Incorporating Symmetry into Deep Dynamics Models for Improved Generalization

2020/02/08 by Rui Wang, Wang, Rui, Robin Walters +3 · 11 citations
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2002.03061

openalex publication_date 2020/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to the real world. We propose to improve accuracy and generalization by incorporating symmetries into convolutional neural networks. Specifically, we employ a variety of methods each tailored to enforce a different symmetry. Our models are both theoretically and experimentally robust to distributional shift by symmetry group transformations and enjoy favorable sample complexity. We demonstrate the advantage of our approach on a variety of physical dynamics including Rayleigh Bénard convection and real-world ocean currents and temperatures. Compared with image or text applications, our work is a significant step towards applying equivariant neural networks to high-dimensional systems with complex dynamics. We open-source our simulation, data, and code at \urlhttps://github.com/Rose-STL-Lab/Equivariant-Net.

Citations

• The Mathematics of Infectious Diseases
• Exploiting Cyclic Symmetry in Convolutional Neural Networks
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Deep learning for turbulent channel flow
• Compressed Convolutional LSTM: An Efficient Deep Learning framework to\n Model High Fidelity 3D Turbulence
• Deep Residual Learning for Image Recognition
• General E(2)-Equivariant Steerable CNNs
• Generalizing Convolutional Neural Networks for Equivariance to Lie\n Groups on Arbitrary Continuous Data

Cited by

• Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
• Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry
• Can Data-Driven Dynamics Reveal Hidden Physics? There Is A Need for Interpretable Neural Operators
• Symmetry and Generalisation in Neural Approximations of Renormalisation Transformations
• A Framework for Hybrid Physics-AI Coupled Ocean Models
• Conditional Clifford-Steerable CNNs with Complete Kernel Basis for PDE Modeling
• Explicit Discovery of Nonlinear Symmetries from Dynamic Data
• Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning
• Rotational equivariant graph neural networks via local eigenbasis transformations
• Physics-informed machine learning: case studies for weather and climate modelling
• Diffeomorphic Neural Operator Learning

Related

• Approximately Equivariant Networks for Imperfectly Symmetric Dynamics
• Learning Layer-wise Equivariances Automatically using Gradients
• Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning\n Dynamics
• Importance of equivariant and invariant symmetries for fluid flow modeling
• Implicit Augmentation from Distributional Symmetry in Turbulence Super-Resolution