Hard Encoding of Physics for Learning Spatiotemporal Dynamics

2021/05/02 by Chengping Rao, Hao Sun, Rao, Chengping +3 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Lattice Boltzmann Simulation Studies #Machine Learning (cs.LG) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2105.00557

openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and epidemiology, remains uncertain or partially unknown, where very limited measurement data is yet available. To tackle this challenge, we propose a novel deep learning architecture that forcibly encodes known physics knowledge to facilitate learning in a data-driven manner. The coercive encoding mechanism of physics, which is fundamentally different from the penalty-based physics-informed learning, ensures the network to rigorously obey given physics. Instead of using nonlinear activation functions, we propose a novel elementwise product operation to achieve the nonlinearity of the model. Numerical experiment demonstrates that the resulting physics-encoded learning paradigm possesses remarkable robustness against data noise/scarcity and generalizability compared with some state-of-the-art models for data-driven modeling.

Citations

• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Bridging the Gaps Between Residual Learning, Recurrent Neural Networks and Visual Cortex
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Understanding and mitigating gradient pathologies in physics-informed neural networks

Cited by

• Physics-Encoded Inverse Modeling for Arctic Snow Depth Estimation
• When do World Models Successfully Learn Dynamical Systems?

Related

• Encoding physics to learn reaction-diffusion processes
• Physics-Guided Deep Learning for Dynamical Systems: A Survey
• Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning
• Deep Hidden Physics Models: Deep Learning of Nonlinear Partial\n Differential Equations
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations