mlsanityData to 14 Oct 2026

Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptation

arXiv 2502.00782 ↗First posted 2 Feb 2025cs.LGcited by 15

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Abstract (arXiv)

AI for PDEs has garnered significant attention, particularly Physics-Informed Neural Networks (PINNs). However, PINNs are typically limited to solving specific problems, and any changes in problem conditions necessitate retraining. Therefore, we explore the generalization capability of transfer learning in the strong and energy form of PINNs across different boundary conditions, materials, and geometries. The transfer learning methods we employ include full finetuning, lightweight finetuning, and Low-Rank Adaptation (LoRA). The results demonstrate that full finetuning and LoRA can significantly improve convergence speed while providing a slight enhancement in accuracy.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 25 of its 45 references that are in the map. First posted on arXiv 2 Feb 2025.

Builds on

25 of 45 references.

References · 25

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2013Visualizing and Understanding Convolutional Networkscited by 2,290
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2019A Comprehensive Survey on Transfer Learningcited by 1,160
  5. 2021Towards a Unified View of Parameter-Efficient Transfer Learningcited by 872
  6. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  7. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  8. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  9. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
  10. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
  11. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  12. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
13 more
  1. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 101
  2. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
  3. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 67
  4. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  5. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 46
  6. 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 44
  7. 2022SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decompositioncited by 13
  8. 2020Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysiscited by 11
  9. 2021CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometriescited by 10
  10. 2024Artificial intelligence for partial differential equations in computational mechanics: A reviewcited by 9
  11. 2023DCEM: A deep complementary energy method for solid mechanicscited by 5
  12. 2023HyperLoRA for PDEscited by 4
  13. 2024Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beamscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 9.

15 papers.

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  1. 2025F-Adapter: Frequency-Adaptive Parameter-Efficient Fine-Tuning in Scientific Machine Learningcited by 3
  2. 2025Convolutional-neural-operator-based transfer learning for solving PDEscited by 2
  3. 2026Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learningcited by 1
  4. 2025Automatic Rank Determination for Low-Rank Adaptation via Submodular Function Maximizationcited by 0
  5. 2025IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimationcited by 0
  6. 2025Uncertainty-Guided Selective Adaptation Enables Cross-Platform Predictive Fluorescence Microscopycited by 0
  7. 2025PGOT: A Physics-Geometry Operator Transformer for Complex PDEscited by 0
  8. 2026Bayesian quantum sensing using graybox machine learningcited by 0
  9. 2026Estimating Dense-Packed Zone Height in Liquid-Liquid Separation: A Physics-Informed Neural Network Approachcited by 0
  10. 2026ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equationscited by 0
  11. 2026Replay-Based Continual Learning for Physics-Informed Neural Operatorscited by 0
  12. 2026Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networkscited by 0
3 more
  1. 2026Architecture Shapes Transfer Specificity in Implicit Neural Representationscited by 0
  2. 2026Adaptive Inference Batching using Policy Gradientscited by 0
  3. 2026A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equationcited by 0