achieve better results on 3D test data than a baseline surrogate model trained on 3D data, while only using 12

\%

of the flops and 20

\%

of the total data size.

Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1

Department of Statistics and Irving Institute for Cancer Dynamics, Columbia University · Division of Applied Mathematics, Brown University · Department of Applied Mathematics and Statistics, Johns Hopkins University

Neural PDE Solvers PDE Surrogate Modeling Transfer Learning Computational Fluid Dynamics

Sep 29, 2026cs.CE

SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Trucks

Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million cells at a Reynolds number of

1.4 \times 10^7

and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.

Riddhiman Raut, Yin Yu, Aashwin Anand Mishra +4

Luminary, San Mateo, CA, USA · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA

Neural Surrogate Modeling Distribution Shift Robustness Computational Fluid Dynamics

Sep 29, 2026cs.AI

CANTO: CAD-Native Transformer Operators for AI-Aided Engineering

Modern engineering systems, from automobiles to aircraft, are designed by using precise, continuous parametric computer-aided design (CAD) models. Evaluating design changes through numerical simulation requires meshing the continuous geometry, a computationally expensive and often brittle process that can require manual intervention and replaces the continuous representation with a discrete approximation. Most neural surrogates accelerate the simulation, but inherit this representation gap by relying on meshes, point clouds, voxels, or other sampled approximations of geometry. We introduce CANTO, a transformer neural operator that maps directly from continuous CAD geometry to physical fields, without meshing the input geometry. We develop a theoretical framework for learning operators from geometric manifolds to function spaces of physical fields, representing geometry through sequences of parametric patches. CANTO instantiates this framework by directly tokenizing non-uniform rational B-spline (NURBS) patches from their control points, knot vectors, and weights, and predicts continuous surface and volume fields at arbitrary query locations. We evaluate CANTO on four automotive and aircraft aerodynamics industry benchmarks: AhmedML, WindsorML, DrivAerML, and HiLiftAeroML. CANTO achieves state-of-the-art accuracy on most evaluated surface and volume prediction tasks, including a 19.8% reduction in surface-pressure relative

L_2

error compared with AB-UPT on HiLiftAeroML. Differentiability with respect to CAD parameters further enables gradient-based inverse design of designs. On AhmedML, CANTO identifies designs with 4.4 to 20.4% lower drag than the best dataset designs satisfying the same volume and lift constraints, with the improvements verified using the same CFD setup used to generate the original dataset.

Daniel Leibovici, Nikola Borislavov Kovachki, Dawon Ahn +8

NVIDIA

PDE Surrogate Modeling Neural Operators Computational Fluid Dynamics

Sep 24, 2026cs.LG

Physics and Data Driven Transformer-Mamba Framework for Flow Field

While deep learning accelerates expensive partial differential equation solving in computational fluid dynamics (CFD), existing methods like PINNs and FNOs often struggle with generalization, noise robustness, and physical consistency. We introduce the Transformer-Mamba for Flow Field (TM4FF) framework, a physics-constrained operator learning model with three key innovations: a Residual Wavelet Mamba (RWM) layer for feature denoising, a Transformer-based attention mechanism for enhanced feature fusion, and a physics-informed loss using Fourier derivatives to enforce the Navier-Stokes equations. Experiments on four CFD datasets show TM4FF achieves high accuracy and robust generalization across varying flow conditions.

Zhuo Zhang, Shun Zou, Canqun Yang +1

College of Computer Science and Technology, National University of Defense Technology, Changsha, China · College of Artificial Intelligence, Nanjing Agricultural University, NanJing, China · National SuperComputer Center in Tianjin, Binhai New Area, Tianjin, China +1

PDE Surrogate Modeling PDE Operator Learning Physics-Informed Neural Operators State Space Models Computational Fluid Dynamics

Sep 23, 2026cs.LG

CFD Correction of Open Tip Clearance Flow in a Compressor Cascade Using VAE Latent Space Adaptation

CFD predictions of open tip clearance flow in compressor cascades are subject to discrepancies relative to experiments, while experimental observations are sparse and high-resolution experimental ground truth is unavailable. This study proposes a non-intrusive correction method based on a variational autoencoder (VAE) and latent-space adaptation. A VAE is first trained using a dataset of 166 parametrically sampled CFD total pressure loss fields to learn a low-dimensional statistical representation of these fields. The VAE is then frozen, and a low-rank latent-space adapter is trained using only 12 paired CFD--experiment operating conditions. An observation operator maps the corrected high-resolution fields to the experimental observation space, allowing supervision to be applied only at the available measurement locations and within the measured pitchwise windows. In the current 12-fold cross-validation, the mean absolute error decreases from 0.1335 to 0.0473, the root mean square error from 0.1717 to 0.0621, and the relative

L_2

error from 0.5108 to 0.1871. These results indicate that the method improves agreement between CFD predictions and sparse experimental observations of open tip clearance flow without modifying the RANS solver or constructing artificial high-resolution experimental labels.

