mlsanityData to 7 Oct 2026

GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs

arXiv 2303.14878 ↗First posted 27 Mar 2023math.NA cs.LG cs.NAcited by 20

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Abstract (arXiv)

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of modern heterogeneous hardware. However, its training is still time-consuming, especially in the multi-query and real-time simulation settings, and its parameterization often overly excessive. In this paper, we propose the Generative Pre-Trained PINN (GPT-PINN) to mitigate both challenges in the setting of parametric PDEs. GPT-PINN represents a brand-new meta-learning paradigm for parametric systems. As a network of networks, its outer-/meta-network is hyper-reduced with only one hidden layer having significantly reduced number of neurons. Moreover, its activation function at each hidden neuron is a (full) PINN pre-trained at a judiciously selected system configuration. The meta-network adaptively ``learns'' the parametric dependence of the system and ``grows'' this hidden layer one neuron at a time. In the end, by encompassing a very small number of networks trained at this set of adaptively-selected parameter values, the meta-network is capable of generating surrogate solutions for the parametric system across the entire parameter domain accurately and efficiently.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 18 of its 51 references that are in the map. First posted on arXiv 27 Mar 2023.

Builds on

18 of 51 references.

References · 18

  1. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2015Automatic differentiation in machine learning: a surveycited by 846
  4. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  5. 2016Error bounds for approximations with deep ReLU networkscited by 567
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  7. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  8. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  9. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  10. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
  11. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  12. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
6 more
  1. 2021Meta-learning PINN loss functionscited by 51
  2. 2018Solving for high dimensional committor functions using artificial neural networkscited by 34
  3. 2018Transferring Knowledge across Learning Processescited by 22
  4. 2022Meta-PDE: Learning to Solve PDEs Quickly Without a Meshcited by 18
  5. 2023MetaNO: How to Transfer Your Knowledge on Learning Hidden Physicscited by 10
  6. 2019On the approximation of rough functions with deep neural networkscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 7; 2025: 7; 2026: 3.

20 papers.

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  1. 2024Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flowscited by 10
  2. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  3. 2023AcademicGPT: Empowering Academic Researchcited by 6
  4. 2023LatentPINNs: Generative physics-informed neural networks via a latent representation learningcited by 5
  5. 2023Evolutionary Optimization of Physics-Informed Neural Networks: Advancing Generalizability by the Baldwin Effectcited by 5
  6. 2024TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNscited by 5
  7. 2025Adaptive Physics-informed Neural Networks: A Surveycited by 5
  8. 2024Resolution invariant deep operator network for PDEs with complex geometriescited by 4
  9. 2024Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networkscited by 2
  10. 2025GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equationscited by 2
  11. 2025S2GPT-PINNs: Sparse and Small models for PDEscited by 2
  12. 2025ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariancecited by 2
8 more
  1. 2025BO-SA-PINNs: Self-adaptive physics-informed neural networks based on Bayesian optimization for automatically designing PDE solverscited by 1
  2. 2026Position: Certifiable State Integrity Should Be Built from Local Validity, Not Global Scalecited by 1
  3. 2024Fiber Transmission Model with Parameterized Inputs based on GPT-PINN Neural Networkcited by 0
  4. 2024Principle Driven Parameterized Fiber Model based on GPT-PINN Neural Networkcited by 0
  5. 2024Enhanced physics-informed neural networks (PINNs) for high-order power grid dynamicscited by 0
  6. 2025IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimationcited by 0
  7. 2026Architecture Shapes Transfer Specificity in Implicit Neural Representationscited by 0
  8. 2026Does Text Steer Neural PDE Surrogates? A Controlled Diagnostic with OperatorCLIPcited by 0