Mathematical models play a crucial role in manufacturing and engineering, offering scientific insights and aiding in process optimization and control. The reliability of simulation and optimization results hinges on the accuracy of the underlying model, which must be validated by experimental data and precise parameter estimates. Recent advancements have led to effective methods for calibrating models and designing optimal experiments for ordinary differential equations (ODEs). Initial efforts toward validating partial differential equations (PDEs) have involved semi-discretization, converting PDEs into large systems of ODEs. However, this transformation complicates the use of modern PDE-constrained optimization methods, making solutions challenging on standard computers. This dissertation addresses these issues by integrating contemporary PDE-constrained optimization techniques with traditional model validation approaches. The experimental design problem is reformulated as a multistage optimization challenge to account for finite measurement time points. Additionally, the evaluation of the objective function necessitates derivative computations. Despite these complexities, the dissertation successfully adapts the adjoint approach for reduced gradient calculation and introduces a positive definite approximation for second-order derivatives, which can be efficiently computed using adjoint PDEs.
