Visualising Energy Landscapes and Quantifying Basin Volumes.

Lead Research Organisation: University of Cambridge
Department Name: Physics

Abstract

The main objective of my research project is to better understand the general features present in the potential energy landscapes defined by atomic or ionic systems, be those discrete or periodic. The context for this work is the goal of material structure prediction, chiefly with crystalline structures in mind (crystal structure prediction). From a theoretical standpoint, the problem of (crystal) structure prediction can be equated to the location of minima on a potential energy landscape, with the most important
structures - generally those which are most likely to be observed in reality - usually corresponding to the lowest energy minima on the appropriate surface. However, for all but the simplest of systems, these surfaces are highly complex, and the number of minima they contain is vast. Hence, the location of all minima on such a surface is essentially never computationally feasible. Thus, techniques for structure prediction require some means to navigate these landscapes and locate the most important, low energy minima, without being exhaustive - i.e. without visiting every minimum. The hope is that the insight gained through my research will provide inspiration for ways in which we can improve the efficiency of existing methods for locating low energy minima, or at the very least justify the success they have already found.

Recently in my research I have also also begun to tackle the question of whether we can gain any insight into energy landscape structures (arrangements and connectivity of the basins, etc.) from an application of stochastic techniques for high dimensional data embedding, such as t-SNE and UMAP, in order to visually represent the surface in two or three dimensions. These tools were predominantly developed within the machine learning community, but they have been found to be incredibly useful when applied to a range of problems in physical and biological sciences for data visualisation. Early investigations by myself and my first supervisor in developing and applying these methods to structural data corresponding to a given landscape has been very promising, and we believe they have the potential to compete with and even outperform existing approaches to energy landscape visualisation such as disconnectivity graphs, or sketch maps. We also believe that our research into these data embedding methods may provide some further insight that would be of interest to the machine learning community, and that many of the developments we make to these techniques will be generally applicable to the datasets appearing in many other fields.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512461/1 01/10/2017 30/09/2021
1948654 Studentship EP/R512461/1 01/10/2017 30/09/2021 Benjamin Shires
 
Description A new algorithm for visualising high-dimensional data through dimensionality reduction has been developed (called SHEAP). The algorithm is designed for dealing with materials structure data, enabling the visualisation of important features of energy landscapes. Application of this algorithm to model systems has revealed an intrinsic low-dimensionality in the distribution of minima (stable structures) across these surfaces.
Exploitation Route The SHEAP algorithm could be very useful within the structure prediction community, providing insight on how searching techniques might be enhanced.
Sectors Chemicals,Digital/Communication/Information Technologies (including Software),Energy,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology