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One-Shot Transfer Learning of Physics-Informed Neural Networks

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arxiv 2110.11286 v2 pith:WY53Q5R4 submitted 2021-10-21 cs.LG physics.comp-ph

Shaan Desai , Marios Mattheakis , Hayden Joy , Pavlos Protopapas , Stephen Roberts This is my paper
classification cs.LGphysics.comp-ph
keywords differentialequationslearningsolvingtransferbenefitsequationlinear
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 6 citations worldwide. Full citation record

  1. ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance

    cs.LG 2025-09 conditional novelty 7.0 of 10

    ReBaNO combines reduced basis greedy selection with PINN activations to learn parametric PDE maps without high-fidelity training data.

  2. Physics-Informed Neural Embeddings of PDE Solution Families

    cs.LG 2026-07 conditional novelty 6.0 of 10

    A multihead PINN with orthogonalized linear heads learns low-dimensional latent embeddings of PDE solution families, with 2–4 principal components capturing 95% of latent variance for Burgers, heat, and wave equations.

  3. Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functions

    cs.LG 2025-07 conditional novelty 6.0 of 10

    Retraining only the final layer of a PINN on a few high-loss collocation points from the adjacent validation interval, plus a learnable activation function, reduces extrapolation error on Allen-Cahn, KdV, and Burgers ...

  4. IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation

    cs.LG 2025-09 conditional novelty 5.0 of 10

    A pre-trained basis network enables fast multi-query inverse parameter estimation by fitting only a linear readout online, demonstrated on harmonic oscillators, Lotka-Volterra, and quantum harmonic oscillator.

  5. Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks

    cs.LG 2025-07 conditional novelty 4.0 of 10

    A physics-informed neural network reproduces the Runge-Kutta solution of the complex 1D acoustic wave equation in ducts with temperature gradients to about 1e-5 relative error.

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