Learning Mesh-Based Simulation with Graph Networks

By Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, Peter W. Battaglia. International Conference on Learning Representations, 2020

1,318 citations recorded by the source corpus.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/9e20f6874feaaf7c9994f9875b1d9cab17a2fd59

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Citations in the corpus

Geometric and Physical Quantities improve E(3) Equivariant Message Passing (2021, methodology): “Such problems are often encountered in physical and astrophysical simulations (Alvaro et al., 2020; Tobias et al., 2020; Mayr et al., 2021), where usually the force (or acceleration) is used to Euler-update the positions.”
Transolver: A Fast Transformer Solver for PDEs on General Geometries (2024, background): “Graph neural networks are representative ones, which employ kernels on connected graphs for representation learning (Hamilton et al., 2017; Gao & Ji, 2019; Pfaff et al., 2021).”
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries (2022, background): “This design difference makes neural operators, especially FNO, have an advantage when the data are fully observed while DeepONet has an advantage when the data are partially observed.”
Transformer for Partial Differential Equations' Operator Learning (2022, methodology): “A common and straightforward approach is to follow an Encoder-Process-Decoder (EPD) scheme to map the input solution at time t to the solution at next time step [7, 27, 57, 60, 64, 70].”
GraphCast: Learning skillful medium-range global weather forecasting (2022, methodology): “Other model details Input normalization Similar to Pfaff et al. (2021); Sanchez-Gonzalez et al. (2020), we normalized all inputs.”
Neural Operator: Learning Maps Between Function Spaces (2021, background): “More sophisticated quadrature rules and adaptive meshes can also be implemented using the general framework of message passing on graphs, see, for example, Pfaff et al. (2020).”
Combinatorial optimization and reasoning with graph neural networks (2021, background): “It should be noted that, concurrently, signi cant strides have been made on using GNNs for physics simulations [107, 99], coming up with a largely equivalent set of prescriptions.”
Deep Generative Models in Engineering Design: A Review (2021, methodology): “Even performance evaluation using conventional simulation tools like FEA or CFD can require an intermediate conversion from an image to a 3D model.”
Geometric deep learning on molecular representations (2021, background): “, non-consistent distance between the vertices in 3D) [116].”
Geometry-Informed Neural Operator for Large-Scale 3D PDEs (2023, methodology): “We set the learning rate to be 1e-4 with an exponential decay with a rate of 0.99985, similar to the original setup in [9].”