Abstracts

On the development of Laplacian eigenfunctions on sub-intervals of the real line via generative AI-assisted frameworks

S Janakiraman, Centre for Development of Advanced Computing, Bangalore

Laplacian eigenfunctions on bounded sub-domains are classically computed by solving Sturm-Liouville Eigenvalue Problems (SL-EVP). However, enforcing specific boundary conditions inherently restricts the basis, leading to slow convergence and pronounced Gibbs phenomena when expanding general functions that violate those boundary conditions. This talk explores an alternative approach: utilizing Generative AI (GenAI) architectures to determine Laplacian eigenfunctions without explicitly solving the classical SL-BVP constraint framework. We present early analytical insights derived from LLM-assisted symbolic and numerical exploration, analyze the mathematical validity of the resulting functions, and discuss the structural methodology of human-AI collaboration in tackling classical spectral problems.