Model Order Reduction for Parameter Estimation and Predictive Modeling:Application to Sintering

Inverse problems in scientific computing often suffer from limited observational data and high computational costs, especially when dealing with complex, nonlinear physical models. This work addresses these challenges by developing surrogate modeling techniques tailored for these data-scarce scenarios. The thesis focuses on developing computational methods for solving inverse problems in the context of sintering. In particular, the emphasis is on estimating hard-to-measure material properties such as viscosity. Inverse problems in sintering are challenging due to the complexity of the governing models, which involve nonlinear viscoelastic behavior coupled with thermal effects. These high-fidelity models are computationally intensive, making their direct use for parameter estimation, design, or real-time process control impractical. To address these challenges, surrogate modeling techniques are built to accelerate the forward model. A non-intrusive, online-efficient surrogate model using proper orthogonal decomposition and Gaussian process regression (PODGPR) is presented. To improve offline training efficiency, a hybrid reduced-order modeling framework- two-stage reduced order model (2sROM) is proposed, which integrates reduced basis empirical quadrature procedure (RBEQP) - a greedy hyper-reduction technique, with Gaussian process regression. Performance of this strategy is investigated on representative model problems, including a nonlinear thermal conduction problem and a hyperelasticity model, assessing its accuracy and efficiency. For parameter estimation, the ensemble Kalman inversion (EKI) method is employed, offering a derivative-free strategy for solving inverse problems. A modified version of EKI is also presented, incorporating model bias correction to mitigate errors introduced by the surrogate model. The effectiveness of the proposed method is demonstrated on a nonlinear macroscopic sintering model for the estimation of temperature-dependent viscosity.