Atomistic descriptor optimization using complementary Euclidean and geodesic distance information

Abstract

Descriptors are physically-inspired, symmetry-preserving schemes for representing atomistic systems that play a central role in the construction of models of potential energy surfaces. Although physical intuition can be flexibly encoded into descriptor schemes, they are generally ultimately guided only by the spatial or topological arrangement of atoms in the system. However, since interatomic potential models aim to capture the variation of the potential energy with respect to atomic configurations, it is conceivable that they would benefit from descriptor schemes that implicitly encode both structural and energetic information rather than structural information alone. Therefore, we propose a novel approach for the optimisation of descriptors based on encoding information about geodesic distances along potential energy manifolds into the hyperparameters of commonly used descriptor schemes. To accomplish this, we combine two ideas: (1) a differential-geometric approach for the fast estimation of approximate geodesic distances [Zhu et al., J. Chem. Phys. 150, 164103 (2019)]; and (2) an information-theoretic evaluation metric – information imbalance – for measuring the shared information between two distance measures [Glielmo et al. PNAS Nexus, 1, 1 (2022)]. Using three example molecules – ethanol, malonaldehyde, and aspirin – from the MD22 dataset, we first show that Euclidean (in Cartesian coordinates) and geodesic distances are inequivalent distance measures, indicating the need for updated ground-truth distance measures that go beyond the Euclidean (or, more broadly, spatial) distance. We then utilize a Bayesian optimisation framework to show that descriptors (in this case, atom-centred symmetry functions) can be optimized to maximally express a certain type of distance information, such as Euclidean or geodesic information. We also show that modifying the Bayesian optimisation algorithm to minimise a combined objective function – the sum of the descriptor$\leftrightarrow$Euclidean and descriptor$\leftrightarrow$geodesic information imbalances – can yield descriptors that not only optimally express both Euclidean and geodesic distance information simultaneously, but in fact resolve substantial disagreements between descriptors optimized to encode only one type of distance measure. We discuss the relevance of our approach to the design of more physically rich and informative descriptors that can encode useful, alternative information about molecular systems.

GRAPHICAL ABSTRACT

KEYWORDS:

• atomistic modeling
• molecular modeling
• machine learning
• information theory
• differential geometry

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The code necessary to reproduce the results of this study is openly available online at https://github.com/gopal-iyer/geodesic_descriptor_optimization/tree/main.

Notes

1 Hereinafter, unless specified otherwise, the term Euclidean distance is assumed to mean that it is measured in Cartesian coordinates.

Additional information

Funding

G.R.I. (concept, derivation, implementation, drafting of the manuscript) was funded by AFOSR Award Number FA9550-19-1-9999 and the Brown University Chemistry Department Vince Wernig Fellowship. B.R. (concept, drafting of the manuscript) was funded by NSF CTMC CAREER Award 2046744. This research was conducted using computational resources and services at the Center for Computation and Visualization, Brown University.