DeepONet revisited: single hidden layer nets can approximate any nonlinear operator
burny_tech · x · 2026-09-03
burnytech resurfaces the classic DeepONet paper (arXiv:1910.03193) by Lu Lu, Pengzhan Jin, and George Em Karniadakis. Building on a less-known universal approximation theorem — a single-hidden-layer network can accurately approximate any nonlinear continuous operator — the authors propose Deep Operator Networks with a branch net encoding input functions at sensor points and a trunk net encoding output locations.
Experiments on dynamical systems and PDEs show DeepONet significantly reduces generalization error versus fully-connected networks while learning operators from relatively small datasets. It remains a foundational piece of the neural operator line of work (FNO, PINO, etc.).
Related event: DeepONet: Single Hidden-Layer Networks Approximate Nonlinear Operators(2 posts)→
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