AI RESEARCH
Universal Approximation of Nonlinear Operators and Their Derivatives
arXiv CS.AI
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ArXi:2605.15285v1 Announce Type: cross Derivative-Informed Operator Learning (DIOL), i.e. learning a (nonlinear) operator and its derivatives, is an open research frontier at the foundations of the influential field of Operator Learning (OL). In particular, Universal Approximation Theorems (UATs) of nonlinear operators and their derivatives are foundational open questions and delicate problems in nonlinear functional analysis.