Eigenvalue Problem

The eigenvalue problem, central to numerous scientific and engineering disciplines, seeks to find the eigenvalues and corresponding eigenfunctions of an operator. Current research focuses on developing efficient and robust numerical methods for solving these problems, employing techniques such as physics-informed neural networks, low-rank tensor models, and neural networks inspired by classical iterative algorithms like the power method. These advancements are improving the accuracy and applicability of eigenvalue problem solutions across diverse fields, including quantum mechanics, nuclear reactor physics, and machine learning, where they enable the analysis of complex systems and the development of novel algorithms.