ABSTRACT:     Optimality is guiding and controlling, in one way or the other, the rise of science and technology. Formulation of the optimality criteria differs from specific problems and research domains and it is often hidden in many engineering problems. An optimal experimental set-up maximizes the value of data for statistical inference and prediction, which is particularly important for experiments that are time consuming or expensive to perform.

   We will first present computational methods for the approximation of the expected information gain using the Laplace approximation. In the context of partial differential equations (PDEs), we discuss about the multilevel methods and the improvements of the computational complexity of their single-level counterparts.

    Then we couple gradient-based optimization methods with the computational methods for the search of the optimal design setup.