“…To tackle this challenge, a category of models known as hybrid models has emerged, wherein the kinetic parameters of first-principles models are forecasted by a data-driven component. , In these hybrid models, hidden chemical mechanisms can then be characterized by parametric uncertainties. These hybrid models have found applications across a wide array of domains, including bacterial cultivations, chemical reactors, − flowsheet simulators for chemical processes, crystallization, , distillation columns, biopharmaceutical industries, polymerization processes, fermentations, − hydraulic fracturing, intracellular signaling pathways, and many more. In prior research, hybrid modeling has proven effective in addressing issues related to parametric uncertainties within simpler model equations. , However, applying this approach to complex systems described by PDEs presents its own distinct challenges.…”