Abstract
Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.
Highlights
Hybrid modeling allows to include process knowledge via first-principles system equations and, simultaneously, to compensate for missing process information via datadriven machine learning (ML) algorithms
In the context of deep uncertainty, the fundamental distinction between aleatoric and epistemic uncertainty seems mandatory in first-principles modeling [11,12,13] and ML algorithms [14,15,16,17]
It has been successfully demonstrated that hybrid modeling approaches can be usefully employed for the mathematical description of electrochemical synthesis problems, including batch and continuous operation
Summary
Hybrid modeling allows to include process knowledge via first-principles system equations and, simultaneously, to compensate for missing process information via datadriven machine learning (ML) algorithms. Nielsen et al combine a deep neural network predicting particle phenomena kinetics with a first-principles model to simulate particle processes [1]. As different as the application fields and the degree of hybridization may be, the fundamental problem of model uncertainty applies to all realizations of hybrid modeling, including system identification and interpretation [8,9]. In the context of deep uncertainty, the fundamental distinction between aleatoric and epistemic uncertainty seems mandatory in first-principles modeling [11,12,13] and ML algorithms [14,15,16,17]. Aleatoric and epistemic uncertainty should be taken into account for uncertainty propagation and parameter sensitivities in the field of hybrid modeling, too. Imprecise uncertainties lead to the aleatoric and epistemic components, which have to be examined according to their dependence
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