Grain Growth Prediction Based on Data Assimilation by Implementing 4DVar on Phase-Field Models*

We propose a method to predict grain growth based on data assimilation by using a four-dimensional variational method (4DVar). The method utilizing a second-order adjoint method, compared with conventional data assimilation methods, can drastically save the computational cost needed to obtain the estimates and uncertainties of parameters involved in phase-field models. When implemented on a multi-phase-field model, the proposed method allows us to calculate the predicted grain structures and uncertainties in them that depend on the quality and quantity of the observational data. We confirm through numerical tests involving synthetic data that the proposed method correctly reproduces the true phase-field assumed in advance. Furthermore, it successfully quantifies uncertainties in the predicted grain structures, where such uncertainty quantifications provide valuable information to optimize the experimental design.