On the Techniques for Efficient Sampling, Uncertainty Quantification and Robust Control of Stochastic Multiscale Systems

Abstract

In order to better understand and leverage natural phenomena to design materials and devices (e.g. biomedical coatings, catalytic reactors, thin conductive films for microprocessors, etc.), stochastic multiscale models have been developed that explicitly model the interactions and feedbacks between the electronic, atomistic/molecular, mesoscopic and macroscopic scales. These models attempt to use the accurate results from the fine scales to inform industrially relevant domain sizes and thereby improve product quality through optimal control actions during industrial manufacturing. However, the presence of stochastic calculations increases the computational cost of such modeling approaches and makes their direct application in uncertainty quantification, optimization and online control challenging. Uncertainty cannot be ignored from simulations, otherwise there will be model-plant mismatch and loss in performance. The added computational intensity necessitates the development of more efficient computational methods that can leverage the accurate predictions of stochastic multiscale models in the industrial setting where accuracy, efficiency and speed are of utmost importance.

A lot of research has been done in the area of stochastic multiscale models over the past few decades, but some gaps in knowledge remain. For instance, the performance of traditional uncertainty quantification techniques such as power series (PSE) and polynomial chaos expansions (PCE) has not been compared in the context of stochastic multiscale systems. Furthermore, a novel sampling technique called Multilevel Monte Carlo (MLMC) sampling emerged from the field of computational finance with the aim of preserving accuracy of estimation of model observables while decreasing the required computational cost. However, its applications in the field of chemical engineering and in particular for stochastic multiscale systems remain limited. Also, the advancements in computing power caused the usefulness of machine learning methods such as Artificial Neural Networks (ANNs) to increase. Because of their flexibility, accuracy and computational efficiency, ANNs are experiencing a resurgence of research interest, but their application for stochastic multiscale chemical engineering systems are still limited at the moment.

This thesis aims to fill the identified gaps in knowledge. The results of the conducted research indicate that PCE can be more computationally efficient and accurate than PSE for stochastic multiscale systems, but it may be vulnerable to the effects of stochastic noise. MLMC sampling provides an attractive advantage over the heuristic methods for uncertainty propagation in stochastic multiscale systems because it allows to estimate the level of noise in the observables. However, the stochastic noise imposes a limit on the maximum achievable MLMC accuracy, which was not observed for continuous systems that were originally used in MLMC development. ANNs appear to be a very promising method for online model predictive control of stochastic multiscale systems because of their computational efficiency, accuracy and robustness to large disturbances not seen in the training data.