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arXiv Machine Learning By YuJie Huang, WenWu He, ZhuoEr Lin, Congcong Liu, Dong Liang, Zhuo-Xu Cui

Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields

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The paper introduces HER-PDE, a scientific-agent framework that simultaneously discovers partial differential equation (PDE) structures and their unknown spatial coefficient fields. Using two noisy trajectories from different excitations, the agent generates expression-tree hypotheses, evaluates them via a Hypothesis Evaluation Interface that only estimates declared fields, and refines candidates through bidirectional cross-excitation transfer. In controlled experiments on five two-dimensional systems with Gaussian noise, HER-PDE accurately recovers the governing operators and attains a median Pearson correlation of ~0.85 and a median relative L2 error of ~0.28 for nine unknown coefficient fields.

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