mlsanityData to 7 Oct 2026

Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning

arXiv 2401.02810 ↗First posted 5 Jan 2024cs.LG cs.AI cs.NAcited by 9

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Abstract (arXiv)

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems. Through two case studies, we discovered that transfer learning can effectively train PINN to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We elaborately described our training strategy, including optimizer selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 22 of its 56 references that are in the map. First posted on arXiv 5 Jan 2024.

Builds on

22 of 56 references.

References · 22

  1. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  2. 2018On the Spectral Bias of Neural Networkscited by 1,321
  3. 2015Automatic differentiation in machine learning: a surveycited by 846
  4. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  5. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  6. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  7. 2020What is being transferred in transfer learning?cited by 365
  8. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  9. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  10. 2017Convolutional Neural Networks for Medical Image Analysis: Full Training or Fine Tuning?cited by 220
  11. 2020On the Theory of Transfer Learning: The Importance of Task Diversitycited by 186
  12. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
10 more
  1. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
  2. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  3. 2020Physics informed deep learning for computational elastodynamics without labeled datacited by 79
  4. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  5. 2021The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?cited by 61
  6. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 44
  7. 2021Adversarial Training Helps Transfer Learning via Better Representationscited by 36
  8. 2021On Learning Domain-Invariant Representations for Transfer Learning with Multiple Sourcescited by 15
  9. 2023Transfer Learning Enhanced Full Waveform Inversioncited by 4
  10. 2023Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controlscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 5; 2026: 4.

9 papers.

  1. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  2. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  3. 2025Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Featurescited by 2
  4. 2025Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functionscited by 0
  5. 2025xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learningcited by 0
  6. 2026NewPINNs: Physics-Informing Neural Networks Using Conventional Solvers for Partial Differential Equationscited by 0
  7. 2026Estimating Dense-Packed Zone Height in Liquid-Liquid Separation: A Physics-Informed Neural Network Approachcited by 0
  8. 2026Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEscited by 0
  9. 2026When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Studycited by 0