  Integrated Computational Materials Engineering (ICME) models have been a
crucial building block for modern materials development, relieving heavy
reliance on experiments and significantly accelerating the materials design
process. However, ICME models are also computationally expensive, particularly
with respect to time integration for dynamics, which hinders the ability to
study statistical ensembles and thermodynamic properties of large systems for
long time scales. To alleviate the computational bottleneck, we propose to
model the evolution of statistical microstructure descriptors as a
continuous-time stochastic process using a non-linear Langevin equation, where
the probability density function (PDF) of the statistical microstructure
descriptors, which are also the quantities of interests (QoIs), are modeled by
the Fokker-Planck equation. We discuss how to calibrate the drift and diffusion
terms of the Fokker-Planck equation from the theoretical and computational
perspectives. The calibrated Fokker-Planck equation can be used as a stochastic
reduced-order model (ROM) to simulate the microstructure evolution of
statistical microstructure descriptors PDF. Considering statistical
microstructure descriptors in the microstructure evolution as QoIs, we
demonstrate our proposed methodology in three integrated computational
materials engineering (ICME) models: kinetic Monte Carlo, phase field, and
molecular dynamics simulations.