Xiang Zuo, Hefang Deng, Caiyan Chen +4

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China · Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai 200240, China

Variational Autoencoders Computational Fluid Dynamics

Sep 20, 2026cs.LG

The Neural Forcing for Three-Dimensional Incompressible Navier-Stokes finite time blowup

We present a two-part neural framework for forced three-dimensional incompressible Navier--Stokes flow. PartI develops the computational forcing system. A physics-informed neural model generates structured external-force trajectories, candidates are optimized through differentiable PDE rollouts or PPO-Clip, and selected forcings are frozen and checked by independent fixed-force replay. PartII provides the mathematical certification layer. It separates neural candidate discovery from continuum analysis, derives integrated reciprocal-vorticity criteria that imply Riccati-type growth and finite-time loss of smooth continuation, develops a validated computational-to-continuum transfer strategy, and establishes a conditional positive-probability closure for a nondegenerate neural output law. The proof is complete at the continuum level.

Beibei Li

Dynamical Systems Computational Fluid Dynamics

Sep 20, 2026cs.CV

Semi-automated reconstruction of indoor geometry from 360-degree video for CFD-based airflow analysis in classrooms

Computational Fluid Dynamics (CFD) is widely used to evaluate ventilation and contaminant transport in occupied buildings, but deployment at scale is limited by three bottlenecks: acquiring room geometry without costly scanning hardware or manual CAD modeling, decomposing the scene into individually manipulable objects, and reconfiguring those objects for alternative layouts without re-capturing the room. We present a semi-automated workflow that converts a single 360-degree video of a room into individually editable, simulation-ready geometry assets. A dense point cloud is reconstructed using Neural Radiance Fields (NeRF), and 2D instance masks from text-prompted SAM 3 segmentation are lifted to 3D using multi-view consensus and depth-band filtering. Points are separated into object instances with an octree, and occlusion gaps are healed with a connectivity graph. Chair templates are fitted by Iterative Closest Point (ICP) alignment, and table geometry is generated procedurally. A browser-based editor supports quality assurance and rapid construction of alternative layout configurations. A steady Reynolds-averaged OpenFOAM solution then drives transient passive-scalar transport; the setup is verified using a mesh-sensitivity study and validated against an IEA Annex 20 benchmark. We apply the workflow to two university classrooms and a tiered lecture-hall auditorium. The capture-to-geometry pass takes two to five hours per room on a consumer workstation. In a controlled obstruction sequence in one classroom, the modeled half-clearance time varies non-monotonically as furniture is added, and a cross-room comparison indicates that clearance behavior cannot be reliably extrapolated between rooms, motivating per-room geometry acquisition. By making that acquisition low-cost, the workflow makes geometry-resolved comparative ventilation studies practical for spaces such as classrooms.

Dhruv Gamdha, James Afful, Shambhavi Joshi +3

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA · Department of Architecture, Iowa State University, Ames, IA 50011, USA

Panoramic 3D Reconstruction 3D Reconstruction Indoor Scene Reconstruction Computational Fluid Dynamics

Sep 17, 2026physics.comp-ph

How Does Distribution Shift Shape Pretraining Gains in Neural PDE Surrogates?

Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added

e^N

transition modeling. At

N=1000

, the pretrained model matches the accuracy of a model trained from scratch on

3.25\times

as many samples for the same-SA target, but

2.58\times

as many for the transition-modeled target. By

N=5000

, this ordering reverses (

1.56\times

versus

1.86\times

). At

N=1000

, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation (

3.3\times

to

4.0\times

). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.

