Schr\"{o}dingerNet: A Universal Neural Network Solver for The Schr\"{o}dinger Equation

TL;DR

Schr"{o}dingerNet introduces a neural network architecture capable of solving the full electronic-nuclear Schr"{o}dinger equation, efficiently generating potential energy surfaces and including non-Born-Oppenheimer effects in a single training process.

Contribution

It presents a novel neural network approach that models the full electronic-nuclear Schr"{o}dinger equation with symmetry considerations, surpassing Born-Oppenheimer limitations.

Findings

Accurately models potential energy surfaces across nuclear configurations.

Includes non-Born-Oppenheimer corrections in a single training.

Demonstrates high efficiency and accuracy on atomic and molecular systems.

Abstract

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, Schr\"{o}dingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wavefunction ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.