Learning to Simulate Complex Physics with Graph Networks

By Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, Peter W. Battaglia. 2020

1,550 citations recorded by the source corpus.

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Graph Learning

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Citations in the corpus

Object-Centric Learning with Slot Attention (2020, background): “[8] Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter W Battaglia.”
Toward Causal Representation Learning (2021, background): “Machine learning models that incorporate or learn structural knowledge of an environment have been shown to be more efﬁcient and generalize better [9], [11], [15], [16], [27], [58], [77], [84], [85], [141], [157], [177], [181], [197], [211], [212], [244], [258], [272], [274].”
Isometric Transformation Invariant and Equivariant Graph Convolutional Networks (2020, background): “Sanchez-Gonzalez et al. (2020) proposed a general framework for learning simulations based on GNNs.”
Generating Molecular Conformer Fields (2023, background): “In addition, recent approaches for learning simulations on graphs (Sanchez-Gonzalez et al., 2020) or pre-training models for molecular prediction tasks (Zaidi et al., 2022) have relied on non-equivariant architectures.”
Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs (2022, methodology): “In message passing networks [29, 62, 63, 5], vij depends on features on nodes i and j with constant aij .”
Geometry-Informed Neural Operator for Large-Scale 3D PDEs (2023, methodology): “Another line of work, mesh graph networks [8–10], further explored PDE s in the context of fluid and solid mechanics.”
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.”
Visual Grounding of Learned Physical Models (2020, background): “Other researchers have extended the model to particle systems, which showed impressive results in simulating objects made of different materials like rigid objects and fluids (Mrowca et al., 2018; Li et al., 2019a; Ummenhofer et al., 2020; Sanchez-Gonzalez et al., 2020).”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “, for rigid-body physics in the context of human reasoning [5, 64, 3] or weather predictions [51], particles are also a popular basis for fluid flow problems [33, 61, 48].”
Learning Mesh-Based Simulation with Graph Networks (2020, methodology): “Various works [22, 38, 33] use graph neural networks (GNNs) [34, 4] to model particle-based granular materials and fluids, as well as glassy dynamics [3].”
EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations (2023, neutral): “SEGNN [15] introduces non-linearity to messages passing [1,39] with equivariant gate activation, and the non-linear messages improve upon linear messages.”
A Generalization of Transformer Networks to Graphs (2020, background): “…network architectures on graph datasets and have achieved signiﬁcant success on a wide range of applications, such as in knowledge graphs (Schlichtkrull et al. 2018; Chami et al. 2020), in social sciences (Monti et al. 2019), in physics (Cranmer et al. 2019; Sanchez-Gonzalez et al. 2020), etc.”
Learning Physical Graph Representations from Visual Scenes (2020, background): “Given the promising results of applying graph neural networks to dynamics prediction problems [36, 32, 33, 43], the structured latent state of PSGNet seems well-poised to connect visual perception with physical understanding.”
UvA-DARE (Digital Academic Repository) Neural Relational Inference for Interacting Systems Neural Relational Inference for Interacting Systems (2018, neutral): “, 2017) and predicting physical interactions of particles (Mrowca et al., 2018; Li et al., 2018; Sanchez-Gonzalez et al., 2020).”
Graph neural networks in particle physics (2020, background): “Recent work by [41] highlights how far this sub-field has advanced: they trained models to predict systems of thousands of particles, which represent fluids, solids, sand, and ‘goop’, and show generalization to orders of magnitude more particles and longer trajectories than experienced during traini”
Hierarchical Relational Inference (2020, background): “…et al. 2020), implicitly by the message passing functions (Sukhbaatar et al. 2015; Battaglia et al. 2016; Santoro et al. 2017; Watters et al. 2017; Sanchez-Gonzalez et al. 2018, 2020) e.g. via attention (Hoshen 2017; van Steenkiste et al. 2018), or explicitly as in NRI (Kipf et al. 2018).”
Learning to simulate and design for structural engineering (2020, background): “…to many new scientific domains including physics systems (Kipf et al., 2018; Sanchez-Gonzalez et al., 2018; Watters et al., 2017), fluid dynamics(Sanchez-Gonzalez et al., 2020), chemical molecules(Fout et al., 2017; Jin et al., 2018b; Do et al., 2019), and traffic networks (Guo et al., 2019;…”