A hierarchical Bayesian framework for force field selection in molecular dynamics simulations

Abstract

We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.

A critical review of statistical calibration/prediction models handling data inconsistency and model inadequacy

“…Model inadequacy can sometimes be seen as a consequence of the use of a unique parameter set in different experimental conditions: a "better" model can indeed be obtained by using different values of the parameters along the control space. This can be achieved by modeling the dependence of the physical parameters on the control variable, [75][76][77] or by splitting the data in series along the control space and using a hierarchical model identical to the one in Section 3.2.2.2 for inference of the hyperparameters describing the model's parameters distribution (model M H2 in Wu et al 9 ). To differentiate both hierarchical schemes, the present one is named HierC.…”

“…46 This has been done in various ways: uncertainty scaling, 10,11,13 embedded stochastic models 30,46 and hierarchical models. 9 Parameters and their enlarged uncertainty are then transferable, but this approach is not without drawbacks: 32,49 the transfer of parameter uncertainty to MPU is governed by the functional shape (with respect to the control variables) of the model sensitivity coefficients. This leads to confidence bands with a model-specific shape, not necessarily representative of the actual model errors.…”

Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment

“…Hierarchical Bayesian modeling is an important concept for Bayesian inference [34], which provides the flexibility to allows all sources of uncertainty and correlation to be learned from the data, and hence potentially produce more reliable system identification results. It has been used recently in Baysian system identification [35][36][37][38][39] where the hierarchical nature is primarily to do with the modeling of the likelihood function. To demonstrate the idea, a graphical hierarchical model representation of the structural system identification problem is illustrated in Figure 1,…”

Hierarchical Bayesian operational modal analysis: Theory and computations

“…Hierarchical Bayesian methods open up new horizons in modeling the uncertainty and have shown great promise in different scientific disciplines [36][37][38][39]. In structural dynamics, Behmanesh et al.…”