Bayesian force fields from active learning for simulation of inter-dimensional transformation of stanene

Yu Xie,Lixin Sun,Andrea Cepellotti,Jonathan Vandermause,Boris Kozinsky

doi:10.1038/s41524-021-00510-y

Yu Xie, Lixin Sun + Show 3 more

Open Access

https://doi.org/10.1038/s41524-021-00510-y

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Abstract

We present a way to dramatically accelerate Gaussian process models for interatomic force fields based on many-body kernels by mapping both forces and uncertainties onto functions of low-dimensional features. This allows for automated active learning of models combining near-quantum accuracy, built-in uncertainty, and constant cost of evaluation that is comparable to classical analytical models, capable of simulating millions of atoms. Using this approach, we perform large-scale molecular dynamics simulations of the stability of the stanene monolayer. We discover an unusual phase transformation mechanism of 2D stanene, where ripples lead to nucleation of bilayer defects, densification into a disordered multilayer structure, followed by formation of bulk liquid at high temperature or nucleation and growth of the 3D bcc crystal at low temperature. The presented method opens possibilities for rapid development of fast accurate uncertainty-aware models for simulating long-time large-scale dynamics of complex materials.

Highlights

Density functional theory (DFT) is one of the most successful methods for simulating condensed matter thanks to a reasonable accuracy for a wide range of systems
Ab initio molecular dynamics (AIMD) offers a way to simulate the atomic motion using forces computed at the DFT level
This way the hierarchical training scheme particular, we show that MGP is capable of rapidly learning to helps to overcome finite size effects and explore phenomena that describe a wide range of temperatures, below and around the cannot be captured with small system sizes, such as phase melting temperature, and that we can efficiently monitor the transformations

Summary

INTRODUCTION

Density functional theory (DFT) is one of the most successful methods for simulating condensed matter thanks to a reasonable accuracy for a wide range of systems. We adopt BAL to achieve automatic training of models for atomic forces, expanding on our earlier workflow[16] This way the predictive variance results in decomposition with twice the accuracy of the GP model increases with time, in the dimension of the corresponding mean function, dramatically configuration regions that are less explored and likely to be increasing the computational cost of their evaluation with spline inaccurate. GP regression cost scales linearly with the high accuracy, modest training data requirement and fast training set size, so the prediction of forces and uncertainties prediction of both forces and their principled Bayesian uncer- becomes more expensive as the BAL algorithm keeps adding data tainty. Bayesian force field (BFF) models for complex materials The This approach has the ability to accelerate prediction of mathematical formalism of the uncertainty mapping is presented the mean, and GP’s internal uncertainty without loss of in “Methods”. Using parallel simulations of largescale structures, we characterize the unusual phase transition, where the 2D monolayer transforms to bcc bulk Sn at the temperature of 200 K, and melts to form a 3D liquid phase at the temperature of 500 K

RESULTS

Background

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