Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks

Michail Koumpanakis; Ricardo Vilalta

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arXiv · 2412.00225

Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks

Michail Koumpanakis·Ricardo Vilalta

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Abstract

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.

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BibTeX RIS

Michail Koumpanakis, Ricardo Vilalta. 2024-11-29. Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks. https://arxiv.org/abs/2412.00225

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