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Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search
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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.
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Cited by 4 Pith papers
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When is a System Discoverable from Data? Discovery Requires Chaos
Uniquely identifying an ODE from trajectory data depends on the trajectory filling enough of the state space: chaos on a high-dimensional attractor yields analytic discoverability, while first integrals preclude it.
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Governing Equation Discovery from Data Based on Differential Invariants
PDE discovery guided by symmetry can be done by building the SINDy library from the differential invariants of the PDE's symmetry group, which shrinks the search space and improves success rates.
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Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback
Reinforcement learning fine-tuning with numerical fitness rewards improves equation discovery accuracy and noise robustness of a pretrained symbolic regression transformer.
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DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience
DrSR improves LLM-based symbolic regression by adding data-aware structural insights and a reflective idea library, beating prior methods on six benchmark tasks.
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