An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation

Key points

• 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.1
• 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.1
• The approach naturally extends to coupled multiphysics systems.1
• 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.1

Sources (1)

• [1]An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 02:07 PM

  PDE solution discovery aims to identify explicit symbolic expressions for unknown physical fields from observations under known physical constraints.

  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.

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