Learning to simulate complex physics
with graph networks
Alvaro Sanchez-Gonzalez*, Jonathan Godwin*, Tobias Pfaff*, Rex Ying*,
Jure Leskovec, Peter Battaglia
Paper pre-print: arxiv.org/abs/2002.09405
![](https://www.google.com/images/icons/product/drive-32.png)
All experiments
![](https://www.google.com/images/icons/product/drive-32.png)
Water-3D
14k particles
800 steps
ground truth simulator: SPH
![](https://www.google.com/images/icons/product/drive-32.png)
Sand-3D
19k particles
400 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
Goop-3D
15k particles
300 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
Water-3D-S
6k particles
800 steps
ground truth simulator: SPH
![](https://www.google.com/images/icons/product/drive-32.png)
Water
2k particles
1000 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
Sand
2k particles
320 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
Goop
2k particles
400 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
WaterDrop
2k particles
1000 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
WaterDrop-XL
8k particles
1000 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
RandomFloor
3.5k particles
600 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
SandRamps
3.5k particles
400 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
WaterRamps
2.5k particles
600 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
FluidShake
1.4k particles
2000 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
BoxBath
1k particles
150 steps
ground truth simulator: PBD
![](https://www.google.com/images/icons/product/drive-32.png)
MultiMaterial
2k particles
1000 steps
ground truth simulator: MPM
![](https://www.google.com/images/icons/product/drive-32.png)
Continuous
5k particles
400 steps
ground truth simulator: MPM
trained on: friction angle range [0, 30], [55-80]
inference: friction angle range [0, 90]
Generalization Experiments
![](https://www.google.com/images/icons/product/drive-32.png)
WaterVortex
Generalization Experiment
trained on WaterRamps (2.5k particles, 600 steps)
inference: 2x2 domain, 28k particles, 2500 steps
![](https://www.google.com/images/icons/product/drive-32.png)
Ramps-Small
Generalization Experiment
trained on WaterRamps (2.5k particles, 600 steps)
inference: 2x2 domain, 5k particles, 2000 steps
![](https://www.google.com/images/icons/product/drive-32.png)
Ramps-Large
Generalization Experiment
trained on WaterRamps (2.5k particles, 600 steps)
inference: 8x4 domain, 85k particles, 5000 steps
![](https://www.google.com/images/icons/product/drive-32.png)
Hourglass
Generalization Experiment
trained on SandRamps (3.5k particles, 400 steps)
inference: 1x2 domain, 3.5k particles, 2000 steps
![](https://www.google.com/images/icons/product/drive-32.png)
MultiHippo
Generalization Experiment
trained on MultiMaterial (2k particles, 1000 steps)
inference: 1x1 domain, 4.5k particles, 2000 steps
Comparisons & Analysis
![](https://www.google.com/images/icons/product/drive-32.png)
Baseline Comparison: DPI
BoxBath domain
While DPI uses hard-coded constraints to keep the box shape consistent, our model achieves this without any special treatment of the solid particles.
![](https://www.google.com/images/icons/product/drive-32.png)
Baseline Comparison: CConv
Comparison in the following domains:
Water-3D-S (SPH)
BoxBath (PBD)
Sand, Water, Goop, MultiMaterial (MPM)
![](https://www.google.com/images/icons/product/drive-32.png)
Examples of failure cases
Above videos are indicative for our model's average performance. However, in our comprehensive experiments we have also found some interesting examples of failure cases:
Over very long rollouts, solids may become deformed
Some model seeds learn to predict large pieces of goop sticking to the wall instead of sliding down
See supplementary material for additional discussion.