Machine learning and enhanced sampling simulations

Abstract

In this thesis, we extend the scope of atomistic simulations through a combination of machine learning and advanced sampling methods. Machine learning techniques, and notably neural networks, enable accurate representation of complex functions, while enhanced sampling can help collect the data needed to train the models. The synergy between these two techniques is particularly fruitful and allows taking a step forward in solving two major limitations of molecular dynamics: the interactions accuracy and the limited accessible time scales. Regarding the former, we show how it is possible to use advanced sampling techniques to construct reliable machine learning-based interatomic potentials to study rare events. We exploit this strategy to study the crystallization of silicon with quantum mechanical accuracy. Moreover, this approach paves the way for many other applications ranging from phase diagram calculations to chemical reactions. Concerning the time scale problem, we focus on the improvement of collective variables-based enhanced sampling techniques. These methods accelerate the occurrence of rare events by applying a bias potential to a set of parameters to alter the dynamics in a controlled manner. First, we employ a neural network to express the bias potential and optimize it by a variational scheme. This allows for a better representation of the free energy surfaces and the handling of several variables. In addition, we propose new methods for the extraction of such collective variables, which are crucial to the success of many advanced sampling procedures. We present a data-driven approach that constructs these variables from knowledge of metastable states alone. Finally, we devise a general procedure to accelerate enhanced sampling simulations by extracting collective variables corresponding to the slow modes that hinder convergence. This provides a way to systematically improve collective variables derived from physical intuition or statistical methods, and thus allows the applicability of enhanced sampling simulations to be extended.