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Variable-Input Deep Operator Networks

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arxiv 2205.11404 v1 pith:7AXBBUEU submitted 2022-05-23 cs.LG cs.NAmath.NAstat.ML

Michael Prasthofer , Tim De Ryck , Siddhartha Mishra This is my paper
classification cs.LGcs.NAmath.NAstat.ML
keywords operatorvidonlearninglocationsoperatorsacrossdeepnumber
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Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their applicability. We address this issue by proposing a novel operator learning framework, termed Variable-Input Deep Operator Network (VIDON), which allows for random sensors whose number and locations can vary across samples. VIDON is invariant to permutations of sensor locations and is proved to be universal in approximating a class of continuous operators. We also prove that VIDON can efficiently approximate operators arising in PDEs. Numerical experiments with a diverse set of PDEs are presented to illustrate the robust performance of VIDON in learning operators.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Time Resolution Independent Operator Learning

    cs.CE 2025-07 conditional novelty 6.0 of 10

    A DeepONet with a neural controlled differential equation branch and a trunk that takes space and time as inputs predicts transient mechanical fields from load histories at arbitrary spatiotemporal query points.

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    cs.LG 2025-08 conditional novelty 5.0 of 10

    DETNO couples a transformer neural operator with a diffusion refiner, achieving lower rollout error and better high-frequency fidelity on synthetic LWR traffic forecasts than ONTraffic and GNOT.

  3. DPNO: A Dual Path Architecture For Neural Operator

    math.NA 2025-07 conditional novelty 4.0 of 10

    Applying a ResNet-like plus DenseNet-like dual path to DeepONet and FNO reduces relative L2 error on Burgers, Darcy flow, and 2D Navier-Stokes benchmarks compared with the original single-path models.

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