Evolving symbolic density functionals

Abstract

Systematic development of accurate density functionals has been a decades-long challenge for scientists. Despite emerging applications of machine learning (ML) in approximating functionals, the resulting ML functionals usually contain more than tens of thousands of parameters, leading to 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 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 ωB97M-V, SyFES found a new functional, GAS22 (Google Accelerated Science 22), that performs better for most of the 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.

Open-Source Machine Learning in Computational Chemistry

“…For example, ML can help to optimize or replace the DFT parameters that are embedded within the theory. With the goal of improving functions for DFT theory, several OSS tools have been developed, including PROPerty Prophet (PROPhet; written in C++), D3-GP, Deep Kohn–Sham (DeepKS), , NeuralXC, NNFunctional, , Differentiable Quantum Chemistry (DQC), JAX-DFT, Compressed scale-Invariant DEnsity Representation (Cider), Fourth-order Expansion of the X Hole, Symbolic Functional Evolutionary Search (SyFES), and CF22D (written in Fortran) . The D3-GP workflow implements Gaussian process regression and batchwise-variance-based (as opposed to sequential-variance-based) sampling to improve D3-type dispersion corrections in DFT calculations .…”

Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions

“…demonstrated for the case of a ML-DFT functional that inclusion of physical priors in the learning process by solving the Kohn–Sham equations during training resulted in improved generalization. Finally, we also point out recent efforts which use ML in a complementary fashion to extract symbolic expressions from data. − …”

“…Finally, we also point out recent efforts which use ML in a complementary fashion to extract symbolic expressions from data. 61 − 65 …”

Machine Learning of a Density Functional for Anisotropic Patchy Particles

“…Learning density functionals for anisotropic particles has not yet been reported, but in an early study, the explicit minimization of a given functional for liquid crystals in confinement was performed using ML methods. 19 The ML literature on density functionals for the quantum electron problem goes back a few more years, 20 recent developments show interesting parallels to the approaches taken for classical systems, e.g., a work on finding analytic functionals in ref 21 or the use of the minimizing equations in the ML networks. 22 In this paper, we aim at finding a density functional for the KF model with ML methods, describing the orientational correlations from Monte Carlo simulation data between hard walls.…”