AI RESEARCH
Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem
arXiv CS.LG
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ArXi:2603.11972v1 Announce Type: new Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$ defined on a compact set $K_1$ (typically a compact subset of a Banach space), and the operator maps $u$ to an output function $G(u)\in C(K_2)$ defined on a compact Euclidean domain $K_2\subset\mathbb{R}^d