# Dynamical continuum simulation of condensed matter from first-principles

## TL;DR

This paper introduces a method to automatically generate first-principles equations of state for continuum mechanics simulations using Gaussian processes on ab initio molecular dynamics data, demonstrated on silicon shock wave simulations.

## Contribution

It presents a novel approach to derive microscale material properties directly from first-principles calculations for macroscale continuum modeling.

## Key findings

- Successfully generated EOS for silicon from DFT data
- Simulated shock wave dynamics using the derived EOS
- Demonstrated the method's applicability to hyperelasticity simulations

## Abstract

Macroscale continuum mechanics simulations rely on material properties stemming from the microscale, which are normally described using phenomenological equations of state (EOS). A method is proposed for the automatic generation of first-principles unconstrained EOSs using a Gaussian process on a set of ab initio molecular dynamics simulations, thereby closing the continuum equations. We illustrate it on a hyperelasticity simulation of bulk silicon using density-functional theory (DFT), following the dynamics of shock waves after a cylindrical region is instantaneously heated.