Data assimilation for phase-field models based on the ensemble Kalman filter

Abstract

We have developed a data assimilation (DA) methodology based on the ensemble Kalman filter (EnKF) for estimating unknown parameters involved in a phase-field model from observational/experimental data. The DA methodology based on Bayesian statistics is able to estimate parameters by incorporating observational/experimental data into the phase-field model and evaluate the uncertainty of the estimated parameters. In this paper, we apply the EnKF-based DA method to estimate the phase-field mobility for a phase-field simulation of the isothermal austenite-to-ferrite transformation in a Fe–C–Mn alloy. Our DA method is validated through numerical experiments called “twin experiments” to verify that the DA method can estimate a priori assumed-true phase-field mobility from synthetic observational data. The results of the twin experiments using various initial phase-field mobilities show that our DA methodology can successfully estimate the true phase-field mobility, even when the initial value largely deviates from the true value. Furthermore, our DA method reveals the sampling interval for observational data necessary to accurately estimate the parameter and its uncertainty.