The computational analysis of high dimensional surfaces is a fundamental problem across a wide range of scientific fields, for example in the study of models of clusters of atoms, glasses, self-assembling systems, and biomolecules; machine learning; physics; and other fields. This work presents a variety of novel methods developed to aid the computational study of the structures, dynamics, and thermodynamics of systems described by these surfaces, traditionally termed energy landscapes.

When studying molecular systems, it is important to be able to quantify measures of similarity or difference between a pair of structures generated from an energy landscape. These measures are needed to make predictions of the properties of a given molecular structure from the known properties of similar others. Equivalently a pair of structures can be aligned into similar orientations to allow an interpolated pathway to be generated between them which can be used to identify the transition states between the pair which is a key limiting step in discrete path sampling. The efficiency of the transition state search is strongly dependent on the quality of the initial interpolation and so the alignment methods used. In this work two novel alignment algorithms are presented and benchmarked against existing algorithms for aligning pairs of structures for both periodic and isolated clusters of atoms. The algorithms respectively demonstrate superior performance for either periodic or isolated structures.

The efficient evaluation of the global thermodynamic properties of an in silico system, or analogously, the evidence in Bayesian inference, is a challenge for many high-dimensional systems due to a phenomenon known as broken ergodicity. This problem occurs when the energy barriers between different regions of the energy landscape make it difficult to sample both uniformly. In this work a novel superposition based approach that is embarrassingly parallel, based on the athermal method nested sampling, is introduced and benchmarked against a model system exhibiting broken ergodicity. It is shown that the method reproduces the key features of the heat capacity