Visualising energy landscapes through manifold learning

TL;DR

This paper introduces SHEAP, a novel manifold learning-based method for visualising high-dimensional energy landscapes, enabling better understanding of their topological features and revealing intrinsic low-dimensional structures.

Contribution

SHEAP is a new visualization technique inspired by t-SNE and UMAP, specifically designed for energy landscapes, providing interpretable low-dimensional representations.

Findings

SHEAP accurately reproduces known topological features like funnels.

It reveals an intrinsic low-dimensionality in local minima distribution.

Applied to various systems, SHEAP offers new insights into energy landscape layouts.

Abstract

Energy landscapes provide a conceptual framework for structure prediction, and a detailed understanding of their topological features is necessary to develop efficient methods for their exploration. The ability to visualise these surfaces is essential, but the high dimensionality of the corresponding configuration spaces makes this difficult. Here we present Stochastic Hyperspace Embedding and Projection (SHEAP), a method for energy landscape visualisation inspired by state-of-the-art algorithms for dimensionality reduction through manifold learning, such as t-SNE and UMAP. The performance of SHEAP is demonstrated through its application to the energy landscapes of Lennard-Jones clusters, solid-state carbon, and the quaternary system C+H+N+O. It produces meaningful and interpretable low-dimensional representations of these landscapes, reproducing well known topological features such as funnels, and providing fresh insight into their layouts. In particular, an intrinsic low dimensionality in the distribution of local minima across configuration space is revealed.