Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks

J A Ellis,A Cangi,J A Stephens,S Rajamanickam,A P Thompson,G A Popoola,N A Modine,L Fiedler

doi:10.1103/physrevb.104.035120

Abstract

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

Highlights

Multiscale materials modeling [1] provides fundamental insights into microscopic mechanisms that determine materials properties
In contrast to prior work on ML-interatomic potentials (IAPs) in which descriptors are evaluated on atom-centered neighborhoods, here we evaluate the SNAP descriptors on the same 200 × 200 × 200 Cartesian grid points at which we evaluated the local density of states (LDOS) training data [see Eq (16) above]
In order to study the variability in LDOS between the three groups (298 K solid, 933 K solid, and 933 K liquid), we reduce the dimensionality of the LDOS data sets and study them using principal component analysis (PCA)

Summary

Introduction

Multiscale materials modeling [1] provides fundamental insights into microscopic mechanisms that determine materials properties. A multiscale modeling framework operating both near first-principles accuracy and across length and time scales would enable key progress in a plethora of applications It would greatly advance materials science research—in gaining understanding of the dynamical processes inherent to advanced manufacturing [2,3], in the search for superhard [4] and energetic materials [5,6], and in the identification of radiation-hardened semiconductors [7,8].

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Results

Conclusion