Evolving symbolic density functionals
This work addresses the problem of creating interpretable and efficient density functionals for computational chemistry, representing a novel direction rather than an incremental improvement.
The researchers tackled the challenge of developing accurate density functionals by proposing SyFES, a framework that automatically constructs symbolic functionals, which are more explainable and efficient than machine learning alternatives. They demonstrated that SyFES reconstructed a known functional from scratch and evolved a new functional, GAS22, that outperforms an existing one for most molecular types in the MGCDB84 test set.
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 $ω$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.