Perspectives on the Integration between First-Principles and Data-Driven Modeling

Supporting data-enhanced hybrid ordinary differential equation model for phosphate dynamics in municipal wastewater treatment

A parallel hybrid ordinary differential equation (ODE) integrating the Activated Sludge Model No. 2d (ASM2d) and an artificial neural network (ANN) was developed to simulate biological phosphorus removal (BPR) with high accuracy and interpretability. Two novelties were introduced; first, the involved supporting data (i.e., phosphate-release activity) were incorporated as an input in the ANN. Second, the outputs of the ANN were selective. Three models were implemented using different ANN outputs, and all three outperformed ASM2d in phosphate estimation for anaerobic/aerobic sequencing batch reactor operation. In particular, the incorporation of four variables responsible for BPR into the ANN enabled the highest performance (R2 = 0.93) owing to the capture of increasing phosphate-accumulating organisms (PAOs). The ANN with the supporting data worked satisfactorily to compensate for ASM2d by adding proper PAOs, resulting in improvement in phosphate estimation. The novel parallel hybrid ODE can simulate BPR while maintaining physical meaning.

Advanced Modeling and Optimization Strategies for Process Synthesis

This article provides a systematic review of recent progress in optimization-based process synthesis. First, we discuss multiscale modeling frameworks featuring targeting approaches, phenomena-based modeling, unit operation-based modeling, and hybrid modeling. Next, we present the expanded scope of process synthesis objectives, highlighting the considerations of sustainability and operability to assure cost-competitive production in an increasingly dynamic market with growing environmental awareness. Then, we review advances in optimization algorithms and tools, including emerging machine learning-and quantum computing-assisted approaches. We conclude by summarizing the advances in and perspectives for process synthesis strategies.

Modeling Mechanochemical Depolymerization of PET in Ball-Mill Reactors Using DEM Simulations

Developing efficient and sustainable chemical recycling pathways for consumer plastics is critical for mitigating the negative environmental implications associated with their end-of-life management. Mechanochemical depolymerization reactions have recently garnered great attention, as they are recognized as a promising solution for solvent-free transformation of polymers to monomers in the solid state. To this end, physics-based models that accurately describe the phenomena within ball mills are necessary to facilitate the exploration of operating conditions that would lead to optimal performance. Motivated by this, in this paper we develop a mathematical model that couples results from discrete element method (DEM) simulations and experiments to study mechanically-induced depolymerization. The DEM model was calibrated and validated via video experimental data and computer vision algorithms. A systematic study on the influence of the ball-mill operating parameters revealed a direct relationship between the operating conditions of the vibrating milling vessel and the total energy supplied to the system. Moreover, we propose a linear correlation between the high-fidelity DEM simulation results and experimental monomer yield data for poly(ethylene terephthalate) depolymerization, linking mechanical and energetic variables. Finally, we train a reduced-order model to address the high computational cost associated with DEM simulations. The predicted working variables are used as inputs to the proposed mathematical expression which allows for the fast estimation of monomer yields.

Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities

Industry 4.0 has embraced process models in recent years, and the use of model-based digital twins has become even more critical in process systems engineering, monitoring, and control. However, the reliability of these models depends on the model parameters available. The accuracy of the estimated parameters is, in turn, determined by the amount and quality of the measurement data and the algorithm used for parameter identification. For the definition of the parameter identification problem, the ordinary least squares framework is still state-of-the-art in the literature, and better parameter estimates are only possible with additional data. In this work, we present an alternative strategy to identify model parameters by incorporating differential flatness for model inversion and neural ordinary differential equations for surrogate modeling. The novel concept results in an input-least-squares-based parameter identification problem with significant parameter sensitivity changes. To study these sensitivity effects, we use a classic one-dimensional diffusion-type problem, i.e., an omnipresent equation in process systems engineering and transport phenomena. As shown, the proposed concept ensures higher parameter sensitivities for two relevant scenarios. Based on the results derived, we also discuss general implications for data-driven engineering concepts used to identify process model parameters in the recent literature.