Efficient estimation of material parameters using DMC-BO: Application to phase-field simulation of solid-state sintering

Phase-field (PF) simulations require data on physical properties and material parameters, which are largely unknown. Although data assimilation (DA) offers a way to estimate unknown material parameters and unobservable states through integration of simulation results and experimental data, conventional DA methods involve high computational costs and implementation difficulties. Therefore, in this study, we developed a new DA method: Data assimilation method Minimizing a four-dimensional Cost function using Bayesian optimization (DMC-BO). Using Bayesian optimization to minimize the data misfit between simulations and experiments leads to overcome the cost and implementation problems under conventional DA methods. To validate the accuracy and computational efficiency of the state and material parameter estimations obtained using DMC-BO, we applied the method to a PF model of highly nonlinear solid-state sintering, and we conducted numerical experiments called twin experiments. The twin experiments demonstrated that DMC-BO can yield highly accurate state estimation results and reasonably accurate material parameter estimation results, at less than half the computational cost of the conventional ensemble 4DVar DA method. Overall, the developed DMC-BO method is an advanced and powerful method whereby unobservable states and unknown material parameters can be obtained, which are essential for elucidating microstructural evolutions, with simplified PF model implementation and low computational costs.