On iteratively regularized predictor–corrector algorithm for parameter identification *

Abstract

Abstract We study a constrained optimization problem of stable parameter estimation given some noisy (and possibly incomplete) measurements of the state observation operator. In order to find a solution to this problem, we introduce a hybrid regularized predictor–corrector scheme that builds upon both, all-at-once formulation, recently developed by B. Kaltenbacher and her co-authors, and the so-called traditional route, pioneered by A. Bakushinsky. Similar to all-at-once approach, our proposed algorithm does not require solving the constraint equation numerically at every step of the iterative process. At the same time, the predictor–corrector framework of the new method avoids the difficulty of dealing with large solution spaces resulting from all-at-once make-up, which inevitably leads to oversized Jacobian and Hessian approximations. Therefore our predictor–corrector algorithm (PCA) has the potential to save time and storage, which is critical when multiple runs of the iterative scheme are carried out for uncertainty quantification. To assess numerical efficiency of novel PCA, two parameter estimation inverse problems in epidemiology are considered. All experiments are carried out with real data on COVID-19 pandemic in Netherlands and Spain.