论文标题
符号物理学习者：通过蒙特卡洛树搜索发现管理方程
Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search
论文作者
论文摘要
非线性动力学本质上是普遍存在的，在各种科学和工程学科中通常都可以看到。从有限数据中控制非线性动力学的分析表达仍然至关重要，但具有挑战性。为了解决这个基本问题，我们提出了一种新颖的符号物理学习者（SPL）机器，以发现非线性动力学的数学结构。关键概念是通过计算规则和符号来解释数学操作和系统状态变量，通过表达式树建立数学公式的象征性推理，并采用蒙特卡洛树搜索（MCT）代理来探索基于测量数据的最佳表达树。 MCTS代理通过表达树的遍历获得了乐观的选择策略，其特征是映射到基础物理学的算术表达式。拟议框架的显着特征包括搜索灵活性和对发现方程式的简约执行。与最先进的基准相比，数值示例证明了SPL机的功效和优势。
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.
