In recent years, remarkable progress in AI and machine learning technologies has led to growing interest in applying neural networks, which have the capability to approximate complex functions, to a wide range of research fields. Among these approaches, Physics-Informed Neural Networks (PINNs), which incorporate physical laws into the loss function, have emerged as a new method for solving partial differential equations that describe various physical phenomena, including fusion plasmas. In this course, participants will explore the fundamental concepts behind numerical methods using PINNs and gain hands-on experience through selected example problems, aiming to develop an understanding of their characteristics and potential for physics applications.

Numerical solution of a boundary layer problem using Physics-Informed Neural Networks (PINNs). The figure compares results obtained from PINNs employing three types of neural network architectures: a standard multilayer perceptron (MLP), an MLP with embedded boundary conditions, and a junction-type MLP incorporating asymptotic connection theory to efficiently capture steep gradients in the boundary layer.