Shin-ichi Ito_a, Hiromichi Nagao_a,b, Tadashi Kasuya_c and Junya Inoue_{c,d
^aEarthquake Research Institute, The University of Tokyo, Tokyo, Japan;
^bGraduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan;
^cGraduate School of Engineering, The University of Tokyo, Tokyo, Japan;
^dResearch Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan}

Science and Technology of Advanced Materials, 18:1, 857-869 http://dx.doi.org/10.1080/14686996.2017.1378921

ABSTRACT
We propose a method to predict grain growth based on data assimilation by using a fourdimensional variational method (4DVar). 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.