mlsanityData to 7 Oct 2026

Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations

arXiv 2212.04663 ↗First posted 9 Dec 2022cs.LG cs.NA math.NAcited by 28

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Abstract (arXiv)

Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution equations in a finite time horizon. Nevertheless, the vanilla DeepONet suffers from the issue of stability degradation in the long-time prediction. This paper proposes a em transfer-learning aided DeepONet to enhance the stability. Our idea is to use transfer learning to sequentially update the DeepONets as the surrogates for propagators learned in different time frames. The evolving DeepONets can better track the varying complexities of the evolution equations, while only need to be updated by efficient training of a tiny fraction of the operator networks. Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of DeepONet while maintaining similar computational cost but also substantially reduces the sample size of the training set.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 10 of its 30 references that are in the map. First posted on arXiv 9 Dec 2022.

Builds on

10 of 30 references.

References · 10

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  5. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  6. 2020Model Reduction and Neural Networks for Parametric PDEscited by 257
  7. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  8. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  9. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  10. 2021SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasetscited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 8; 2024: 5; 2025: 10; 2026: 5.

28 papers.

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  1. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  2. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 98
  3. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  4. 2023CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamicscited by 40
  5. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 30
  6. 2025PDE-Transformer: Efficient and Versatile Transformers for Physics Simulationscited by 29
  7. 2025Walrus: A Cross-Domain Foundation Model for Continuum Dynamicscited by 26
  8. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  9. 2025Recurrent Neural Operators: Stable Long-Term PDE Predictioncited by 15
  10. 2025TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolationcited by 14
  11. 2025MORPH: PDE Foundation Models with Arbitrary Data Modalitycited by 12
  12. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
16 more
  1. 2025AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulationcited by 7
  2. 2023Size Lowerbounds for Deep Operator Networkscited by 6
  3. 2024A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problemscited by 6
  4. 2023Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONetscited by 3
  5. 2024What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applicationscited by 3
  6. 2025Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networkscited by 3
  7. 2026Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledgecited by 2
  8. 2024Long-time Integration of Nonlinear Wave Equations with Neural Operatorscited by 1
  9. 2024Implicit factorized transformer approach to fast prediction of turbulent channel flowscited by 1
  10. 2025Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulencecited by 1
  11. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  12. 2026Neural Operators for Multi-Task Control and Adaptationcited by 1
  13. 2026Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagatorscited by 1
  14. 2025An optimal Petrov-Galerkin framework for operator networkscited by 0
  15. 2026Convolution Operator Network for Forward and Inverse Problems (FI-Conv): Application to Plasma Turbulence Simulationscited by 0
  16. 2026Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problemscited by 0