Pochinapeddi Sai Bhargav, Nithin Somasekharan, Rohit Sunil Kanchi +2

Rensselaer Polytechnic Institute Troy, NY 12180 · University of Tennessee Knoxville, TN 37996

Distribution Shift Robustness PDE Surrogate Modeling Computational Fluid Dynamics

Sep 17, 2026physics.flu-dyn

Well-posedness of neural turbulence closures and tangent dissipation

A neural turbulence closure defines a new boundary-value problem,

R(U)=N(U)+F(U)=0

, with a coupled Jacobian

J(U)=N'(U)+F'(U)

, where

N

is the original mean-flow operator and

F

the learned closure. We establish two consequences of global tangent dissipation. For a monotone original operator, a positive uniform margin supplied by the original operator and closure together guarantees existence, uniqueness and a global inverse-sensitivity bound relating a posteriori solution error to the a priori residual. For a general original operator, a dissipative closure cannot worsen tangent dissipation, but this alone does not guarantee uniqueness. Tangent dissipation depends on both diffusion and reaction. We study two complementary ways to promote it: (1) an exact-integral construction enforcing non-negative tangent diffusion while leaving reaction unconstrained, and (2) a penalty on tangent-reaction violations at sampled states. Tangent diffusion enters the Jacobian, and non-negative secant eddy viscosity alone does not control its coercivity. We conduct tests with channel flow at

Re_τ=180

--

5200

, which provides a strongly monotone baseline. Both constrained closures reach accurate solutions in all 50 training-seed/Reynolds-number cases. At

Re_τ=1000

, we conduct tests with 10,000 starts for one fixed network per closure and we find one root for each constrained closure and multiple roots for the other closures. Although this does not prove uniqueness, it provides strong empirical evidence for uniqueness of the tested constrained closures. At

Re_τ=5200

, the construction and penalty reduce the reported inverse sensitivity relative to the original operator by approximately

372\times

and

11\times

, respectively.

Zhen Zhang, George Em Karniadakis

Division of Applied Mathematics, Brown University, Providence, RI 02912, USA

Neural PDE Solvers Computational Fluid Dynamics

Sep 15, 2026cs.LG

Neural Field Ensembles for Aerodynamic Surface Prediction: Winning Solution to the ONERA CRM Wall Distribution 2025 Challenge

Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and

k

-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.

Lionel Salesses, Caroline Sainvitu, Tariq Benamara

Cenaero, Gosselies, Belgium

Neural Surrogate Modeling Implicit Neural Representations Computational Fluid Dynamics

Sep 15, 2026cs.LG

High-Fidelity Digital Twin Data Models by Randomized Dynamic Mode Decomposition and Deep Learning with Applications in Fluid Dynamics

The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a model of reduced complexity that has the main feature of mirroring the original process behavior. The significant advantage of a DTM is to reproduce the dynamics with high accuracy and reduced costs in CPU time and hardware for settings difficult to explore because of the complexity of the dynamics over time. This paper introduces a new framework for creating efficient digital twin data models by combining two state-of-the-art tools: randomized dynamic mode decomposition and deep learning artificial intelligence. It is shown that the outputs are consistent with the original source data with the advantage of reduced complexity. The DTMs are investigated in the numerical simulation of three shock wave phenomena with increasing complexity. The author performs a thorough assessment of the performance of the new digital twin data models in terms of numerical accuracy and computational efficiency.

Diana A. Bistrian

University Politehnica Timisoara, Department of Electrical Engineering and Industrial Informatics, Romania

Neural Surrogate Modeling Reduced-Order Modeling Digital Twins Computational Fluid Dynamics

Sep 14, 2026physics.flu-dyn

Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning

Rotating detonation engines (RDEs) exhibit strongly nonlinear, multiscale wave dynamics that set the observed thermal field. High-fidelity simulations (DNS/LES) resolve these structures but remain computationally prohibitive, while low-order models such as the one-dimensional Koch-Kutz model capture circumferential wave motion yet lack the expressivity for high-frequency content. We use continuous data assimilation (nudging) to synchronize the Koch-Kutz solver with processed high-fidelity temperature data, introducing the prediction-observation mismatch as a relaxation source in the conserved energy equation; where observations are temporally sparse, interpolation supplies a target at every source update. As the nudging strength increases, the reduced model is progressively drawn onto the high-fidelity trajectory, and the forcing recorded along it provides an explicit, state-dependent estimate of the correction the model requires. We then train a Jacobian-regularized closure a priori on this recorded source. With the observation term removed, the corrected model advances autonomously, remains bounded, and recovers the temperature spectrum and the marginal statistics of the conserved variables relative to the baseline.

