Deep hybrid modeling of chemical process: Application to hydraulic fracturing

Hybrid deep modeling of a CHO-K1 fed-batch process: combining first-principles with deep neural networks

Introduction: Hybrid modeling combining First-Principles with machine learning is becoming a pivotal methodology for Biopharma 4.0 enactment. Chinese Hamster Ovary (CHO) cells, being the workhorse for industrial glycoproteins production, have been the object of several hybrid modeling studies. Most previous studies pursued a shallow hybrid modeling approach based on three-layered Feedforward Neural Networks (FFNNs) combined with macroscopic material balance equations. Only recently, the hybrid modeling field is incorporating deep learning into its framework with significant gains in descriptive and predictive power. Methods: This study compares, for the first time, deep and shallow hybrid modeling in a CHO process development context. Data of 24 fed-batch cultivations of a CHO-K1 cell line expressing a target glycoprotein, comprising 30 measured state variables over time, were used to compare both methodologies. Hybrid models with varying FFNN depths (3-5 layers) were systematically compared using two training methodologies. The classical training is based on the Levenberg-Marquardt algorithm, indirect sensitivity equations and cross-validation. The deep learning is based on the Adaptive Moment Estimation Method (ADAM), stochastic regularization and semidirect sensitivity equations. Results and conclusion: The results point to a systematic generalization improvement of deep hybrid models over shallow hybrid models. Overall, the training and testing errors decreased by 14.0% and 23.6% respectively when applying the deep methodology. The Central Processing Unit (CPU) time for training the deep hybrid model increased by 31.6% mainly due to the higher FFNN complexity. The final deep hybrid model is shown to predict the dynamics of the 30 state variables within the error bounds in every test experiment. Notably, the deep hybrid model could predict the metabolic shifts in key metabolites (e.g., lactate, ammonium, glutamine and glutamate) in the test experiments. We expect deep hybrid modeling to accelerate the deployment of high-fidelity digital twins in the biopharma sector in the near future.

Hybrid modeling in bioprocess dynamics: Structural variabilities, implementation strategies, and practical challenges

Hybrid modeling, with an appropriate blend of the mechanistic and data-driven framework, is increasingly being adopted in bioprocess modeling, model-based experimental design (digital-twin), identification of critical process parameters, and optimization. However, the development of a hybrid model from experimental data is an inherently complex workflow, involving designed experiments, selection of the data-driven process, identification of model parameters, assessment fitness, and generalization capability. Depending on the complexity of the process system and purpose, each piece of these modules can flexibly be incorporated into the puzzle. However, this extra flexibility can be a cause of concern to trace an "optimal" model structure. In this paper, the development of hybrid models in a common bioprocess system, selection of data-driven components and their mapping to states, choice of parameter identification techniques, and model quality assurance are revisited. The challenges associated with hybrid-model development, and corrective actions have also been reviewed. The review also suggests the lack of data, and code sharing in communal repositories can be a hurdle in the exploration, and expansion of those tools in a bioprocess system.

Machine learning methods for predicting the key metabolic parameters of Halomonas elongata DSM 2581 T

Ectoine is generally produced by the fermentation process of Halomonas elongata DSM 2581 ^T, which is one of the primary industrial ectoine production techniques. To effectively monitor and control the fermentation process, the important parameters require accurate real-time measurement. However, for ectoine fermentation, three critical parameters (cell optical density, glucose, and product concentration) cannot be measured conveniently in real-time due to time variation, strong coupling, and other constraints. As a result, our work effectively created a series of hybrid models to predict the values of these three parameters incorporating both fermentation kinetics and machine learning approaches. Compared with the traditional machine learning models, our models solve the problem of insufficient data which is common in fermentation. In addition, a simple kinetic modeling is only applicable to specific physical conditions, so different physical conditions require refitting the function, which is tedious to operate. However, our models also overcome this limitation. In this work, we compared different hybrid models based on 5 feature engineering methods, 11 machine-learning approaches, and 2 kinetic models. The best models for predicting three key parameters, respectively, are as follows: CORR-Ensemble (R²: 0.983 ± 0.0, RMSE: 0.086 ± 0.0, MAE: 0.07 ± 0.0), SBE-Ensemble (R²: 0.972 ± 0.0, RMSE: 0.127 ± 0.0, MAE: 0.078 ± 0.0), and SBE-Ensemble (R²:0.98 ± 0.0, RMSE: 0.023 ± 0.001, MAE: 0.018 ± 0.001). To verify the universality and stability of constructed models, we have done an experimental verification, and its results showed that our proposed models have excellent performance. KEY POINTS: • Using the kinetic models for producing simulated data • Through different feature engineering methods for dimension reduction • Creating a series of hybrid models to predict the values of three parameters in the fermentation process of Halomonas elongata DSM 2581 ^T.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

