mlsanityData to 7 Oct 2026

One-Shot Transfer Learning of Physics-Informed Neural Networks

arXiv 2110.11286 ↗First posted 21 Oct 2021cs.LG physics.comp-phcited by 49

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Abstract (arXiv)

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 21 Oct 2021.

Builds on

23 of 40 references.

References · 23

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019Hamiltonian Neural Networkscited by 702
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  6. 2020Lagrangian Neural Networkscited by 388
  7. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  8. 2018Training behavior of deep neural network in frequency domaincited by 174
  9. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  10. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  11. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  12. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
11 more
  1. 2020Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structurescited by 52
  2. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  3. 2019Variational Integrator Networks for Physically Structured Embeddingscited by 36
  4. 2020Hamiltonian neural networks for solving equations of motioncited by 33
  5. 2020Deep learning of free boundary and Stefan problemscited by 33
  6. 2020Solving Differential Equations Using Neural Network Solution Bundlescited by 20
  7. 2021Unsupervised Reservoir Computing for Solving Ordinary Differential Equationscited by 11
  8. 2021Learning Contact Dynamics using Physically Structured Neural Networkscited by 10
  9. 2020Variational Integrator Graph Networks for Learning Energy Conserving Dynamical Systemscited by 7
  10. 2020Transfer learning of chaotic systemscited by 5
  11. 2021Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modellingcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 8; 2023: 13; 2024: 8; 2025: 11; 2026: 9.

49 papers.

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  1. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  2. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  3. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  4. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  5. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  6. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  7. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
  8. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 30
  9. 2023L-HYDRA: Multi-Head Physics-Informed Neural Networkscited by 29
  10. 2022Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equationscited by 28
  11. 2022Physics-Informed Neural Networks for Quantum Eigenvalue Problemscited by 18
  12. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
37 more
  1. 2024Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Datacited by 14
  2. 2025Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptationcited by 14
  3. 2022SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decompositioncited by 13
  4. 2023TransNet: Transferable Neural Networks for Partial Differential Equationscited by 13
  5. 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
  6. 2024Gravitational Duals from Equations of Statecited by 10
  7. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  8. 2023Metalearning generalizable dynamics from trajectoriescited by 9
  9. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  10. 2023Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scanscited by 7
  11. 2023Dream to Adapt: Meta Reinforcement Learning by Latent Context Imagination and MDP Imaginationcited by 6
  12. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  13. 2023Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problemscited by 5
  14. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  15. 2022DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networkscited by 3
  16. 2022Real-time Health Monitoring of Heat Exchangers using Hypernetworks and PINNscited by 3
  17. 2023A Sequential Meta-Transfer (SMT) Learning to Combat Complexities of Physics-Informed Neural Networks: Application to Composites Autoclave Processingcited by 3
  18. 2023One-Shot Transfer Learning for Nonlinear ODEscited by 3
  19. 2024Solving Differential Equations with Constrained Learningcited by 3
  20. 2025Enforcing hidden physics in physics-informed neural networkscited by 3
  21. 2024A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoringcited by 2
  22. 2025ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariancecited by 2
  23. 2023Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Mediacited by 1
  24. 2025Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulencecited by 1
  25. 2025A Physics-preserved Transfer Learning Method for Differential Equationscited by 1
  26. 2026Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networkscited by 1
  27. 2026Learning Physics from an Imperfect Ancestorcited by 1
  28. 2025Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functionscited by 0
  29. 2025Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networkscited by 0
  30. 2025IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimationcited by 0
  31. 2026Learning embeddings of non-linear PDEs: the Burgers' equationcited by 0
  32. 2026Transferable Physics-Informed Representations via Closed-Form Head Adaptationcited by 0
  33. 2026Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equationscited by 0
  34. 2026RealDiffusion: Physics-informed Attention for Multi-character Storybook Generationcited by 0
  35. 2026Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networkscited by 0
  36. 2026Linearized PINN with pretrained nonlinear layerscited by 0
  37. 2026Transferability of Learned States in Neural PDE Solverscited by 0