Ashwin Suriyanarayanan, Romit Maulik

School of Mechanical Engineering, Purdue University, West Lafayette, IN-47906

Data Assimilation Reduced-Order Modeling Computational Fluid Dynamics

Sep 14, 2026physics.flu-dyn

Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows

Numerical simulations reveal how vortices stretch and transfer energy, but establishing smooth evolution requires bounds that remain valid beyond the simulated resolution. Here I develop a computer-assisted framework that establishes global regularity for continuous families of three-dimensional periodic Navier-Stokes flows. Its central construction combines finite reference trajectories with a common error bound that covers an interval of centre fields and infinitely many smooth perturbation modes. The method retains the complete nonlinear residual before spectral truncation and controls the evolution until viscous decay guarantees regularity for all subsequent times. Applications to cyclic-shear, Arnold-Beltrami-Childress and three-component Taylor-Green fields yield explicit perturbation radii and include initial conditions outside the direct Fourier-Wiener smallness criterion. A parameter-uniform extension covers a connected family of non-Beltrami Taylor-Green centres without repeating the proof for individual parameter values. An ensemble of 4,096 configurations, supplemented by 1,600 refinement trajectories and public turbulence data, connects the mathematical observables to spectral transfer and vortex geometry. Matched neural-operator experiments show that physics-informed training improves physical prediction, while also revealing that these gains do not necessarily improve the discovery of proof-limiting initial conditions. Together, these results provide a reusable method for establishing regularity across prescribed flow families and a quantitative setting for evaluating how learned predictions can assist rigorous computation.

Jose Luis Lima de Jesus Silva

Federal University of Bahia, Department of Geophysics Salvador, BA 40170-115, Brazil · Grupo de Estudos e Aplicação de Inteligência2026 Artificial em Geofísica (GAIA) Federal University of Bahia, Salvador, BA 40170-115, Brazil

Computational Fluid Dynamics

Sep 14, 2026physics.flu-dyn

Physics Informed Neural Network model for the dynamical study of Abdominal Aortic Aneurysm

We present the development and application of a three-dimensional Physics-Informed Neural Network (PINN) framework for the investigation of haemodynamic behaviour in the human aorta. The model incorporates a time-resolved simulation of pulsatile blood flow over a two-minute interval, enabling the extraction of pressure and velocity fields with high temporal fidelity. The mechanical stress exerted on the aortic wall was quantified through Laplace's law, with temporal averaging applied to derive representative stress distributions. This approach circumvents the computational overhead associated with conventional computational fluid dynamics (CFD) methods by eliminating mesh generation and exploiting the automatic differentiation capabilities inherent to neural networks. The proposed methodology demonstrates that PINNs can serve as an efficient and accurate alternative for modelling complex vascular flow phenomena, offering significant advantages in scalability and computational cost reduction while maintaining physical consistency.

Adrián Robles Arques, Martín Ruiz Fernandez, Javier Sanchis +2

Lucentia Research; Instituto Universitario de Investigación en Informática, Universidad de Alicante, Carr. San Vicent del Raspeig, Alicante, 03690, Comunidad Valenciana, España

Neural PDE Solvers Physics-Informed ML Computational Fluid Dynamics

Sep 14, 2026cs.AI

DU-NO: A Parameter-Efficient Double U-Shaped Neural Operator for Phase-Resolving Wave Modeling

Phase-resolving wave models such as FUNWAVE-TVD are the accuracy standard for nearshore dynamics, resolving the shoaling, refraction, and breaking of individual waves, but their cost rules them out for the ensembles, uncertainty quantification, and real-time warning that operational forecasting demands. Neural operators promise solver-level accuracy at a fraction of that cost, yet on wave-dominated fields the accurate ones are large: hybrid spectral-convolutional operators such as U-FNO (the strongest baseline in our study after DU-NO) buy their fidelity with tens of millions of parameters. We introduce DU-NO (Double U-shaped Neural Operator), a multiscale U-shaped spectral operator that attaches lightweight convolutional U-Net branches only at its two shallowest encoder and decoder levels. The placement follows a sampling argument: high-wavenumber content exists only on fine grids, so the local, full-band pathways go where that content lives, while the coarse, band-limited levels stay purely spectral. A depth-decaying mode schedule holds the model to 3.64M parameters, an order of magnitude below U-FNO. On our publicly released FUNWAVE-TVD benchmark, DU-NO attains the best autoregressive rollout error of six identically trained architectures, improving on U-FNO by 14.9% with 10.8x fewer parameters, and a frequency-band analysis shows the gain holds across all bands, including the high-wavenumber band where truncated-spectral operators collapse. Parameter-matched controls confirm the gain is architectural: rescaled to the same 3.6M budget, the best baseline still trails DU-NO by 28.6%. The advantage carries beyond nearshore waves: DU-NO matches the strongest baselines on 2D Navier-Stokes and wins clearly on PDEBench shallow-water rollouts. Code, trained models, and evaluation artifacts are available at https://anonymous.4open.science/r/duno-code-5A7B/.

