תיאור כללי של אופרטורים לא-לינאריים ומשתנים דריבטיביים

תקציר מקורי באנגליתarXiv:2605.15285v4 Announce Type: replace Abstract: We show that Universal Approximation (UA) of nonlinear operators and their derivatives via Operator Learning (OL) architectures fails in ${C^k_F}$ (Fr\'echet) compact-open topologies and in Fr\'echet--Sobolev norms (i.e. under operator norms). We solve this obstruction by restoring UA in natural weaker topologies: $C^k_B$ (Bastiani) compact-open topologies and (novel) weighted Bastiani--Sobolev spaces for general finite input measures. In full Banach-space generality, these are the first complete generalizations of the corresponding influential classical results in [Hornik, 1991] to infinite-dimensional spaces and OL. Based on our UATs, we formulate Bastiani--Sobolev training in DIOL. These results launch Derivative-Informed Operator Lear