# Learning to Simulate Complex Physics with Graph Networks

ICML 2020, 2020.

关键词：

Physical Simulationtraditional simulatorcomplex dynamicsmoothed particle hydrodynamics”position-based dynamics”更多(18+)

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摘要：

Here we present a general framework for learning simulation, and provide a single model implementation that yields state-of-the-art performance across a variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simula...更多

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简介

- Realistic simulators of complex physics are invaluable to many scientific and engineering disciplines, traditional simulators can be very expensive to create and use.
- An attractive alternative to traditional simulators is to use machine learning to train simulators directly from observed data, the large state spaces and complex dynamics have been difficult for standard end-to-end learning approaches to overcome.
- The authors' framework imposes strong inductive biases, where rich physical states are represented by graphs of interacting particles, and complex dynamics are approximated by learned message-passing among nodes

重点内容

- Realistic simulators of complex physics are invaluable to many scientific and engineering disciplines, traditional simulators can be very expensive to create and use
- Our framework imposes strong inductive biases, where rich physical states are represented by graphs of interacting particles, and complex dynamics are approximated by learned message-passing among nodes
- We explored how our Graph Network-based Simulators” learns to simulate in datasets which contained three diverse, complex physical materials: water as a barely damped fluid, chaotic in nature; sand as a granular material with complex frictional behavior; and “goop” as a viscous, plastically deformable material
- Our main findings are that our Graph Network-based Simulators” model can learn accurate, high-resolution, long-term simulations of different fluids, deformables, and rigid solids, and it can generalize well beyond training to much longer, larger, and challenging settings
- General-purpose machine learning framework for learning to simulate complex systems, based on particle-based representations of physics and learned message-passing on graphs
- Our experimental results show our single Graph Network-based Simulators” architecture can learn to simulate the dynamics of fluids, rigid solids, and deformable materials, interacting with one another, using tens of thousands of particles over thousands time steps

方法

- The authors explored how the GNS learns to simulate in datasets which contained three diverse, complex physical materials: water as a barely damped fluid, chaotic in nature; sand as a granular material with complex frictional behavior; and “goop” as a viscous, plastically deformable material
- These materials have very different behavior, and in most simulators, require implementing separate material models or even entirely different simulation algorithms.
- The authors used SPlisHSPlasH (Bender & Koschier, 2015), a SPH-based fluid simulator with strict volume preservation to generate this dataset

结果

- The authors' main findings are that the GNS model can learn accurate, high-resolution, long-term simulations of different fluids, deformables, and rigid solids, and it can generalize well beyond training to much longer, larger, and challenging settings.
- In Section 5.5 below, the authors compare the GNS model to two recent, related approaches, and find the approach was simpler, more generally applicable, and more accurate.
- To challenge the robustness of the architecture, the authors used a single set of model hyperparameters for training across all of the experiments.

结论

- General-purpose machine learning framework for learning to simulate complex systems, based on particle-based representations of physics and learned message-passing on graphs.
- The authors' experimental results show the single GNS architecture can learn to simulate the dynamics of fluids, rigid solids, and deformable materials, interacting with one another, using tens of thousands of particles over thousands time steps.
- There are natural ways to incorporate stronger, generic physical knowledge into the framework, such as Hamiltonian mechanics (Sanchez-Gonzalez et al, 2019) and rich, architecturally imposed symmetries.
- Differentiable simulators will be valuable for solving inverse problems, by not strictly optimizing for forward prediction, but for inverse objectives as well

总结

## Introduction:

Realistic simulators of complex physics are invaluable to many scientific and engineering disciplines, traditional simulators can be very expensive to create and use.- An attractive alternative to traditional simulators is to use machine learning to train simulators directly from observed data, the large state spaces and complex dynamics have been difficult for standard end-to-end learning approaches to overcome.
- The authors' framework imposes strong inductive biases, where rich physical states are represented by graphs of interacting particles, and complex dynamics are approximated by learned message-passing among nodes
## Methods:

The authors explored how the GNS learns to simulate in datasets which contained three diverse, complex physical materials: water as a barely damped fluid, chaotic in nature; sand as a granular material with complex frictional behavior; and “goop” as a viscous, plastically deformable material- These materials have very different behavior, and in most simulators, require implementing separate material models or even entirely different simulation algorithms.
- The authors used SPlisHSPlasH (Bender & Koschier, 2015), a SPH-based fluid simulator with strict volume preservation to generate this dataset
## Results:

The authors' main findings are that the GNS model can learn accurate, high-resolution, long-term simulations of different fluids, deformables, and rigid solids, and it can generalize well beyond training to much longer, larger, and challenging settings.- In Section 5.5 below, the authors compare the GNS model to two recent, related approaches, and find the approach was simpler, more generally applicable, and more accurate.
- To challenge the robustness of the architecture, the authors used a single set of model hyperparameters for training across all of the experiments.
## Conclusion:

General-purpose machine learning framework for learning to simulate complex systems, based on particle-based representations of physics and learned message-passing on graphs.- The authors' experimental results show the single GNS architecture can learn to simulate the dynamics of fluids, rigid solids, and deformable materials, interacting with one another, using tens of thousands of particles over thousands time steps.
- There are natural ways to incorporate stronger, generic physical knowledge into the framework, such as Hamiltonian mechanics (Sanchez-Gonzalez et al, 2019) and rich, architecturally imposed symmetries.
- Differentiable simulators will be valuable for solving inverse problems, by not strictly optimizing for forward prediction, but for inverse objectives as well

- Table1: List of maximum number of particles N , sequence length K, and quantitative model accuracy (MSE) on the held-out test set. All domain names are also hyperlinks to the video website. Note, since K varies across datasets, the errors are not directly comparable to one another

相关工作

- Our approach focuses on particle-based simulation, which is used widely across science and engineering, e.g., computational fluid dynamics, computer graphics. States are represented as a set of particles, which encode mass, material, movement, etc. within local regions of space. Dynamics are computed on the basis of particles’ interactions within their local neighborhoods. One popular particle-based method for simulating fluids is “smoothed particle hydrodynamics” (SPH) (Monaghan, 1992), which evaluates pressure and viscosity forces around each particle, and updates particles’ velocities and positions accordingly. Other techniques, such as “position-based dynamics” (PBD) (Muller et al, 2007) and “material point method” (MPM) (Sulsky et al, 1995), are more suitable for interacting, deformable materials. In PBD, incompressibility and collision dynamics involve resolving pairwise distance constraints between particles, and directly predicting their position changes. Several differentiable particle-based simulators have recently appeared, e.g., DiffTaichi (Hu et al, 2019), PhiFlow (Holl et al, 2020), and Jax-MD (Schoenholz & Cubuk, 2019), which can backpropagate gradients through the architecture.

引用论文

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