Data to 7 Oct 2026

Accelerating Eulerian Fluid Simulation With Convolutional Networks

arXiv 1607.03597 ↗First posted 13 Jul 2016cs.CVcited by 128

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Abstract (arXiv)

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.

Key facts. Cited by 128 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Jul 2016.

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Citing papers per year: 2021: 35; 2022: 23; 2023: 21; 2024: 16; 2025: 25; 2026: 8.

128 papers.

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2021Machine learning accelerated computational fluid dynamicscited by 461
2021Factorized Fourier Neural Operatorscited by 237
2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
2022SNUG: Self-Supervised Neural Dynamic Garmentscited by 83
2021Gradients are Not All You Needcited by 82
2022Blending Neural Operators and Relaxation Methods in PDE Numerical Solverscited by 53
2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
2022Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNNcited by 43
2021Simulating Continuum Mechanics with Multi-Scale Graph Neural Networkscited by 39
2021Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNscited by 38

38 more

2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
2022Learning to Solve PDE-constrained Inverse Problems with Graph Networkscited by 37
2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generationcited by 28
2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
2023Data-Free Learning of Reduced-Order Kinematicscited by 19
2025Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulationcited by 19
2023Inferring Hybrid Neural Fluid Fields from Videoscited by 18
2023Learning Vortex Dynamics for Fluid Inference and Predictioncited by 17
2023Solving Inverse Physics Problems with Score Matchingcited by 15
2023Grounding Graph Network Simulators using Physical Sensor Observationscited by 15
2021Artificial Intelligence for Satellite Communication: A Reviewcited by 14
2021Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamicscited by 14
2021DEBOSH: Deep Bayesian Shape Optimizationcited by 14
2022Finite Element Method-enhanced Neural Network for Forward and Inverse Problemscited by 13
2021Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flowscited by 12
2022A Deep Conjugate Direction Method for Iteratively Solving Linear Systemscited by 12
2023Fluid Simulation on Neural Flow Mapscited by 12
2021Direct Prediction of Steady-State Flow Fields in Meshed Domain with Graph Networkscited by 11
2022Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networkscited by 11
2023NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decompositioncited by 11
2021Physics perception in sloshing scenes with guaranteed thermodynamic consistencycited by 10
2021Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulationscited by 10
2021NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEscited by 10
2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Datacited by 10
2024Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanicscited by 9
2021SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasetscited by 8
2021Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Networkcited by 8
2024NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Designcited by 8
2025MeshMask: Physics-Based Simulations with Masked Graph Neural Networkscited by 8
2021Accelerating GMRES with Deep Learning in Real-Timecited by 7
2023Invariant preservation in machine learned PDE solvers via error correctioncited by 7
2024Metamizer: a versatile neural optimizer for fast and accurate physics simulationscited by 7
2023Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Modelscited by 6
2024UGrid: An Efficient-And-Rigorous Neural Multigrid Solver for Linear PDEscited by 6
2025Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Methodcited by 6

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