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 Schrödinger 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.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

“…Since this is intractable for any interesting system, we approximate the integral using random sampling, giving the technique its name. There have also been attempts to apply the "physics-informed neural networks" (PINNs) [413][414][415][416] formulation to solve the SE. The approach is similar to VQMC but has not yet been demonstrated to scale to relevant systems for making routine quantum chemistry predictions.…”