Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks
This work addresses the challenge of efficiently solving parametric PDEs for computational physics and engineering applications, representing an incremental improvement in meta-learning techniques for physics-informed neural networks.
The paper tackles the problem of learning parametric partial differential equations (PDEs) by proposing a method to meta-learn loss functions using Generalized Additive Models, applied to Burger's and 2D Heat Equations, resulting in improved efficiency, performance, and convergence of the meta-learner.
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.