Optimal experimental design for the well and the ill(-posed problems)
Seminar Room 1, Newton Institute
The talk discusses both recent applications and extensions of model-based optimal experimental design (OED) theory for challenging problems motivated from chemical engineering. Despite the progress of advanced modeling and simulation methods, experiments will continue to form the basis of all engineering and science. Since experiments are usually require significant effort, best use of these resources should be made. Model-based optimal experimental design provides a rigorous framework to achieve this goal by determining the best settings for the experimental degrees of freedom for the question of interest. In this work, the benefits of applying optimal experimental methods will be demonstrated for the determination of physical properties in chemical engineering applications. In particular, the application to diffusion measurements is considered. Since diffusion is slow, current experiments tend to be very time-consuming. Recently, lab-on-a-chip technology brought the promise of speeding up the measurements due to a drastic decrease in characteristic distances and thus diffusion time. Here, a rigorous optimization of microfluidic experiments for the determination of diffusion coefficients is performed. The OED results are quantitatively validated in experiments showing that the accuracy in diffusion measurements can be increased by orders of magnitude while reducing measurement times to minutes. After discussing applications, extensions of classical OED methods are presented. In particular, the experimental design of ill-posed problems is considered. Here, classical design approaches lead to even qualitatively wrong designs whereas the recently introduced METER criterion allows for a sound solution. The METER criterion aims at the minimization of the expected total error and thereby captures the bias-variance trade-off in ill-posed problems. For the development of predictive models for physical properties, model discrimination and validation are critical steps. For this task, a rational framework is proposed to identify the components and mixtures that allow for optimal model discrimination. The proposed framework combines model-based methods for optimal experimental design with approaches from computer-aided molecular design (CAMD). By selecting the right mixtures to test, a targeted and more efficient approach towards predictive models for physical properties becomes viable.