Scalable Machine Learning and Advanced Algorithms for Large Scale Ab Initio Simulations

Abstract

In the first part of this dissertation, we study machine learning representations of the potential energy surface (PES) which is often obtained from ab initio calculations like density functional theory. Ab initio calculations require huge computational resources and are often limited only to a few hundred atoms. We discuss non-parametric Gaussian process regression algorithms which can represent the PES with a small number of ab initio data in contrast to neural networks which require large data sets for training their hyper-parameters. The computational cost of the Gaussian process regression algorithm is dominated by the inversion of the covariance matrix between the data components, such as energy and forces. Inversion of a huge matrix is computationally very costly. For this, we developed sparse Gaussian process representations for PES where the large data set is projected into a smaller inducing set and thereby inversion of the huge covariance matrix is bypassed. Several orders of magnitude improvement in computational cost is achieved. Additionally we have devised an optimal adaptive sampling algorithm which can generate the data required for the regression on-the-fly with molecular dynamics. This formalism is called ``sparse Gaussian process Potentials". We applied this methodology to the study of ionic diffusion is solid electrolytes which are instrumental for the development of safe, nonflammable, all-solid-state batteries. In the next part, we use a modern Monte Carlo algorithm called event chain Monte Carlo (ECMC) for the melting study of a huge number of Argon-like particles with Lennard-Jones interaction in 2D. Unlike the Metropolis algorithm, ECMC breaks detailed balance but preserves global balance. Melting of such particles in 2D has been controversial in physics for almost half a century. A new phase diagram for this prominent system is obtained where the boundaries of the hexatic phase with solid and liquid phases are obtained and the melting mechanism is explained.