Evolving symbolic density functionals

TL;DR

This paper introduces SyFES, a framework that automatically evolves symbolic density functionals, making them more interpretable and efficient, demonstrated by reconstructing known functionals and discovering improved ones.

Contribution

SyFES is a novel evolutionary search method that constructs accurate, explainable symbolic density functionals, bridging the gap between traditional and machine learning approaches.

Findings

Successfully reconstructed a known functional from scratch.

Discovered a new functional GAS22 with improved performance.

Demonstrated the framework's effectiveness on molecular datasets.

Abstract

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite the emerging application of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain more than tens of thousands parameters, which makes a huge gap in the formulation with the conventional human-designed symbolic functionals. We propose a new framework, Symbolic Functional Evolutionary Search (SyFES), that automatically constructs accurate functionals in the symbolic form, which is more explainable to humans, cheaper to evaluate, and easier to integrate to existing density functional theory codes than other ML functionals. We first show that without prior knowledge, SyFES reconstructed a known functional from scratch. We then demonstrate that evolving from an existing functional $\omega$B97M-V, SyFES found a new functional, GAS22 (Google Accelerated Science 22), that performs better for the majority of molecular types in the test set of Main Group Chemistry Database (MGCDB84). Our framework opens a new direction in leveraging computing power for the systematic development of symbolic density functionals.