Stochastic-based methods—both Bayesian statistics and kinetic Monte Carlo techniques—provide powerful techniques for integrating over variability in models, and extending time-scales of DFT or classical potential approaches.
Given a mathematical model to describe a set of data (experimental measurements, or even other computational predictions), an ensemble of model parameters can be found that describe that model description of the data. This ensemble of parameters give models that reproduce the data “similarly well,” and the ensemble also gives a variance of model predictions. This variance is an estimate of the error in the absence of experimental validation.
Rather than integrating time forward with equally spaced steps—as in molecular dynamics—we can evolve time forward from state to state, provided we can (a) enumerate the possible transitions from a given state, and (b) find the individual rates for each transition in a computationally efficient way. We use methods, such as dimer search and nudged elastic-band method with DFT and atomistics to find states, transitions, and energy barriers.
This work in collaboration with Yuguo Chen, UIUC Statistics.