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Memory matters : Beyond Markovian models of rare event kinetics

Student: Hubert Naguszewski

David Quigley

Summary: Rare events involve rapid but infrequent transitions between two states of a system, e.g. a metastable parent liquid A and a stable crystal B. This project will extend the state-of-the-art for models of how often a system transitions from state A to state B with two key developments; (1) techniques from signal processing to fit models of collective dynamics which incorporate memory (2) machine learning of committor functions, the probability that a microstate will evolve to B before returning to A. Combined, these two developments will allow us to make enhanced predictions from atomistic simulations.

Background: In many heterogenous systems, behaviour at the atomistic scale is governed by rare events, by which we mean transitions between two states A and B that occur rapidly but sufficiently infrequently that they will never be observed during a simulation of achievable duration. Modelling these is challenging, and often relies on parameterisation of simple models which describe the rare event via the kinetics of a single collective degree of freedom.

Such descriptions can make accurate predictions, but rely on identifying the optimal degree of freedom and choosing an appropriate model of its kinetics. In most cases crude (but inexpensive) approximations are used. In this project we will combine two state-of-the-art numerical techniques to improve on these systematically. The optimal collective variable is known to the committor, the probability that a microstate will reach state B before state A. We will extend existing work in the group on using machine learning to predict the committor (and associated uncertainty). We will also model the time evolution of less-optimal collective variables using autoregressive techniques from the signal processing literature to build kinetic models with memory, i.e. beyond the usual assumption of Markovian dynamics.

The two techniques will be compared and contrasted when applied to simple on-lattice models governed by rare events, before extending to atomistic simulations in later years. The project would suit a student interested in computational methods, statistical mechanics and data science.