A deep learning framework to emulate density functional theory

Abstract

Density functional theory (DFT) has been a critical component of computational materials research and discovery for decades. However, the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale. Here, we propose an end-to-end machine learning (ML) model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density, followed by the prediction of other properties such as density of states, potential energy, atomic forces, and stress tensor, by using the atomic structure and charge density as input. Our deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup (linear scaling with system size with a small prefactor), while maintaining chemical accuracy. We demonstrate the capability of this ML-DFT concept for an extensive database of organic molecules, polymer chains, and polymer crystals.

Machine learning for accuracy in density functional approximations

“…Given the promise of significantly improved computational efficiency of such an orbital-free DFT approach, further ML models directly predicting the charge density have been developed. [182][183][184][185][186][187] Shao et al 188 furthermore learned maps from external potential to the one-body density matrix.…”

From Characterization to Discovery: Artificial Intelligence, Machine Learning and High-Throughput Experiments for Heterogeneous Catalyst Design

“…213 Del Rio et al ( 2023) conducted a comparison between the computation of the Kohm-Sham equation and a ML-based approach. 239 They estimated that the DFT-based algorithm had a cubic dependence on the system size, while the ML model had a linear dependence and was orders of magnitude faster on larger systems. Fiedler et al 2023 240 found similar results.…”

“…A positive aspect of the use of ML with regards to the challenge of complexity is the potential to dramatically reduce the computational cost of theoretical computations . Del Rio et al (2023) conducted a comparison between the computation of the Kohm-Sham equation and a ML-based approach . They estimated that the DFT-based algorithm had a cubic dependence on the system size, while the ML model had a linear dependence and was orders of magnitude faster on larger systems.…”

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

“…Considering the difficulties for both human and artificial intelligence to arrive at the exact universal functional, alternative approaches to use DFT but circumventing this search have been proposed. [321,[341][342][343][344][345][346] The practical solution to finding the energy of the electronic ground state in DFT is given by KS equations. A non-interacting system is defined, where all the interactions among electrons are neglected, assuming that the density of the non-interacting and the real system are equivalent.…”