Despite the success of multiscale modeling in science and engineering, embedding molecular-level information into nonlinear reactor design and control optimization problems remains challenging. In this work, we propose a computationally tractable scale-bridging approach that incorporates information from multi-product microkinetic (MK) models with thousands of rates and chemical species into nonlinear reactor design optimization problems. We demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. We assemble a library of six candidate ROK models based on literature and MK model structure. We find that three metrics—quality of fit (e.g., mean squared logarithmic error), thermodynamic consistency (e.g., low conversion of exothermic reactions at high temperatures), and model identifiability—are all necessary to train and select ROK models. The ROK models that closely mimic the structure of the MK model offer the best compromise to emulate the product distribution. Using the four best ROK models, we optimize the temperature profiles in staged reactors to maximize conversions to heavier oligomerization products. The optimal temperature starts at 630–900K and monotonically decreases to approximately 560 K in the final stage, depending on the choice of ROK model. For all models, staging increases heavier olefin production by 2.5% and there is minimal benefit to more than four stages. The choice of ROK model, i.e., model-form uncertainty, results in a 22% difference in the objective function, which is twice the impact of parametric uncertainty; we demonstrate sequential eigendecomposition of the Fisher information matrix to identify and fix sloppy model parameters, which allows for more reliable estimation of the covariance of the identifiable calibrated model parameters. First-order uncertainty propagation determines this parametric uncertainty induces less than a 10% variability in the reactor optimization objective function. This result highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multi-scale reactor and process design and optimization. Moreover, the fast dynamic optimization solution times suggest the ROK strategy is suitable for incorporating molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.

Hybrid Models for Efficient Control, Optimization, and Monitoring of Thermo-Chemical Processes and Plants

This paper describes a procedure and an IT product that combine numerical models, expert knowledge, and data-based models through artificial intelligence (AI)-based hybrid models to enable the integrated control, optimization, and monitoring of processes and plants. The working principle of the hybrid model is demonstrated by NOx reduction through guided oscillating combustion at the pulverized fuel boiler pilot incineration plant at the Institute for Technical Chemistry, Karlsruhe Institute of Technology. The presented example refers to coal firing, but the approach can be easily applied to any other type of nitrogen-containing solid fuel. The need for a reduction in operation and maintenance costs for biomass-fired plants is huge, especially in the frame of emission reductions and, in the case of Germany, the potential loss of funding as a result of the Renewable Energy Law (Erneuerbare-Energien-Gesetz) for plants older than 20 years. Other social aspects, such as the departure of experienced personnel may be another reason for the increasing demand for data mining and the use of artificial intelligence (AI).

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.

An intracellular signaling pathway is often represented by a set of nonlinear ordinary differential equations, which translate our current knowledge about the signaling pathway into a testable mathematical model. However, predictions from such models are often subject to high uncertainty since many signaling pathways are only partially known beforehand. In this study, we propose a systematic approach to develop a hybrid model to improve model accuracy by combining machine learning and the first-principle modeling. Specifically, model correction terms are learned from discrepancy between model predictions and measurements, and these terms are added to the first-principle model to enhance the prediction accuracy. Once these correction terms are learned from the data, an artificial neural network (ANN) model is developed to find an empirical relation between the model and the correction terms so that the developed ANN can be used to posses improved predictive capabilities even in new operating conditions (i.e., generalizability). The final hybrid model is then constructed by coupling the first-principle model with the developed ANN.

Combining model structure identification and hybrid modelling for photo-production process predictive simulation and optimisation

Integrating physical knowledge and machine learning is a critical aspect of developing industrially focused digital twins for monitoring, optimisation, and design of microalgal and cyanobacterial photo-production processes. However, identifying the correct model structure to quantify the complex biological mechanism poses a severe challenge for the construction of kinetic models, while the lack of data due to the time-consuming experiments greatly impedes applications of most data-driven models. This study proposes the use of an innovative hybrid modelling approach that consists of a simple kinetic model to govern the overall process dynamic trajectory and a data-driven model to estimate mismatch between the kinetic equations and the real process. An advanced automatic model structure identification strategy is adopted to simultaneously identify the most physically probable kinetic model structure and minimum number of data-driven model parameters that can accurately represent multiple data sets over a broad spectrum of process operating conditions. Through this hybrid modelling and automatic structure identification framework, a highly accurate mathematical model was constructed to simulate and optimise an algal lutein production process. Performance of this hybrid model for long-term predictive modelling, optimisation, and online self-calibration is demonstrated and thoroughly discussed, indicating its significant potential for future industrial application.

Responsive Economic Model Predictive Control for Next-Generation Manufacturing

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types would advance the move toward artificial intelligence properties for this controller beyond those which it has today and would provide new thoughts on interpretability and verification for the controller. This work provides theoretical studies which relate nonlinear systems considerations for EMPC to these higher-level concepts using two ideas for EMPC formulations motivated by specific situations related to self-modification of a control design after human perceptions of the process response are received and to controller handling of anomalies.