Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks
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Abstract (arXiv)
This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations. The goal is to learn a new loss function for each parametric PDE using meta-learning. The derived loss function replaces the traditional data loss, allowing us to learn each parametric PDE more efficiently, improving the meta-learner's performance and convergence.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 26 references that are in the map. First posted on arXiv 29 Nov 2024.
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14 of 26 references.
References · 14
- 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
- 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
- 2018Meta-Learning for Semi-Supervised Few-Shot Classificationcited by 456
- 2018Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learningcited by 270
- 2018Meta-Learning for Low-Resource Neural Machine Translationcited by 105
- 2020GAMI-Net: An Explainable Neural Network based on Generalized Additive Models with Structured Interactionscited by 82
- 2017On Loss Functions for Deep Neural Networks in Classificationcited by 68
- 2021Meta-learning PINN loss functionscited by 51
- 2021A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEscited by 31
- 2022PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Datacited by 20
- 2023GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEscited by 20
- 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
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