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Visualizing Energy Landscapes through Manifold Learning

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Shires, BWB 
Pickard, CJ 


Energy landscapes provide a conceptual framework for structure prediction, and a detailed under- standing 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 correspond- ing 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 partic- ular, an intrinsic low dimensionality in the distribution of local minima across configuration space is revealed.



51 Physical Sciences, 7 Affordable and Clean Energy

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Physical Review X

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American Physical Society (APS)
Engineering and Physical Sciences Research Council (EP/L015552/1)
BS acknowledges the EPSRC CDT in Computational Methods for Materials Science for funding under grant number EP/L015552/1. CJP has been supported by the Royal Society through a Royal Society Wolfson Research Merit award.