Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search
This addresses a fundamental problem in science and engineering for researchers needing analytical models from data, but it appears incremental as it builds on existing symbolic regression and search methods.
The paper tackles the challenge of discovering governing equations for nonlinear dynamics from limited data by proposing a Symbolic Physics Learner (SPL) that uses Monte Carlo tree search to explore expression trees, demonstrating efficacy and superiority over state-of-the-art baselines in numerical examples.
Nonlinear dynamics is ubiquitous in nature and commonly seen in various science and engineering disciplines. Distilling analytical expressions that govern nonlinear dynamics from limited data remains vital but challenging. To tackle this fundamental issue, we propose a novel Symbolic Physics Learner (SPL) machine to discover the mathematical structure of nonlinear dynamics. The key concept is to interpret mathematical operations and system state variables by computational rules and symbols, establish symbolic reasoning of mathematical formulas via expression trees, and employ a Monte Carlo tree search (MCTS) agent to explore optimal expression trees based on measurement data. The MCTS agent obtains an optimistic selection policy through the traversal of expression trees, featuring the one that maps to the arithmetic expression of underlying physics. Salient features of the proposed framework include search flexibility and enforcement of parsimony for discovered equations. The efficacy and superiority of the SPL machine are demonstrated by numerical examples, compared with state-of-the-art baselines.