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First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces. (arXiv:2211.04607v2 [cs.LG] UPDATED)
Nov. 15, 2022, 2:13 a.m. | Marios Mattheakis, Gabriel R. Schleder, Daniel T. Larson, Efthimios Kaxiras
cs.LG updates on arXiv.org arxiv.org
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 …
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