Improving machine learning methods for the calculation of potential energy surfaces

Atomic environment descriptors or fingerprints are widely used in computational materials
science to machine learn potential energy surfaces and for the quantification of similarities
and differences between atomic configurations. Many approaches to the construction of such
atomic fingerprints have been proposed and their performance in machine learning potentials
has been studied. But a systematic study of the structural resolution of these fingerprints and a
comparison between them has been missing for long in the community. Therefore, we propose
in the second chapter of this thesis a criterion to evaluate the structural resolution of various
fingerprints and based on this criterion we compare the performance of some fingerprints,
popular in the computational physics community. In chapter 3 we explore the existence of
manifolds on which atoms can move without changing the fingerprint significantly and study
the detrimental consequences of such manifolds in machine learning. In chapter 4, we introduce
an unsupervised method for the classification of atomic configurations and dimensionality re-
duction in large structural datasets. In chapter 5, we use the fingerprints to capture the quantum
long-ranged effects in molecules. We conclude this thesis by developing a machine learning
force field for the potential energy surface of multi-atom systems in chapter 6.