用元学习优化物理神经网络的损失函数，提升微分方程求解效率。

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

• 通过广义加性模型元学习参数化偏微分方程的损失函数
• 在Burgers和二维热方程上实现更快收敛与更优性能
• 适合研究物理信息神经网络与自动损失设计的学者

本文提出一种新方法，利用广义加性模型（Generalized Additive Models）进行元学习，以构建物理信息神经网络（Physics-Informed Neural Networks）的损失函数。该方法应用于参数化偏微分方程（PDEs），涵盖Burgers方程和二维热方程。目标是为每个参数化PDE学习一个新型损失函数，替代传统数据损失项。所导出的损失函数可显著提升元学习器在求解各类参数化偏微分方程时的效率、性能及收敛速度。

原文摘要 · Abstract (English)

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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