Scholarlink

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.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 会议论文

  • 发表日期：

    2025年

查看全文
  • Michail Koumpanakis,
  • Ricardo Vilalta

摘要

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.