Visualising energy landscapes through manifold learning

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.

References in corpus (27)

• Auto-Encoding Variational Bayes
• UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• CALYPSO: a method for crystal structure prediction
• Crystal Structure Prediction via Particle Swarm Optimization
• On representing chemical environments
• Ab initio Random Structure Searching
• DScribe: Library of Descriptors for Machine Learning in Materials Science
• Comparing molecules and solids across structural and alchemical space
• High-pressure phases of silane
• Machine-learning based interatomic potential for amorphous carbon
• A Perspective on Conventional High-Temperature Superconductors at High Pressure: Methods and Materials
• Crystal structure prediction using the Minima Hopping method
• Phase changes in 38 atom Lennard-Jones clusters. I: A parallel tempering study in the canonical ensemble
• Evolution of the Potential Energy Surface with Size for Lennard-Jones Clusters
• Reinforcement Learning with Neural Networks for Quantum Feedback
• How to quantify energy landscapes of solids
• A fingerprint based metric for measuring similarities of crystalline structures
• Crystal structure prediction using ab initio evolutionary techniques: principles and applications
• Characterizing the network topology of the energy landscapes of atomic clusters
• Band gap prediction for large organic crystal structures with machine learning
• Efficient moves for global geometry optimization methods and their application to binary systems
• Manifold Learning of Four-dimensional Scanning Transmission Electron Microscopy
• Power-law distributions for the areas of the basins of attraction on a potential energy landscape
• Time-Lagged t-Distributed Stochastic Neighbor Embedding (t-SNE) of Molecular Simulation Trajectories
• Hyperspatial optimisation of structures
• Computationally Efficient Characterization of Potential Energy Surfaces Based on Fingerprint Distances

Cited by in corpus (3)

• Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations
• Manifold Learning in Atomistic Simulations: A Conceptual Review
• Mapping the metastability of Lennard-Jones clusters by the maximum vibrational frequency