Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

תקציר מקורי באנגליתarXiv:2510.25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems. Existing scientific machine learning paradigms learn evolution largely from data, impose equations as soft constraints, or hard-code physical terms into network updates; none exploits knowledge of this form. Here we introduce the hierarchical physics-embedded adaptive Fourier neural operator, encoding such knowledge as computational architecture rather than penalizing or appending it: a first level learns or embeds fundamental physical expressions as intermediate representations, and a second level learns or embeds their governing combination, with adaptive Fourier layers capturing nonlocal, high-order