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pith:WKMJUTOS

pith:2019:WKMJUTOSTJZWJ2PMCT2J4DBGJ2

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DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

George Em Karniadakis, Lu Lu, Pengzhan Jin

DeepONets learn nonlinear operators from small datasets by splitting input encoding from output evaluation points.

arxiv:1910.03193 v3 · 2019-10-08 · cs.LG · stat.ML

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Claims

C1strongest claim

We propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset... we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.

C2weakest assumption

The universal approximation theorem guarantees only a small approximation error for a sufficiently large network, and does not consider the important optimization and generalization errors; the paper assumes these practical errors remain controllable with the branch-trunk split and standard training.

C3one line summary

DeepONet learns nonlinear operators for differential equations via branch and trunk sub-networks, achieving high-order error convergence on small datasets.

References

34 extracted · 34 resolved · 3 Pith anchors

[1] L. Bottou and O. Bousquet. The tradeoﬀs of large scale learning. InAdvances in Neural Information Processing Systems, pages 161–168, 2008 2008

[2] S. L. Brunton, J. L. Proctor, and J. N. Kutz. Discovering governing equations from data by sparse identiﬁcation of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15) 2016

[3] T. Chen and H. Chen. Approximations of continuous functionals by neural networks with application to dynamic systems.IEEE Transactions on Neural Networks, 4(6):910–918, 1993 1993

[4] Approximationcapabilitytofunctionsofseveralvariables,nonlinearfunctionals, and operators by radial basis function neural networks 1995

[5] T.ChenandH.Chen. Universalapproximationtononlinearoperatorsbyneuralnetworkswitharbitrary activation functions and its application to dynamical systems.IEEE Transactions on Neural Networks, 6(4):911–91 1995

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Cited by

43 papers in Pith

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First computed	2026-05-17T23:38:53.698823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2989a4dd29a7364e9ec14f49e0c264eb600310b9aad4ca462a18b6319f55ec7

Aliases

arxiv: 1910.03193 · arxiv_version: 1910.03193v3 · doi: 10.48550/arxiv.1910.03193 · pith_short_12: WKMJUTOSTJZW · pith_short_16: WKMJUTOSTJZWJ2PM · pith_short_8: WKMJUTOS

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Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2019-10-08T03:21:14Z",
    "title_canon_sha256": "19440d79637affb4adfee66015557e726c4b03aea5f8ad978d4eb496c4f622fe"
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