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

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.

References in corpus (28)

• emcee: The MCMC Hammer
• Interatomic potentials from first-principles calculations: the force-matching method
• Universally Sloppy Parameter Sensitivities in Systems Biology
• A Performance and Cost Assessment of Machine Learning Interatomic Potentials
• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• Active subspace methods in theory and practice: applications to kriging surfaces
• Interatomic Potential for Silicon Defects and Disordered Phases
• Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
• Parameter Space Compression Underlies Emergent Theories and Predictive Models
• The geometry of nonlinear least squares with applications to sloppy models and optimization
• Why are nonlinear fits so challenging?
• The sloppy model universality class and the Vandermonde matrix
• Force-matched embedded-atom method potential for niobium
• Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization
• Likelihood-informed dimension reduction for nonlinear inverse problems
• Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves
• Uncertainty Quantification in Classical Molecular Dynamics
• The limitations of model-based experimental design and parameter estimation in sloppy systems
• Bridging Mechanistic and Phenomenological Models of Complex Biological Systems
• Hybrid neural network potential for multilayer graphene
• Error Analysis in Nuclear Density Functional Theory
• Visualizing probabilistic models: Intensive Principal Component Analysis
• KLIFF: A framework to develop physics-based and machine learning interatomic potentials
• On the correspondence between thermodynamics and inference
• Uncertainty quantification for classical effective potentials: an extension to potfit
• Chebyshev approximation and the global geometry of sloppy models
• A KIM-compliant potfit for fitting sloppy interatomic potentials: Application to the EDIP model for silicon
• The underlying connections between identifiability, active subspaces, and parameter space dimension reduction

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• An information-matching approach to optimal experimental design and active learning
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