Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D
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Abstract (arXiv)
Physically plausible fluid simulations play an important role in modern computer graphics and engineering. However, in order to achieve real-time performance, computational speed needs to be traded-off with physical accuracy. Surrogate fluid models based on neural networks have the potential to achieve both, fast fluid simulations and high physical accuracy. However, these approaches rely on massive amounts of training data, require complex pipelines for training and inference or do not generalize to new fluid domains. In this work, we present significant extensions to a recently proposed deep learning framework, which addresses the aforementioned challenges in 2D. We go from 2D to 3D and propose an efficient architecture to cope with the high demands of 3D grids in terms of memory and computational complexity. Furthermore, we condition the neural fluid model on additional information about the fluid's viscosity and density which allows simulating laminar as well as turbulent flows based on the same surrogate model. Our method allows to train fluid models without requiring fluid simulation data beforehand. Inference is fast and simple, as the fluid model directly maps a fluid state and boundary conditions at a moment t to a subsequent fluid state at t+dt. We obtain real-time fluid simulations on a 128x64x64 grid that include various fluid phenomena such as the Magnus effect or Karman vortex streets and generalize to domain geometries not considered during training. Our method indicates strong improvements in terms of accuracy, speed and generalization capabilities over current 3D NN-based fluid models.
Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Dec 2020.
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Citing papers per year: 2021: 1; 2022: 5; 2023: 6; 2024: 9; 2025: 4; 2026: 1.
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- 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
- 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
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- 2023Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representationcited by 11
- 2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Datacited by 10
- 2024Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equationscited by 9
- 2024Pi-fusion: Physics-informed diffusion model for learning fluid dynamicscited by 9
- 2025PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulationscited by 8
- 2024A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle acceleratorscited by 7
- 2024Metamizer: a versatile neural optimizer for fast and accurate physics simulationscited by 7
14 more
- 2022Towards Size-Independent Generalization Bounds for Deep Operator Netscited by 6
- 2023ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equationscited by 6
- 2024Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversalcited by 6
- 2022Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learningcited by 4
- 2022RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Networkcited by 4
- 2023LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometrycited by 4
- 2023Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solvingcited by 2
- 2023Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUpcited by 2
- 2024Preconditioned FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problemscited by 2
- 2025Noisy PDE Training Requires Bigger PINNscited by 2
- 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured gridscited by 1
- 2025Learning an Implicit Physics Model for Image-based Fluid Simulationcited by 1
- 2024Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditionscited by 0
- 2026Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equationscited by 0
- 2026Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations24 Mar 2026
- 2025MORPH: PDE Foundation Models with Arbitrary Data Modality25 Sep 2025
- 2025Learning an Implicit Physics Model for Image-based Fluid Simulation11 Aug 2025
- 2025Noisy PDE Training Requires Bigger PINNs9 Jul 2025
- 2025PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations3 Jul 2025
- 2024Metamizer: a versatile neural optimizer for fast and accurate physics simulations10 Oct 2024
- 2024Preconditioned FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problems6 Sep 2024
- 2024Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal14 Aug 2024
- 2024Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions30 Jul 2024
- 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations9 Jul 2024
- 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids15 Jun 2024
- 2024Pi-fusion: Physics-informed diffusion model for learning fluid dynamics6 Jun 2024
14 more
- 2024Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations23 May 2024
- 2024A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators19 Mar 2024
- 2023Investigating the Ability of PINNs To Solve Burgers' PDE Near Finite-Time BlowUp8 Oct 2023
- 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEs1 Sep 2023
- 2023Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving12 Jul 2023
- 2023ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations15 Jun 2023
- 2023Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation10 Feb 2023
- 2023LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometry3 Feb 2023
- 2022RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network6 Dec 2022
- 2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data19 Jun 2022
- 2022Accelerating hydrodynamic simulations of urban drainage systems with physics-guided machine learning24 May 2022
- 2022Towards Size-Independent Generalization Bounds for Deep Operator Nets23 May 2022
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics9 May 2022
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method29 Oct 2021
- 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
- 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
- 2025MORPH: PDE Foundation Models with Arbitrary Data Modalitycited by 12
- 2023Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representationcited by 11
- 2022LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Datacited by 10
- 2024Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equationscited by 9
- 2025PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulationscited by 8
- 2024A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle acceleratorscited by 7
- 2024Metamizer: a versatile neural optimizer for fast and accurate physics simulationscited by 7
- 2022Towards Size-Independent Generalization Bounds for Deep Operator Netscited by 6
12 most cited of 25 All 25 (JSON)
- 2026Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations24 Mar 2026
- 2025MORPH: PDE Foundation Models with Arbitrary Data Modality25 Sep 2025
- 2025Learning an Implicit Physics Model for Image-based Fluid Simulation11 Aug 2025
- 2025Noisy PDE Training Requires Bigger PINNs9 Jul 2025
- 2025PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations3 Jul 2025
- 2024Metamizer: a versatile neural optimizer for fast and accurate physics simulations10 Oct 2024
- 2024Preconditioned FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problems6 Sep 2024
- 2024Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal14 Aug 2024
- 2024Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions30 Jul 2024
- 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations9 Jul 2024
- 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids15 Jun 2024
- 2024Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations23 May 2024
12 newest of 25 All 25 (JSON)