Accelerating Eulerian Fluid Simulation With Convolutional Networks

By Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, Ken Perlin. 2016

616 citations recorded by the source corpus.

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.

Subfields: Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

In Statistical and Nonlinear Physics

Citations in the corpus

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow (2018, background): “…meth-c ods, e.g., for computing local interactions of particle based liquids [LJS ∗ 15], to perform divergence free projections for a single point in time [TSSP16], or for adversarial training of high resolution ﬂows [XFCT18], few works exist that target temporal evolutions of physical systems.”
DGM: A deep learning algorithm for solving partial differential equations (2017, positive): “[49] use a convolutional neural network to solve a large sparse linear system which is required in the numerical solution of the Navier-Stokes PDE.”
Prediction of aerodynamic flow fields using convolutional neural networks (2019, methodology): “[41] proposed a data-driven approach for calculating numerical solutions to the inviscid Euler equations for fluid flow.”
Fluid directed rigid body control using deep reinforcement learning (2018, background): “Indeed, it has been shown in [Tompson et al. 2016] that the fluid’s velocity field is internally correlated so that most of the dimensions can be redundant.”
Machine learning–accelerated computational fluid dynamics (2021, neutral): “For example, ML can replace (31) or accelerate (32) iterative solves used inside some simulation methods without reducing accuracy.”
Geometric Deep Learning for Volumetric Computational Fluid Dynamics (2019, methodology): “Then in [47] they accelerated eulerian fluid simulations using deep learning, approximating a solution to the enforced incompressibility condition, thus having one system”
Generating Liquid Simulations with Deformation-aware Neural Networks (2017, methodology): “Our model shares the goal to learn flow physics based on examples with other methods [23, 39, 9], but in contrast to these we focus on 4D volumes of physics data, instead of localized windows at single instances of time.”
Deep learning for determining a near-optimal topological design without any iteration (2018, background): “…the potential of applying deep learning to computational physics and engineering fields, such as quantum and particle physics as well as fluid dynamics simulation (Carleo and Troyer 2017; Tompson et al. 2017; Singh et al. 2017; Mills et al. 2017) In regard to structural analysis, Lee et al .”
Hamiltonian Neural Networks (2019, background): “A variety of previous works have taken this path and produced excellent results [41, 14, 43, 34, 17, 6].”
Weak Adversarial Networks for High-dimensional Partial Differential Equations (2019, methodology): “In [22], convolutional neural networks (CNN) is used to solve the large linear system derived from the discretization of incompressible Euler equations.”
Towards Physics-informed Deep Learning for Turbulent Flow Prediction (2019, background): “[3, 4] develop deep learning models in the context of fluid animation, 32 where being physically meaningful is less of a concern.”
Deep Generative Design: Integration of Topology Optimization and Generative Models (2019, methodology): “[11] accelerate Eulerian fluid simulation by approximating a linear system with CNN.”
Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems (2016, neutral): “Section III shows the relationship between our result and model-based and spectral compressed sensing [1], [12].”
Learning A Physical Long-term Predictor (2017, background): “Other approaches also focused on learning the production of realistic future scenarios ((Tompson et al., 2016) and (Jeong et al., 2015)), or inferring collision parameters from monocular videos (Monszpart et al., 2016).”