Gold-standard solutions to the Schr\"odinger equation using deep learning: How much physics do we need?

TL;DR

This paper introduces a novel deep learning architecture that significantly improves the accuracy and efficiency of solving the Schrödinger equation, establishing new benchmarks in computational chemistry.

Contribution

It presents a new deep-learning method that reduces energy error by 40-70% and computational cost by 6 times, and investigates the impact of physical prior knowledge on accuracy.

Findings

Achieves 40-70% lower energy error

Reduces computational cost by 6x

Increasing physical prior knowledge can decrease accuracy

Abstract

Finding accurate solutions to the Schr\"odinger equation is the key unsolved challenge of computational chemistry. Given its importance for the development of new chemical compounds, decades of research have been dedicated to this problem, but due to the large dimensionality even the best available methods do not yet reach the desired accuracy. Recently the combination of deep learning with Monte Carlo methods has emerged as a promising way to obtain highly accurate energies and moderate scaling of computational cost. In this paper we significantly contribute towards this goal by introducing a novel deep-learning architecture that achieves 40-70% lower energy error at 6x lower computational cost compared to previous approaches. Using our method we establish a new benchmark by calculating the most accurate variational ground state energies ever published for a number of different atoms and molecules. We systematically break down and measure our improvements, focusing in particular on the effect of increasing physical prior knowledge. We surprisingly find that increasing the prior knowledge given to the architecture can actually decrease accuracy.