Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials

Yonatan Kurniawan, Cody L. Petrie, Kinamo J. Williams, Mark K. Transtrum, Ellad B. Tadmor, Ryan S Elliott, Daniel S Karls, Mingjian Wen

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models.

Original languageEnglish (US)
Article number214103
JournalJournal of Chemical Physics
Volume156
Issue number21
DOIs
StatePublished - Jun 7 2022

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation under Award Nos. DMR-1834251 and DMR-1834332. Some of the calculations were done on computational facilities provided by the Brigham Young University Office of Research Computing.

Publisher Copyright:
© 2022 Author(s).

PubMed: MeSH publication types

  • Journal Article

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