Learning to Simulate Complex Physics with Graph Networks

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.

[1]  Yousef Saad,et al.  Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection , 2009, J. Mach. Learn. Res..

[2]  Le Song,et al.  Know-Evolve: Deep Temporal Reasoning for Dynamic Knowledge Graphs , 2017, ICML.

[3]  H. Francis Song,et al.  Relational Forward Models for Multi-Agent Learning , 2018, ICLR.

[4]  Barbara Solenthaler,et al.  Data-driven fluid simulations using regression forests , 2015, ACM Trans. Graph..

[5]  Joshua B. Tenenbaum,et al.  A Compositional Object-Based Approach to Learning Physical Dynamics , 2016, ICLR.

[6]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[7]  Kyle Cranmer,et al.  Hamiltonian Graph Networks with ODE Integrators , 2019, ArXiv.

[8]  Elsevier Sdol,et al.  Journal of Visual Communication and Image Representation , 2009 .

[9]  E. D. Cubuk,et al.  JAX, M.D.: End-to-End Differentiable, Hardware Accelerated, Molecular Dynamics in Pure Python , 2019, 1912.04232.

[10]  Dahua Lin,et al.  Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition , 2018, AAAI.

[11]  Bernhard Schölkopf,et al.  A Kernel Two-Sample Test , 2012, J. Mach. Learn. Res..

[12]  Daniel L. K. Yamins,et al.  Flexible Neural Representation for Physics Prediction , 2018, NeurIPS.

[13]  Geoffrey E. Hinton,et al.  NeuroAnimator: fast neural network emulation and control of physics-based models , 1998, SIGGRAPH.

[14]  Kai Li,et al.  Efficient k-nearest neighbor graph construction for generic similarity measures , 2011, WWW.

[15]  Vladlen Koltun,et al.  Lagrangian Fluid Simulation with Continuous Convolutions , 2020, ICLR.

[16]  Samuel S. Schoenholz,et al.  Neural Message Passing for Quantum Chemistry , 2017, ICML.

[17]  Jiajun Wu,et al.  Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids , 2018, ICLR.

[18]  Max Welling,et al.  Semi-Supervised Classification with Graph Convolutional Networks , 2016, ICLR.

[19]  Jiajun Wu,et al.  Propagation Networks for Model-Based Control Under Partial Observation , 2018, 2019 International Conference on Robotics and Automation (ICRA).

[20]  Chen Sun,et al.  Stochastic Prediction of Multi-Agent Interactions from Partial Observations , 2019, ICLR.

[21]  Razvan Pascanu,et al.  Relational inductive biases, deep learning, and graph networks , 2018, ArXiv.

[22]  Raia Hadsell,et al.  Graph networks as learnable physics engines for inference and control , 2018, ICML.

[23]  Frédo Durand,et al.  DiffTaichi: Differentiable Programming for Physical Simulation , 2020, ICLR.

[24]  Ah Chung Tsoi,et al.  The Graph Neural Network Model , 2009, IEEE Transactions on Neural Networks.

[25]  Nils Thürey,et al.  Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow , 2018, Comput. Graph. Forum.

[26]  Tao Wang,et al.  Scale MLPerf-0.6 models on Google TPU-v3 Pods , 2019, ArXiv.

[27]  Wei Chen,et al.  Learning to predict the cosmological structure formation , 2018, Proceedings of the National Academy of Sciences.

[28]  Alessandro Rozza,et al.  Dynamic Graph Convolutional Networks , 2017, Pattern Recognit..

[29]  J. Monaghan Smoothed particle hydrodynamics , 2005 .

[30]  Hongyuan Zha,et al.  DyRep: Learning Representations over Dynamic Graphs , 2019, ICLR.

[31]  C. Villani Topics in Optimal Transportation , 2003 .

[32]  Vladlen Koltun,et al.  Learning to Control PDEs with Differentiable Physics , 2020, ICLR.

[33]  D. Sulsky Erratum: Application of a particle-in-cell method to solid mechanics , 1995 .

[34]  Raia Hadsell,et al.  Neural Execution of Graph Algorithms , 2020, ICLR.

[35]  Andre Pradhana,et al.  A moving least squares material point method with displacement discontinuity and two-way rigid body coupling , 2018, ACM Trans. Graph..

[36]  Tae-Yong Kim,et al.  Unified particle physics for real-time applications , 2014, ACM Trans. Graph..

[37]  Marco Cuturi Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances , 2013, 1306.0895.

[38]  Matthias Müller,et al.  Position based dynamics , 2007, J. Vis. Commun. Image Represent..

[39]  Razvan Pascanu,et al.  Interaction Networks for Learning about Objects, Relations and Physics , 2016, NIPS.

[40]  Jan Bender,et al.  Divergence-free smoothed particle hydrodynamics , 2015, Symposium on Computer Animation.