D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory

TL;DR

This paper introduces a deep learning method for Kohn-Sham Density Functional Theory that directly minimizes energy, reducing computational complexity and improving efficiency over traditional SCF methods.

Contribution

It proposes a novel deep learning framework that reparameterizes the orthogonal constraint and reduces computational complexity from O(N^4) to O(N^3).

Findings

Reduces computational complexity from O(N^4) to O(N^3)

Demonstrates improved efficiency and stability over traditional methods

Enables exploration of more complex neural wave functions

Abstract

Kohn-Sham Density Functional Theory (KS-DFT) has been traditionally solved by the Self-Consistent Field (SCF) method. Behind the SCF loop is the physics intuition of solving a system of non-interactive single-electron wave functions under an effective potential. In this work, we propose a deep learning approach to KS-DFT. First, in contrast to the conventional SCF loop, we propose to directly minimize the total energy by reparameterizing the orthogonal constraint as a feed-forward computation. We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity from O(N^4) to O(N^3). Second, the numerical integration which involves a summation over the quadrature grids can be amortized to the optimization steps. At each step, stochastic gradient descent (SGD) is performed with a sampled minibatch of the grids. Extensive experiments are carried out to demonstrate the advantage of our approach in terms of efficiency and stability. In addition, we show that our approach enables us to explore more complex neural-based wave functions.