Incorporating Physics-Based Knowledge into Neural Ordinary Differential Equations for Dynamical Systems Modeling

Speaker

Cyrus Neary

Affiliation

PhD Candidate
The Olden Institute
University of Texas at Austin

Abstract

The inclusion of physics-based knowledge into neural network models of dynamical systems can greatly improve data efficiency and generalization. It also enables the development of compositional approaches to learning. Such a priori knowledge might arise from physical principles (e.g., conservation laws) or the system's design (e.g., the Jacobian matrix of a robot), even if large portions of the system dynamics remain unknown. We develop a framework to learn dynamics models from trajectory data while incorporating such a priori system knowledge as inductive bias. We experimentally demonstrate the benefits of the proposed approach on a suite of simulated robotics systems: it learns to predict the system dynamics an order of magnitude more accurately than a baseline approach, while also learning to enforce physics-based constraints. Beyond improving data efficiency, we additionally use this framework to define a compositional approach to learning. Neural network submodels are trained on data generated by relatively simple subsystems, and the dynamics of more complex composite systems are then predicted without requiring additional data generated by the composite systems themselves. We demonstrate these novel compositional learning capabilities through experiments involving interacting mass-spring-damper systems.

Bio

Cyrus Neary is a Ph.D. student within The Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin, where he is a member of the Center for Autonomy. Prior to his graduate studies, he obtained a Bachelor of Applied Science degree in Engineering Physics from The University of British Columbia. His research interests include reinforcement learning, data-driven modeling, control, and multiagent systems. His recent work has studied how prior knowledge can be incorporated into deep learning and reinforcement learning algorithms in order to improve their data efficiency and their generalizability, as well as to yield policies with verifiable properties.