Adaptive framework for data-driven probabilistic design space identification

Chemical and biochemical processes require systematic approaches to identify operating regions that meet predefined performance criteria. Design space identification and its probabilistic extension, probabilistic design space identification (PDSI), enable rigorous characterization of feasible operating conditions. While traditionally based on mechanistic models, such models may be incomplete or unavailable for novel or complex processes, where limited mechanistic knowledge constrains their applicability. These settings necessitate data-driven alternatives. However, generating experimental data is costly, and real-world data are further characterized by uncertainties. Consequently, efficient strategies for data-based PDSI are essential. To address these challenges, this work proposes an adaptive framework that integrates Gaussian Process-based PDSI with a Delaunay triangulation-guided experimental design. The method iteratively selects informative batches of experiments, updates the surrogate model with new data, and progressively refines the feasible operating region. This procedure reduces redundant experimentation and accelerates convergence toward an accurate representation of the design space. The effectiveness of the proposed framework is demonstrated through benchmark numerical case studies and a batch reactor system.