mlsanityData to 7 Oct 2026

What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

arXiv 2411.18459 ↗First posted 27 Nov 2024cs.LG cs.NA math.NAcited by 3

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Abstract (arXiv)

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 20 of its 35 references that are in the map. First posted on arXiv 27 Nov 2024.

Builds on

20 of 35 references.

References · 20

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2014How transferable are features in deep neural networks?cited by 1,216
  5. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 784
  6. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 572
  7. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  8. 2017Supervised Learning of Universal Sentence Representations from Natural Language Inference Datacited by 428
  9. 2016Deep Convolutional Neural Networks for Computer-Aided Detection: CNN Architectures, Dataset Characteristics and Transfer Learningcited by 209
  10. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  11. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  12. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
8 more
  1. 2020Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networkscited by 76
  2. 2022A Review of Deep Transfer Learning and Recent Advancementscited by 56
  3. 2022Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equationscited by 28
  4. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  5. 2024Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solvingcited by 17
  6. 2023A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel constructioncited by 12
  7. 2024DeepONet as a Multi-Operator Extrapolation Model: Distributed Pretraining with Physics-Informed Fine-Tuningcited by 11
  8. 2023Efficient kernel surrogates for neural network-based regressioncited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2025Operator Learning for Consolidation: An Architectural Comparison for DeepONet Variantscited by 0
  2. 2026The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositionscited by 0
  3. 2026Improving the accuracy of physics-informed neural networks via last-layer retrainingcited by 0