Bayesian Calibration of Force-fields from Experimental Data: TIP4P Water
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Molecular dynamics (MD) simulations give access to equilibrium and/or dynamic properties given an ergodic sampling and a force-field accuracy. These force-fields are indexed by many parameters that need to be calibrated given available experimental observations. The main contribution of this paper is a rigorous Bayesian framework for the calibration of the force-field parameters and for their uncertainty quantification. To this aim, since the likelihood function of the MD simulation models are intractable, we use a likelihood-free inference scheme known as approximate Bayesian computation (ABC). The second contribution is the adaption of ABC algorithms for High Performance computing to MD simulation within the Python ecosystem ABCpy. This adaptation includes a novel dynamic allocation scheme for MPI that we prove to be particularly efficient in the context of MD simulation. We illustrate the performance of the developed methodology to learn posterior distribution and Bayesian estimates of Lennard-Jones force-field parameters of TIP4P system of water implemented both for simulated and experimental datasets collected using Neutron and X-ray diffraction. For simulated data, the Bayesian estimate is in close agreement with the true parameter value used to generate the dataset. For experimental as well as for simulated data, the Bayesian posterior distribution shows a strong correlation pattern between the force-field parameters. Providing an estimate of the entire posterior distribution, our methodology allows to perform uncertainty quantification of the estimated parameter values. This research opens up the possibility to rigorously calibrate force-fields from available experimental datasets.
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