Memory matters: Beyond Markovian models of rare event kinetics

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.

Impact on Students. The primary impact will be on the 50+ PhD students trained by the Centre. They will be high-quality computational scientists who can develop and implement new methods for modelling complex systems in collaboration with scientists and end-users, who are comfortable working in interdisciplinary environments, have excellent communication skills and be well prepared for a wide range of future careers. The students will tackle and disseminate results from exciting PhD projects with strong potential for direct impact. Exemplar research themes we have identified together with our industrial and international partners: (i) design of electronic devices, (ii) catalysis across scales, (iii) high-performance alloys, (iv) direct drive laser fusion, (v) future medicine exploration, (vi) smart nanofluidic interfaces, (vii) composite materials with enhanced functionality, (viii) heterogeneity of underground systems.

Impact on Industry. Students trained by HetSys will make a significant impact on UK industry as they will be ideally prepared for R&D careers to help to address the skills shortage in science and engineering. They will be in high demand for their ability to (i) work across disciplines, (ii) perform calculations that come along with error estimates, and (iii) develop well-designed software that other researchers can readily use and modify which implements novel solutions to scientific problems. More generally, incorporating error bars into models to take account of incomplete data and insufficient models could lead to significantly enhanced adoption of materials modelling in industry, reducing trial and error, and costly/time-consuming R&D procedures. The global market for simulation software is expected to more than double from now to 2022 indicating a very strong absorptive capacity for graduates. Moreover, a recent European Materials Modelling Consortium report identified a typical eight-fold return on investment for materials modelling research, leading to cost savings of 12M Euros per industrial project.

Impact on Society. Scarcity of resources and high energy requirements of traditional materials processing techniques raise ever-increasing sustainability concerns. Limitations on jet engine fuel efficiency and the difficulties of designing materials for fusion power stations reflect the social and economic cost of our incomplete knowledge of how complex heterogeneous systems behave. High costs of laboratory investigations mean that theory must aid experiment to produce new knowledge and guidance. By training students who can develop the new methodology needed to model such issues, HetSys will support society's long term need for improved materials and processes.

There will also be a direct impact locally and regionally through engagement by HetSys in outreach projects. For example we will encourage CDT students to be involved with annual 'Inspire' residential courses at Warwick for Year 11 girls, which will show what STEM subjects are like at degree level. CDT students will present highlights from projects to secondary-school pupils during these courses and also visit local schools, particularly in areas currently under-represented in the student body, in coordination with relevant professional bodies.

Impact on collaboration. Our international partners have identified the same urgent challenges for computational modelling. We will build flourishing links with research institutes abroad with long term benefit on UK research via our links to computational science networks. Shared research projects will strengthen links between academic staff and industry R&D personnel and across disciplines. The work will also lead to accessible, robust and reusable software. The Centre will achieve cross-disciplinary academic impact on the physical and materials sciences, engineering, manufacturing and mathematics communities at Warwick and beyond, and on the generation of new ideas, insights and techniques.