slinky-is-sliding

This repository contains the code for the paper:

• Rapidly encoding generalizable dynamics in a Euclidean symmetric neural network: a Slinky case study

In this work, we propose a physics-informed deep learning approach to build reduced-order models of physical systems. We use Slinky as a demonstration. The approach introduces a Euclidena symmetric neural network architecture (ESNN), trained under the neural ordinary differential equation framework. The ESNN implements a physics-guided architecture that simultaneously preserves energy invariance and force equivariance on Euclidean transformations of the input, including translation, rotation, and reflection. We demonstrate that the ESNN approach is able to accelerate simulation by roughly 60 times compared to traditional numerical methods and achieve a superior generalization performance, i.e., the neural network, trained on a single demonstration case, predicts accurately on unseen cases with different Slinky configurations and boundary conditions.

Requirements

To run the code, you must install the following dependencies first:

• PyTorch (1.8.1)
• torchdiffeq

Files

• main.py trains the Euclidean symmetric neural network
• slinky/neuralnets.py contains the DenseNet-like structure
• slinky/transformation.py contains the rigid body motion removal module and chirality module
• slinky/func.py contains ODEFunc for generating equivariant surrogate forces using Euclidean symmetric neural networks and ODEPhys for generating derivatives used by ODE solvers
• slinky/misc.py contains utility functions
• PlotHist.m is the MATLAB code for visualizing training loss history
• VisualizeData_Slinky.m is the MATLAB code for visualizing training results (Slinky motion)

Citation

If you use this code for part of your project or paper, or get inspired by the associated paper, please cite:

@misc{Li2022Rapidly,
    doi = {10.48550/ARXIV.2203.11546},
    url = {https://arxiv.org/abs/2203.11546},
    author = {Li, Qiaofeng and Wang, Tianyi and Roychowdhury, Vwani and Jawed, M. Khalid},
    keywords = {Computational Physics (physics.comp-ph), FOS: Physical sciences, FOS: Physical sciences},
    title = {Rapidly encoding generalizable dynamics in a Euclidean symmetric neural network: a Slinky case study},
    publisher = {arXiv},
    year = {2022},
    copyright = {Creative Commons Attribution Non Commercial Share Alike 4.0 International}
}