Adjoint model for estimating material parameters based on microstructure evolution during spinodal decomposition

Abstract

Data assimilation techniques are attracting increasing attention because they enable researchers to estimate material parameters by integrating an advanced computational model with experimental data of microstructure evolution. In this study, we develop an adjoint model to integrate a phase-field model for spinodal decomposition with time-series measurement data of compositional field maps to estimate the unknown parameters in the phase-field model. As a case study, simultaneous estimation of six parameters (Gibbs energy parameters, gradient energy coefficient, etc.) in the phase-field model is considered. To confirm the effectiveness of the developed adjoint model, numerical tests called ``twin experiments'' are conducted using synthetic measurement data prepared in advance through phase-field simulation. In the twin experiments, the optimum estimates of six model parameters of interest are shown to coincide with true values, indicating that several model parameters can be successfully estimated. Furthermore, the effects of the standard deviation of measurement noise $(\ensuremath{\sigma})$ and the time interval of measurements $(\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}})$ on uncertainties of optimum estimates of parameters $({\ensuremath{\sigma}}^{\mathrm{est}})$ are examined by conducting twin experiments. It is shown that there is a positive correlation between $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$ or between $\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}}$ and ${\ensuremath{\sigma}}^{\mathrm{est}}$, which is essential information for designing experiments to estimate model parameters. The developed adjoint model is assumed to be useful for estimating unknown parameters (e.g., Gibbs energy parameters of a nonequilibrium phase) using time-series measurement data of microstructure evolution during spinodal decomposition.