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Approximate Bayesian Computation for Granular and Molecular Dynamics Simulations

The effective integration of models with data through Bayesian uncertainty quantification hinges on the formulation of a suitable likelihood function. In many cases such a likelihood may not be readily available or it may be difficult to compute. The Approximate Bayesian Computation (ABC) proposes the formulation of a likelihood function through the comparison between low dimensional summary statistics of the model predictions and corresponding statistics on the data. In this work we report a computationally efficient approach to the Bayesian updating of Molecular Dynamics (MD) models through ABC using a variant of the Subset Simulation method. We demonstrate that ABC can also be used for Bayesian updating of models with an explicitly defined likelihood function, and compare ABC-SubSim implementation and efficiency with the transitional Markov chain Monte Carlo (TMCMC). ABC-SubSim is then used in force-field identification of MD simulations. Furthermore, we examine the concept of relative entropy minimization for the calibration of force fields and exploit it within ABC. Using different approximate posterior formulations, we showcase that assuming Gaussian ensemble fluctuations of molecular systems quantities of interest can potentially lead to erroneous parameter identification.