Enrique Hernandez Noguera, Md Meftahul Ferdaus, Nathan Cooper +2

Canizaro-Livingston Gulf States Center for Environmental Informatics, LSU New Orleans, New Orleans, LA, USA · U.S. Naval Research Laboratory, Stennis Space Center, MS, USA

U-Net PDE Operator Learning Neural Operators Computational Fluid Dynamics

Sep 14, 2026physics.comp-ph

Physics-enriched neural solvers for transient ice-flow simulation

Transient glacier simulations with higher-order ice flow require the repeated solution of a nonlinear problem as the geometry evolves. In the online mode of the Instructed Glacier Model, the velocity field is represented by a neural network whose weights are warm-started from the previous time step and updated with a few optimizer iterations. We show that supplying the network with inexpensive input fields derived from low-order ice-flow balances improves this online solver. Unlike residual-based physics-informed neural networks, which incorporate physics through governing-equation penalties in the loss, our approach leaves the governing energy objective unchanged, adding physical structure through the network inputs. Across three real-world glacier configurations, the enriched solver is markedly more robust to solver settings. On the two alpine cases, it also improves the tuned accuracy--runtime trade-off, reducing surface-velocity errors by factors of two to four at fixed runtime and reaching few-percent relative errors with only

10^4

--

10^5

trainable parameters, far fewer than comparable raw-input baselines. A 300-year Aletsch simulation then completes in under one minute, and the larger Valais domain in about two minutes, on a single GPU---a budget once reserved for much simpler shallow-ice models. Gains are smaller for the fast marine-terminating glacier, where nonlocal stress coupling favors larger or spectral networks. More broadly, the results suggest that enriching a neural solver's inputs with reduced-order physics can make repeated higher-order solves much cheaper, with no training data and no offline training.

Thomas Gregov, Sebastian Rosier, Brandon Finley +2

Institute of Earth Surface Dynamics, Universit´e de Lausanne, Lausanne, Switzerland · Department of Geography, Universität Zürich, Zürich, Switzerland

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

Sep 11, 2026cs.LG

Attention Is All You Need (to Avoid Spurious Oscillations)

Can attention move a shock across several cells in one update without breaking it? We develop a conservative, fixed grid finite-volume scheme in which a CFL-conditioned attention flux selects upstream information according to the transport required by the current time step. One-dimensional inviscid Burgers transport is used as the central mechanism test: the same learned flux remains reliable in the conventional small-step regime and, with a time step four times larger, preserves sharp shocks while using one stage per update. A standard fifth-order WENO scheme with third-order strong-stability-preserving Runge-Kutta time integration (WENO-5+SSP-RK3) is included alongside controlled Forward Euler comparisons to separate flux selection from time integration. The learned attention shifts upstream with the local transport reach and becomes more selective near shocks; inference-time interventions and retrained ablations show that transport-scale information and state-dependent selection contribute directly to performance. Directional two-dimensional scalar Burgers transport and the one-dimensional shallow-water system then test whether the conservation-scale-selection principle transfers beyond the original scalar setting. The results support attention as a learnable information stencil for conservative large-step shock transport, while identifying finite candidate reach and problem-dependent robustness as the present limits.

