HER-PDE Agent Discovers Governing Laws in Heterogeneous Media

Summary

Researchers present HER-PDE, a scientific-agent framework that jointly discovers compositional PDE structures and unknown nonparametric spatial coefficient fields. Using two differently excited noisy trajectories, it generates and refines complete hypotheses, evaluates them through bidirectional cross-excitation transfer, and audits the selected law on sealed data. It recovered the generating operator in all five tested two-dimensional systems and estimated nine unknown fields with a median Pearson correlation of about 0.85 and median relative L2 error of about 0.28.