mlsanityData to 7 Oct 2026

SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition

arXiv 2211.08760 ↗First posted 16 Nov 2022cs.LG cs.NA math.NAcited by 13

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Abstract (arXiv)

Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However, the most disadvantage of PINNs is that one neural network corresponds to one PDE. In practice, we usually need to solve a class of PDEs, not just one. With the explosive growth of deep learning, many useful techniques in general deep learning tasks are also suitable for PINNs. Transfer learning methods may reduce the cost for PINNs in solving a class of PDEs. In this paper, we proposed a transfer learning method of PINNs via keeping singular vectors and optimizing singular values (namely SVD-PINNs). Numerical experiments on high dimensional PDEs (10-d linear parabolic equations and 10-d Allen-Cahn equations) show that SVD-PINNs work for solving a class of PDEs with different but close right-hand-side functions.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 12 of its 28 references that are in the map. First posted on arXiv 16 Nov 2022.

Builds on

12 of 28 references.

References · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2014How transferable are features in deep neural networks?cited by 1,216
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  6. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 144
  7. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  8. 2020Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learningcited by 77
  9. 2014Grammar as a Foreign Languagecited by 70
  10. 2019Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networkscited by 63
  11. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  12. 2021Can Transfer Neuroevolution Tractably Solve Your Differential Equations?cited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 2; 2025: 6; 2026: 1.

13 papers.

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  1. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  2. 2023Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networkscited by 42
  3. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
  4. 2024PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Lawscited by 30
  5. 2023Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domainscited by 14
  6. 2025Transfer Learning in Physics-Informed Neural Networks: Full Fine-Tuning, Lightweight Fine-Tuning, and Low-Rank Adaptationcited by 14
  7. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  8. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  9. 2023Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Times Using Physics-Informed Neural Networkscited by 1
  10. 2025Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulencecited by 1
  11. 2025Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networkscited by 0
  12. 2025IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimationcited by 0
1 more
  1. 2026Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solverscited by 0