Jinyoung Jeong, Joseph B. Choi, Xinlun Cheng +3

School of Mechanical Engineering & IEDT, Kyungpook National University, Daegu, South Korea · School of Data Science, University of Virginia, Charlottesville, VA 22903, USA · Department of Mechanical Engineering, University of Iowa, Iowa City, Iowa 52242, USA +1

Neural PDE Solvers PDE Solving Computational Fluid Dynamics

Sep 8, 2026physics.flu-dyn

ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows

Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, their development is limited by the scarcity of benchmark datasets spanning multiple flow regimes and standardized protocols for long-horizon autoregressive prediction. We introduce ONECYL (ONE CYLinder), a new benchmark for unsteady flow past a circular cylinder across laminar, transitional, and high-Reynolds-number regimes. The benchmark comprises 450 high-fidelity Variational Multiscale finite-element simulations (270,000 flow snapshots) with randomized cylinder geometries, providing time-resolved velocity and pressure fields together with mesh connectivity, geometric descriptors, Reynolds numbers, and integrated aerodynamic quantities. Beyond the dataset, ONECYL establishes a unified evaluation framework combining full-field rollout errors, virtual probes, and drag and lift predictions to assess numerical accuracy and physical fidelity. To accompany the benchmark, we develop a Graph Transformer as a reference baseline predicting velocity and pressure fields autoregressively on unstructured meshes. Using ONECYL, we investigate geometric representations and physics-based regularization across the three Reynolds-number regimes. The results show that explicitly encoding the cylinder geometry through a level-set representation consistently improves long-horizon prediction accuracy and generalization to unseen geometries, while divergence-based regularization becomes increasingly beneficial as flow complexity increases. The ONECYL benchmark and its Graph Transformer baseline provide a reproducible framework for evaluating graph-based surrogate models and establish a foundation for future research on long-horizon prediction of unsteady bluff-body flows.

Théodore Michel, Antoine Campos, Alban Dujardin +3

Mines Paris PSL University Centre for Material Forming (CEMEF) UMR CNRS, Sophia Antipolis, 06904, France

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

Sep 7, 2026cs.AI

Distance-Aware Attention and Wall-Distance Expert Routing for Transformer-Based 3D Flow Prediction

Transformer surrogates for 3D flow prediction compress an industrial mesh into a small set of tokens from which every prediction point reads. Two operations follow: the retrieval step in which a point gathers information from the compressed representation, and the feed-forward layer that transforms what it retrieved. In current backbones both are blind to where the point sits in the flow. We condition both on wall-related physical signals. Distance-aware cross-attention (DA-CA) reshapes each volume query by its wall distance before retrieval, so that a point deep in the boundary layer draws different geometric information than one in the outer flow. Surface-volume mixture-of-experts (SVMoE) replaces the shared feed-forward layer with a small set of experts, routed by wall distance for volume points and by local geometry for surface points. Neither mechanism is tied to one architecture, so we apply both unchanged to AB-UPT and Transolver-3. On DrivAerML with 50 training cases, DA-CA reduces the volume pressure error by 10.1%, and DA-CA and SVMoE together reduce it by 12.5%; DA-CA improves the near-wall region at some cost in the far region, which SVMoE recovers, and the volume experts settle into near-wall, transition, and free-stream bands without routing supervision. Retrained on 300 cases, the conditioning improves every field quantity, reducing volume pressure and velocity errors by 33.1% and 18.6% on AB-UPT and by 21.4% and 21.3% on Transolver-3. Under Leave-One-Body-Out evaluation on DrivAerNet++, it reduces the volume pressure error on unseen body types by up to 14.2%.

Sanghyeon Kim, Sunwoong Yang, Namwoo Kang

Division of Future Vehicle Korea Advanced Institute of Science and Technology Daejeon, 34051, Republic of Korea · Department of Mechanical Engineering Hanyang University Ansan, 15588, Republic of Korea · Cho Chun Shik Graduate School of Mobility Korea Advanced Institute of Science and Technology Narnia Labs Daejeon, 34051, Republic of Korea

Cross-Attention Mixture of Experts PDE Surrogate Modeling Transformer Attention Computational Fluid Dynamics

Sep 2, 2026cs.LG

Learnable composition for neural operators

Neural operators are fast, differentiable surrogates for physical simulation, but their accuracy often degrades when domain geometry, size, or operating conditions differ from training. Supervised adaptation can recover accuracy, but even a small target set requires costly high-fidelity simulations. We therefore ask how pretraining and transfer can be designed together to reduce this deployment cost. LatentDDM first pretrains a neural operator to predict fields on small subdomains. For a new setting, it freezes this operator and trains only a lightweight module that composes the local predictions. We evaluate our method on two complementary problems: steady Darcy flow, where long-range pressure coupling must extend across increasingly large porous domains, and unsteady incompressible flow around a pitching airfoil, where rollout errors compound as target pitching frequencies exceed the training range. Compared with the capacity-matched models that process the full domain at once, LatentDDM's error is 36-56% lower on larger Darcy domains after adaptation with 16 target simulations. It also improves 20-step field rollouts in fast-pitching airfoil flow, both zero-shot and after few-shot calibration. These results identify the co-designed local pretraining and composition-level transfer as a promising design principle for physical foundation models.

