Model compendium, data, and optimization benchmarks for sector-coupled energy systems

Decarbonization and defossilization of energy supply as well as increasing decentralization of energy gen- eration necessitate the development of efficient strategies for design and operation of sector-coupled energy systems. Today, design and operation of process and energy systems rely on powerful numeri- cal methods, in particular, optimization methods. The development of such methods benefits from re- producible benchmarks including transparent model equations and complete input data sets. However, to the authors’ best knowledge and with respect to design and optimal control of sector-coupled en- ergy systems, there is a lack of available benchmarks. Hence, this article provides a model compendium, exemplary realistic data sets, as well as two case studies (i.e., optimization benchmarks) for an in- dustrial/research campus in an open-source description. The compendium includes stationary, quasi- stationary, and dynamic models for typical components as well as linearization schemes relevant for optimization of design, operation, and control of sector-coupled energy systems

Dynamic optimization strategies for monoclonal antibody production

Monoclonal antibodies (mAbs) constitute a high-value biopharmaceutical product with a wide range of applications, e.g., autoimmune diseases and cancer treatment. To meet the increasing market demand, address the entrance of biosimilar products and align with the quality by design (QbD) principles, considerable research effort has been devoted to the development of model-based approaches for mAb-producing processes. The complex nature and the dynamics of the biological systems used in the production of mAbs lead to nonlinear and conconvex mathematical models. Thus, the resulting dynamic optimization problems aiming at an increased process performance are typically multimodal. Although deriving suboptimal local solutions can have negative economical and safety impacts, deterministic global dynamic optimization is not yet tractable for these models. In this thesis, different dynamic optimization strategies for process intensification of antibody production to overcome the limitations resulting from convergence to suboptimal local solutions are investigated and theory on deterministic global dynamic optimization of a specific class of surrogate models is established. First, utilizing a predictive energy-based model for mAb production, it is shown how incorporating biological process knowledge into the optimization problem formulation expedites the derivation of superior local solutions. Furthermore, model reformulation and reduction techniques are investigated to improve the numerical properties of the model and lead to reduced computational effort and increased production outcome. In a similar direction, the advantages of decomposing the optimization problem into smaller more flexible optimization tasks are illustrated. In a next step, optimization incorporating product quality aspects is investigated, as increased antibody production should coincide with meeting certain quality specifications. To this end, different dynamic optimization problems are introduced to examine the effect of process intensification on glycosylation. Then, process performance is maximized with simultaneous control on product quality. The results successfully illustrate an example of how model-based dynamic optimization can be employed for implementation of the QbD approach in biopharmaceutics. Finally, to guarantee convergence of an optimization-based operating strategy to an ε-optimal solution, theory for deterministic global dynamic optimization is developed for a specific class of nonlinear data-driven dynamic models, namely Hammerstein-Wiener (HW) models. The presented method exploits the specific structure of HW models, and thereby extends existing theory on global optimization of systems with linear dynamics. The solution strategy is implemented in our open-source global optimization software MAiNGO to numerically solve examples from offline and online optimization. Additionally, an example motivated from antibody production is solved to global optimality using the described methodology, highlighting the potential and also the limitations of deterministic global dynamic optimization for bioprocess optimization

Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?

Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions

Model compendium, data, and optimization benchmarks for sector-coupled energy systems

Decarbonization and defossilization of energy supply as well as increasing decentralization of energy generation necessitate the development of efficient strategies for design and operation of sector-coupled energy systems. Today, design and operation of process and energy systems rely on powerful numerical methods, in particular, optimization methods. The development of such methods benefits from reproducible benchmarks including transparent model equations and complete input data sets. However, to the authors’ best knowledge and with respect to design and optimal control of sector-coupled energy systems, there is a lack of available benchmarks. Hence, this article provides a model compendium, exemplary realistic data sets, as well as two case studies (i.e., optimization benchmarks) for an industrial/research campus in an open-source description. The compendium includes stationary, quasi-stationary, and dynamic models for typical components as well as linearization schemes relevant for optimization of design, operation, and control of sector-coupled energy systems

Model compendium, data, and optimization benchmarks for sector-coupled energy systems

Decarbonization and defossilization of energy supply as well as increasing decentralization of energy gen- eration necessitate the development of efficient strategies for design and operation of sector-coupled energy systems. Today, design and operation of process and energy systems rely on powerful numeri- cal methods, in particular, optimization methods. The development of such methods benefits from re- producible benchmarks including transparent model equations and complete input data sets. However, to the authors’ best knowledge and with respect to design and optimal control of sector-coupled en- ergy systems, there is a lack of available benchmarks. Hence, this article provides a model compendium, exemplary realistic data sets, as well as two case studies (i.e., optimization benchmarks) for an in- dustrial/research campus in an open-source description. The compendium includes stationary, quasi- stationary, and dynamic models for typical components as well as linearization schemes relevant for optimization of design, operation, and control of sector-coupled energy systems