Rapidly Encoding Generalizable Dynamics in a Euclidean Symmetric Neural Network
arXiv:2203.11546 · doi:10.1016/j.eml.2022.101925
Abstract
Slinky, a helical elastic rod, is a seemingly simple structure with unusual mechanical behavior; for example, it can walk down a flight of stairs under its own weight. Taking Slinky as a test-case, we propose a physics-informed deep learning approach for building reduced-order models of physical systems. The approach introduces a Euclidean symmetric neural network (ESNN) architecture that is trained under the neural ordinary differential equation framework to learn the 2D latent dynamics from the motion trajectory of a reduced-order representation of the 3D Slinky. The ESNN implements a physics-guided architecture that simultaneously preserves energy invariance and force equivariance under Euclidean transformations of the input, including translation, rotation, and reflection. The embedded Euclidean symmetry provides physics-guided interpretability and generalizability, while preserving the full expressive power of the neural network. We demonstrate that the ESNN approach is able to accelerate simulation by one to two orders of magnitude compared to traditional numerical methods and achieve a superior generalization performance while classic neural networks fail to learn the Slinky dynamics, i.e., the ESNN, trained on a single demonstration case, predicts the motions accurately for unseen cases of different Slinky configurations and boundary conditions. Further investigation into the ESNN reveals that it explicitly learns the nonlinear coupling between stretching and bending of the Slinky.
arXiv commentSupplementary video available at https://youtu.be/mHCFa8U9Xpw
References in corpus (22)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
- B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
- Machine learning accelerated computational fluid dynamics
- Data-driven discovery of coordinates and governing equations
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
- Learning data driven discretizations for partial differential equations
- Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
- Discovering physical concepts with neural networks
- ParticleNet: Jet Tagging via Particle Clouds
- Neural Network Based in Silico Simulation of Combustion Reactions
- Machine Learning Topological Invariants with Neural Networks
- Energy Flow Networks: Deep Sets for Particle Jets
- Physics-Informed Neural Operator for Learning Partial Differential Equations
- AI Poincaré: Machine Learning Conservation Laws from Trajectories
- Time-series learning of latent-space dynamics for reduced-order model closure
- Artificial Neural Network Approach to the Analytic Continuation Problem
- Reduced-order modeling with artificial neurons for gravitational-wave inference
- Learning hidden elasticity with deep neural networks
- Propulsion and instability of a flexible helical rod rotating in a viscous fluid
- Equilibria and Instabilities of a Slinky: Discrete Model