First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces
Abstract
Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We apply our method to solve the hydrogen molecular ion. This is an ab-initio deep learning method that solves the Schrodinger equation with the Coulomb potential yielding realistic wavefunctions that include a cusp at the ion positions. The neural solutions are continuous and differentiable functions of the interatomic distance and their derivatives are analytically calculated by applying automatic differentiation. Such a parametric and analytical form of the solutions is useful for further calculations such as the determination of force fields.
Cite
@article{arxiv.2211.04607,
title = {First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces},
author = {Marios Mattheakis and Gabriel R. Schleder and Daniel T. Larson and Efthimios Kaxiras},
journal= {arXiv preprint arXiv:2211.04607},
year = {2022}
}