Physics-constrained Graph Symbolic Regression

Ziyu Xiang, Kenna Ashen, Xiaofeng Qian, Xiaoning Qian

Keywords: Symbolic Regression, Physics-constrained, Graph Neural Network, Reinforcement Learning, Monte-Carlo Tree Search, Expression Tree, Automated Feature Engineering, Symbolic Graph

TL;DR: Physics-constrained symbolic regression, Monte-Carlo tree search with symmetric invariant representations and graph neural networks.

Abstract:

As data-driven scientific discovery increasingly demands explainable over ‘black-box’ machine learning (ML) methods, Symbolic Regression (SR) that derives analytical expressions can help identify key functional dependencies in complex systems. However, traditional SR methods often suffer from (a) inefficient exploration due to their inability to compress the search space of equivalent expressions, and (b) non-physical solutions that violate fundamental physics constraints. We here introduce a symmetric invariant representation of candidate analytical expressions using a Symbolic Graph (SG), on which the Symbolic Graph Neural Network (SGNN) encodes operators, symmetries, constraints and constant fitting knowledge. We further develop reinforcement learning (RL) algorithms with Monte-Carlo Tree Search (MCTS) on our SGNN for SR. Such a physics-constrained graph symbolic regression (PCGSR) method effectively compresses the search space for efficient SR. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of our PCGSR in discovering underlying expressions and adhering to physical laws, yielding physically meaningful solutions.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 7682