基于蒙特卡洛树搜索的控制方程发现

来自今天的爱可可AI前沿推介

[LG] Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search

F Sun, Y Liu, J Wang, H Sun
[Northeasern University & University of Chinese Academy of Sciences & ...]

符号物理学习器：基于蒙特卡洛树搜索的控制方程发现

要点:

1. 提出 SPL 通过使用计算规则和符号解释数学运算和系统状态变量，从有限数据中发现非线性动力学的数学结构，并采用蒙特卡洛树搜索(MCTS)代理来探索基于测量数据的最佳表达树；
2. SPL机是灵活的，对发现的方程强制执行解析，并在数值实例中被证明优于最先进的基线；
3. SPL机在发现物理规律和非线性动力学方面优于最先进的符号回归方法。

一句话总结:
提出一种称为符号物理学习机(SPL)的模型，基于蒙特卡洛树形搜索，用于从有限数据中发现非线性动力学。

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.

论文链接：https://arxiv.org/abs/2205.13134