Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy

TL;DR

This paper introduces a machine learning framework for calculating shock Hugoniots with ab initio accuracy, significantly accelerating computations while maintaining high precision, and applies it to multiple materials across a wide temperature range.

Contribution

The authors develop an on-the-fly machine learned force field method that accelerates Kohn-Sham DFT calculations for shock Hugoniots, enabling efficient and accurate simulations for various materials.

Findings

Accelerates Hugoniot calculations by up to two orders of magnitude.

Achieves good agreement with existing first-principles results.

Confirms temperature-dependent decrease in inter-element interactions in compounds.

Abstract

We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the electronic free energy, atomic forces, and pressure; in conjunction with a linear regression model between the electronic internal and free energies to compute the internal energy, with all training data generated from Kohn-Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn-Sham DFT results in the literature. In so doing, we demonstrate that Kohn-Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.