arXiv AI
Oct 9

An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation

The paper introduces SED-MCTS, a Monte Carlo tree search method that enhances PDE solution discovery by distilling structural experience from evaluated expressions. Unlike previous approaches that rely on a single terminal score, SED-MCTS uses counterfactual subtree interventions to estimate local structural contributions, guiding the search toward reliable construction edges and preserving useful components in a structural archive. The method extends naturally to coupled multiphysics systems and demonstrates improved performance, efficiency, and robustness across diverse PDE benchmarks, especially under noisy or scarce observations.

By Yunpeng Gong, Huolong Wu, Can Yang, Min Jiang