发表机构
School of Informatics, Xiamen University（厦门大学信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对PDE解发现方法可解释性不足的问题，提出SED-MCTS方法，通过蒸馏结构经验优化搜索，在PDE基准测试中提升了性能、效率与鲁棒性。
AI 中文摘要
PDE解发现旨在从已知物理约束下的观测数据中识别未知物理场的显式符号表达式。然而，现有方法将数据保真度与物理一致性合并为单一的最终得分，作为唯一反馈信号，几乎无法提供哪些子表达式对候选解最终性能负责的信息。这种不透明的最终反馈严重限制了搜索过程本身的可解释性，无法洞察候选解成功或失败的原因。因此，次优候选解中的可复用结构常被丢弃，而成功搜索轨迹中的偶然语法可能被反复强化。我们提出SED-MCTS，一种从已评估表达式中蒸馏结构经验并将其复用以指导后续符号解搜索的蒙特卡洛树搜索方法。通过反事实子树干预，SED-MCTS估计局部结构贡献，将可靠证据路由至负责的构建边，并在优化的结构存档中保留有用组件。该方法可自然扩展至耦合多物理场系统。在多样的PDE基准测试套件中，SED-MCTS在固定评估预算下实现了优异性能，并在观测数据存在噪声或稀缺时提升了搜索效率与鲁棒性。
英文摘要
PDE solution discovery aims to identify explicit symbolic expressions for unknown physical fields from observations under known physical constraints. Existing methods, however, collapse data fidelity and physical consistency into a single terminal score used as the sole feedback signal, providing little information about which subexpressions are responsible for a candidate's final performance. This opaque terminal feedback severely limits the interpretability of the search process itself, offering no insight into why a candidate succeeds or fails. Consequently, reusable structures in otherwise suboptimal candidates are often discarded, whereas incidental syntax along successful search trajectories may be repeatedly reinforced. We propose SED-MCTS, a Monte Carlo tree search approach that distills structural experience from evaluated expressions and reuses it to guide subsequent symbolic solution search. Through counterfactual subtree interventions, SED-MCTS estimates local structural contributions, routes reliable evidence to the responsible construction edges, and preserves useful components in a refined structural archive. The approach naturally extends to coupled multiphysics systems. Across a diverse suite of PDE benchmarks, SED-MCTS achieves strong performance under a fixed evaluation budget and improves search efficiency and robustness under noisy or scarce observations.
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