Probabilistic Design Space Identification for Upstream Bioprocesses under Limited Data Availability�

Design space identification (DSId) and flexibility analysis are critical in process systems engineering, enabling efficient design of operating conditions. For bioprocess, these tasks are often hindered by the absence of reliable mechanistic models and limited experimental data. This paper presents an algorithm to address these challenges in bioprocesses. The methodology begins by constructing a Gaussian process (GP) model to predict key performance indicators (KPIs) from process inputs. Leveraging the probabilistic nature of GP predictions, we perform probabilistic design space identification (PDSId), characterizing each input point by its probability of feasibility which is the likelihood that constraints imposed on KPIs are satisfied. To visualize and analyse the feasibility space, contours at varying probability levels are identified using alpha shapes, which define deterministic boundaries corresponding to different confidence levels. This enables the quantification of volumetric process flexibility and operating ranges for each confidence level. The proposed methodology is applied to an antibody-producing Chinese hamster ovary (CHO) cell culture process, optimizing culture temperature and osmolality with respect to product yield and purity. Results are presented through probability heat maps and flexibility metrics, providing both qualitative and quantitative insights into feasibility and operational flexibility, thereby supporting informed decision-making in process design.