Abstract
Algorithms capable of extracting information from data are increasingly finding application in condensed matter physics. Two particularly successful application domains have been the automatic construction of atomic force fields and the compact representation of electronic wave functions. In spite of their accuracy, previously proposed data-driven approaches for learning these two quantities often suffer from poor interpretability and transferability.This thesis develops new accurate and interpretable machine learning models for atomic force fields and for electronic wave functions, based on Gaussian process (GP) regression and on a careful design of GP kernel functions.
To learn atomic force fields, various scalar local energy kernels and matrix-valued force kernels are proposed, all encoding the force field fundamental symmetries (translations, rotations, reflections and permutations) and a controllable degree of complexity provided by the force field interaction order. Tests on a wide range of materials prove the efficiency of the models proposed and show that low order models often represent the best compromise between accuracy and transferability. Furthermore, predictions of low order GP models can be sped up by orders of magnitude, reaching the typical evaluation speed of traditional parametrised potentials.
To learn electronic wave functions, a log-GP model is proposed, along with a set of kernels representing well-defined many-body correlations. Such kernels are benchmarked on the one dimensional Hubbard model with excellent initial results.
| Date of Award | 1 May 2019 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | George Booth (Supervisor) & Peter Sollich (Supervisor) |