DeepONet paper: branch-trunk dual networks cut operator learning generalization error
burny_tech · x · 2026-09-03
burnytech shares the classic DeepONet paper (arXiv:1910.03193; Lu Lu, Pengzhan Jin, George Em Karniadakis) with the full arXiv text.
- Core theorem: beyond universal approximation of continuous functions, a single-hidden-layer network can accurately approximate any nonlinear continuous operator — the theoretical basis for learning operators from data.
- Architecture: a branch net encodes the input function at fixed sensor points, a trunk net encodes output locations; the two are combined to evaluate the operator.
- Results: systematic experiments on dynamical systems and PDEs show DeepONet significantly reduces generalization error versus fully-connected networks, learning efficiently from relatively small datasets.
- Impact: a foundational work for the neural operator line (FNO, PINO, etc.) in scientific machine learning and equation discovery.
Related event: DeepONet: Single Hidden-Layer Networks Approximate Nonlinear Operators(2 posts)→
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