Neural Constitutive Laws

Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics

ICML 2023 / Website / arXiv

https://github.com/PingchuanMa/NCLaw/assets/16499005/e1fed91f-da58-4a79-a130-5ccd054091fa

@inproceedings{ma2023learning,
    title={Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics},
    author={Ma, Pingchuan and Chen, Peter Yichen and Deng, Bolei and Tenenbaum, Joshua B and Du, Tao and Gan, Chuang and Matusik, Wojciech},
    booktitle={International Conference on Machine Learning},
    year={2023},
    organization={PMLR}
}

Prerequisites

This codebase is tested using the environment with the following key packages:

• Ubuntu 20.04
• CUDA 11.7
• GCC 11
• Python 3.10.11
• PyTorch 2.0.1
• Warp 0.6.1

Installation

Prepare conda environment with proper Python:

conda create -n nclaw python=3.10  # create env
conda activate nclaw               # activate env

Install required packages:

conda install pytorch torchvision torchaudio pytorch-cuda=11.7 -c pytorch -c nvidia
conda install numpy scipy pyvista hydra-core trimesh einops tqdm psutil tensorboard -c defaults -c conda-forge

Compile warp and install nclaw:

bash ./build.sh

Experiments

Generate dataset:

python experiments/scripts/dataset/main.py

Train NCLaw:

python experiments/scripts/train/invariant_full_meta-invariant_full_meta.py

Evaluate NCLaw:

# Reconstruction
python experiments/scripts/eval/dataset.py --gt

# Generalization
python experiments/scripts/eval/time.py --gt  # (a) time
python experiments/scripts/eval/vel.py --gt   # (b) velocity
python experiments/scripts/eval/shape.py --gt # (c) geometry
python experiments/scripts/eval/slope.py      # (d) boundary

# Extreme
python experiments/scripts/eval/large.py   # (a) one-million
python experiments/scripts/eval/contact.py # (b) collision

# Multi-physics
python experiments/scripts/eval/pool.py    # (a) coupled-physics
python experiments/scripts/eval/melting.py # (b) phase-transition

Results

https://github.com/PingchuanMa/NCLaw/assets/16499005/4860bce0-8d20-4641-9052-ea7430361bca

https://github.com/PingchuanMa/NCLaw/assets/16499005/7ea44615-564a-4fa1-bfd8-0ce5cfdecc31

https://github.com/PingchuanMa/NCLaw/assets/16499005/e1fed91f-da58-4a79-a130-5ccd054091fa

https://github.com/PingchuanMa/NCLaw/assets/16499005/37917f41-522c-4b3b-a845-cb2055b78c92