  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.
