Using Bayes formula to estimate rates of rare events in transition path sampling simulations

Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in which these rare trajectories have become frequent. Then, a multistate reweighting scheme is implemented to postprocess data collected from the staged simulations. Herein, we show how Bayes formula allows to directly construct a biased sample containing an enhanced fraction of reactive trajectories and to concomitantly estimate the transition rate from this sample. The approach can remediate the convergence issues encountered in free energy perturbation or umbrella sampling simulations when the transformed distribution insufficiently overlaps with the reference distribution.Comment: 11 pages, 8 figure

Free energy reconstruction from steered dynamics without post-processing

Various methods achieving importance sampling in ensembles of nonequilibrium trajectories enable to estimate free energy differences and, by maximum-likelihood post-processing, to reconstruct free energy landscapes. Here, based on Bayes theorem, we propose a more direct method in which a posterior likelihood function is used both to construct the steered dynamics and to infer the contribution to equilibrium of all the sampled states. The method is implemented with two steering schedules. First, using non-autonomous steering, we calculate the migration barrier of the vacancy in Fe-alpha. Second, using an autonomous scheduling related to metadynamics and equivalent to temperature-accelerated molecular dynamics, we accurately reconstruct the two-dimensional free energy landscape of the 38-atom Lennard-Jones cluster as a function of an orientational bond-order parameter and energy, down to the solid-solid structural transition temperature of the cluster and without maximum-likelihood post-processing.Comment: Accepted manuscript in Journal of Computational Physics, 7 figure

Path factorization approach to stochastic simulations

International audienceThe computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetictrapping of the simulated trajectories within low energy basins. Here we present a new method thatovercomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins.The method is based on path factorization of the evolution operator and requires no prior knowledge of theunderlying energy landscape. The efficiency of the new method is demonstrated in simulations ofanomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetictrapping

Kinetics of phase transformations in Metallic Alloys : Monte Carlo simulations versus experiments

International audienc

Kinetics of phase transformations in Metallic Alloys : Monte Carlo simulations versus experiments

International audienc