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

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 adjoint integrate a phase-field for spinodal decomposition time-series measurement compositional field maps the unknown in model. As case simultaneous estimation six (Gibbs energy parameters, gradient coefficient, etc.) is considered. To confirm effectiveness developed model, numerical tests called ``twin experiments'' conducted using synthetic prepared advance through simulation. twin experiments, optimum estimates interest shown coincide true values, indicating that several can be successfully estimated. Furthermore, effects standard deviation noise $(\ensuremath{\sigma})$ and time interval measurements $(\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}})$ on uncertainties $({\ensuremath{\sigma}}^{\mathrm{est}})$ examined conducting experiments. It there positive correlation between $\ensuremath{\sigma}$ ${\ensuremath{\sigma}}^{\mathrm{est}}$ or $\mathrm{\ensuremath{\Delta}}{t}_{\mathrm{meas}.}^{\ensuremath{'}}$ ${\ensuremath{\sigma}}^{\mathrm{est}}$, which essential information designing experiments parameters. The assumed useful estimating (e.g., Gibbs nonequilibrium phase) evolution during decomposition.