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

• URL: http://arxiv.org/abs/2412.00225v1
• Date: Fri, 29 Nov 2024 19:35:42 GMT
• Title: Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks
• Authors: Michail Koumpanakis, Ricardo Vilalta,
• Abstract summary: We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations.<n>The goal is to learn a new loss function for each parametric PDE using meta-learning.
• Score: 0.8287206589886881
• License: http://creativecommons.org/licenses/by/4.0/
• 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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