Mathematical modeling, problem inversion and design of distributed chemical and biological systems

The central focus of this thesis is the design of distributed systems with uncertain parameters using first principles based distributed models. Many systems of significance in chemical and bioengineering are spatially distributed. Current methods to design these systems often deploy models that neglect their spatial distribution. We will show with the analysis of systems like a fixed bed catalytic pellet reactor, drug distribution in the human brain and Plutonium storage that the simplifications of physical phenomena in chemical and biological systems are often not justifiable.;While the simulation of distributed systems is well established, this work makes progress in that it provides mathematical models as well as algorithms to optimize distributed systems. The challenge over prior work is that not only do we have to determine optimal parameters through constrained optimization, but we will have to address the issue of discretizing problems with spatially distributed properties and solve optimization problems in which the constraints may contain partial differential equations (PDE's). This optimization of distributed systems is still in its infancy and this thesis has made first steps towards a rigorous mathematical treatment.;The second issue that this thesis addresses is the significance of the use of quality of information. Classical design optimization assumes system parameters to be perfectly known. In reality, specifically in new emerging problems in chemical engineering and systems biology, we use data driven mathematical models whose parameters are not exactly known. The use of experimental knowledge leads to estimated physical parameters like kinetic rates or transport properties that are known in their mean value, but at the same time also have, depending on the quality of the experimental information, finite bounds of uncertainty. In contrast to the traditional method, which proposes to optimize and make design decisions under the assumption of perfect information, this thesis proposes and demonstrates the advantages of using a probabilistic approach in which not only the nominal values of the parameters are used but the uncertainty associated with the quality of experimental knowledge is also accounted for rigorously. The inclusion of design uncertainty introduces a probabilistic element into the already infinite distributed design optimization problem. This thesis proposes how to effectively integrate rigorous mathematical methods for inclusion of uncertainty into the design optimization.