mlsanityData to 14 Oct 2026

Adaptive Physics-informed Neural Networks: A Survey

arXiv 2503.18181 ↗First posted 23 Mar 2025cs.LG cs.AIcited by 5

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Abstract (arXiv)

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability. However, limitations related to convergence and the need for re-optimization with each change in PDE parameters hinder their widespread adoption across scientific and engineering applications. This survey reviews existing research that addresses these limitations through transfer learning and meta-learning. The covered methods improve the training efficiency, allowing faster adaptation to new PDEs with fewer data and computational resources. While traditional numerical methods solve systems of differential equations directly, neural networks learn solutions implicitly by adjusting their parameters. One notable advantage of neural networks is their ability to abstract away from specific problem domains, allowing them to retain, discard, or adapt learned representations to efficiently address similar problems. By exploring the application of these techniques to PINNs, this survey identifies promising directions for future research to facilitate the broader adoption of PINNs in a wide range of scientific and engineering applications.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 38 of its 65 references that are in the map. First posted on arXiv 23 Mar 2025.

Builds on

38 of 65 references.

References · 38

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019A Comprehensive Survey on Transfer Learningcited by 1,160
  4. 2018On First-Order Meta-Learning Algorithmscited by 1,018
  5. 2020Meta-Learning in Neural Networks: A Surveycited by 950
  6. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  7. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  8. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  9. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  10. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  11. 2022On Neural Differential Equationscited by 268
  12. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
26 more
  1. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  2. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  3. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  4. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  5. 2021DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equationscited by 66
  6. 2021Meta-learning PINN loss functionscited by 51
  7. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  8. 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 44
  9. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 38
  10. 2021Meta-Auto-Decoder for Solving Parametric Partial Differential Equationscited by 36
  11. 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
  12. 2022Learning differentiable solvers for systems with hard constraintscited by 34
  13. 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 32
  14. 2018Transferring Knowledge across Learning Processescited by 22
  15. 2024Active Learning for Neural PDE Solverscited by 22
  16. 2023GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEscited by 20
  17. 2024Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operatorscited by 20
  18. 2022Meta-PDE: Learning to Solve PDEs Quickly Without a Meshcited by 18
  19. 2020Accelerating Physics-Informed Neural Network Training with Prior Dictionariescited by 17
  20. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
  21. 2022SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decompositioncited by 13
  22. 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
  23. 2023XLB: A differentiable massively parallel lattice Boltzmann library in Pythoncited by 11
  24. 2024Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learningcited by 9
  25. 2023Meta-learning of Physics-informed Neural Networks for Efficiently Solving Newly Given PDEscited by 5
  26. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 4.

5 papers.

  1. 2026A Fast and Generalizable Fourier Neural Operator-Based Surrogate for Melt-Pool Prediction in Laser Processingcited by 2
  2. 2026Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappingscited by 2
  3. 2025Learning Generalizable Neural Operators for Inverse Problemscited by 0
  4. 2026RealDiffusion: Physics-informed Attention for Multi-character Storybook Generationcited by 0
  5. 2026Transferability of Learned States in Neural PDE Solverscited by 0