Abstract
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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Cite this article
APA 7
Gong, Y., Wu, H., Yang, C., & Jiang, M. (2026). An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation. https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation
MLA 9
Gong, Yunpeng, et al. "An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation." https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation.
Chicago (author–date)
Gong, Yunpeng, Huolong Wu, Can Yang, and Min Jiang. 2026. "An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation." https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation.
Harvard
Gong, Y., Wu, H., Yang, C. and Jiang, M. (2026) 'An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation', Available at: https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation.
Vancouver
Gong Y, Wu H, Yang C, Jiang M. An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation. https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation
IEEE
Y. Gong, H. Wu, C. Yang, and M. Jiang, "An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation," https://omanscience.com/en/articles/an-interpretable-approach-to-pde-solution-discovery-via-structural-experience-distillation.