Zituo Chen, Baiming Zhang, Sili Deng

MIT MechE · University of Toronto

Neural Surrogate Modeling Transfer Learning Neural Operators Computational Fluid Dynamics

Sep 1, 2026cs.LG

VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil Flows

Accurate prediction of unsteady separated flows is challenging because the aerodynamic loads depend on nonlinear separation and vortex-shedding dynamics. Although high-fidelity CFD resolves these mechanisms, its cost limits repeated use in design and control. Standard field-level surrogate training, however, does not distinguish the flow regions that contribute most strongly to the aerodynamic loads. We introduce VATO (Vortex-Force-Aware Transformer Operator), which couples the Vortex Force Map (VFM) method to a geometry-aware neural operator through two complementary mechanisms. VATO-S adds training-only supervision of the local VFM force-contribution field, with no increase in model size or inference cost. VATO-A uses VFM contribution and sensitivity fields to prioritise force-relevant source locations for residual cross attention. The methods are evaluated on unsteady CFD data for double-edged-plate aerofoils over 54 trajectories from nine geometries. Over lead times of 1-20~ms, VATO-S reduces velocity, pressure, and vorticity errors by 10.4%, 1.0%, and 15.6%, respectively, while VATO-A achieves reductions of 15.8%, 7.5%, and 31.2%. VATO-S gives the lowest VFM-derived drag error, whereas VATO-A gives the lowest pressure-derived lift and drag errors. Over lead times extending 50% beyond the training range, VATO-A retains a 26.9% reduction in vorticity error and larger improvements in all four force readouts, despite reduced gains in velocity and pressure. These results show that force-aware operator learning can improve both flow-field prediction and aerodynamic functional accuracy in unsteady separated flows.

Xingxin Yang, Zhan Zhang, Yichen Li +1

aDepartment of Engineering, King’s College London, London, WC2R 2LS, UK

PDE Operator Learning Neural Operators Computational Fluid Dynamics

Aug 30, 2026physics.flu-dyn

Data-Driven Design Optimization of Streaming-Potential-Mediated Electrokinetic Transport of Viscoelastic Fluids in Microchannels

Streaming-potential-mediated transport of viscoelastic fluids has attracted research attention owing to its applications in electrokinetic energy conversion and microfluidic transport. Existing analytical and semi-analytical models in published literature provide valuable physical insights, but require repeated numerical evaluations for exploring large design spaces and identifying the optimal operating conditions. In this work, a surrogate-assisted framework is developed for rapid design optimization of pressure-driven electrokinetic transport of simplified Phan-Thien-Tanner fluids in a slit microchannel. A high-fidelity numerical database is generated over a broad range of governing dimensionless parameters, which includes the zeta potential, the Debye parameter, the Dukhin number, and the viscoelastic parameter. A Machine Learning surrogate model is subsequently trained to accurately approximate the nonlinear relationship between the governing parameters and the streaming potential, while the volumetric flow rate and hydroelectric energy conversion efficiency were calculated from closed form equation by using the streaming potential predicted by the surrogate. This is coupled with a multi-objective optimization strategy to identify operating conditions that simultaneously maximize energy conversion efficiency and volumetric flow rate. The proposed methodology can significantly accelerate parametric exploration compared with repeated numerical simulations across different parameters and provides practical design guidelines for electrokinetic microfluidic devices. The study demonstrates the potential of combining computational fluid mechanics with data-driven surrogate modeling for efficient engineering design and optimization.

Ankan Basu, Sumanta Banerjee

Department of Computer Science and Engineering, Jadavpur University, Kolkata, India. · 2*Department of Mechanical Engineering, Heritage Institute ofAug Technology, Kolkata, India.

Surrogate-Assisted Optimization Computational Fluid Dynamics