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 PSL machine are demonstrated by numerical examples, compared with state-of-the-art baselines.
翻译:非线性动态在性质上是无处不在的,在各种科学和工程学科中常见。从有限数据中提炼非线性动态的分析表达方式仍然至关重要,但具有挑战性。为了解决这一根本问题,我们提议了一台新型的象征物理学习器(SPL)机器,以发现非线性动态的数学结构。关键概念是通过计算规则和符号解释数学操作和系统变量,通过表达树对数学公式进行象征性推理,并使用蒙特卡洛树搜索代理物,以根据测量数据探索最佳表达树。MCTS代理物通过表达树的穿行获得了乐观的选择政策,其特点是绘制基本物理的算术表达图。拟议框架的突出特征包括搜索灵活性和对所发现的方程式执行等同性。PSL机器的功效和优越性通过数字示例,与最先进的基线相比较,以数字示例为证明。