Identifying Invariant Physical Dynamics Across Multiple Environments

Abstract: Data-driven machine learning methods have been widely employed in dynamical systems, but they fail to generalize to unseen dynamical environments where data is sparse and noisy. While few recent works have proposed to address this problem by introducing domain adaptation techniques based on deep neural networks (DNNs), these black-box methods fail to explain and understand the underlying system behaviors. In this work, we propose an Invariant PhysicAl Dynamics identification framework (IPAD), designed to extract common physical laws from data collected from multiple environments. Specifically, IPAD combines Monte Carlo Tree Search (MCTS) and multi-environment reward to effectively uncover physical dynamics from imbalanced data across multiple environments. Moreover, it incorporates a variational formulation (VF) loss function to enhance the robustness in noisy conditions and then introduces a post-hoc purification approach to further refine discovered equations. We also theoretically prove the convergence rate of VF for symbolic regression. The evaluation results demonstrate that IPAD significantly outperforms existing methods in discovering invariant physical dynamics across both simulated and real-world datasets. The source code will be publicly available upon publication.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Niki_Kilbertus1

Submission Number: 7195