Solving the electronic Schr\"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks

TL;DR

This paper introduces a weight-sharing neural network approach to efficiently solve the electronic Schrödinger equation across multiple molecular geometries, significantly reducing computational costs and enabling transfer learning in quantum chemistry.

Contribution

The study proposes a novel weight-sharing constraint in neural network models to accelerate solutions for multiple molecular geometries, leveraging regularity in wavefunctions.

Findings

Accelerates neural network optimization by an order of magnitude.

Enables transfer learning for wavefunctions across different molecules.

Shows potential for high-accuracy pre-trained neural network wavefunctions.

Abstract

Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining Monte Carlo methods with unsupervised training of neural networks has recently been proposed as a promising approach to overcome the curse of dimensionality in this setting and to obtain accurate wavefunctions for individual molecules at a moderately scaling computational cost. These methods currently do not exploit the regularity exhibited by wavefunctions with respect to their molecular geometries. Inspired by recent successful applications of deep transfer learning in machine translation and computer vision tasks, we attempt to leverage this regularity by introducing a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. That is, we restrict the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude and that it opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.