(403d) Development of a Hybrid Model to Describe the Dynamics of a Partially Known System

Mathematical modeling plays a critical role in the design, optimization, and control of chemical processes [1]. In order to apply models to a wide range of process conditions, it is often desirable to describe the system using a first principles model. However, the formulation of such models can be challenging if the underlying mechanisms are only partially understood [2, 3, 4]. Under such circumstances, a data-driven model can be built from measured data, and the resultant model can describe the system adequately, even when mechanistic understanding is limited [5, 6]. However, a data-driven model has narrow applicability as it is tailored to describe the input-output relationships contained in the training datasets [7]. As an alternative, a hybrid modeling approach that combines first-principles and data-driven modeling has been proposed to describe a partially known process [7, 8]. Hybrid models have better prediction capabilities than first-principle models, and thus will have better generalizability and interpretability than data-driven models.

In this work, we proposed a new numerical scheme to construct a hybrid model for a system that has partial mechanistic information. A hybrid model was constructed by introducing correction terms for estimating process-model mismatches between mechanistic model predictions and experimental measurements [9]. Here, a nominal model refers to a mechanistic model based on our prior knowledge of the system of interest, and the correction terms are assigned to differential equations of the nominal model so that the resultant hybrid model has improved prediction capabilities. The proposed methodology consists of three steps. First, observability analysis was performed for the nominal model to determine a subset of states that are observable from the available measurements. This step is critical to reduce the computational load of the estimation and avoid potential overfitting issues. Second, the available measurements were used to estimate the correction terms associated with the observable states through solving a L2-regularized least-squares problem [10]. Lastly, once the correction terms were estimated, the trajectories of the states were simulated based on the hybrid model. Then, an artificial neural network (ANN) model was developed for predicting the correction terms for a given set of state values, and the developed ANN was used within the hybrid model. Through incorporating the ANN, the hybrid model was able to predict dynamic responses to an input, which was not in the measurement data used for estimating the correction terms.

The validity of the proposed method was demonstrated by constructing a hybrid model for the NFκB signaling pathway induced by both lipopolysaccharide (LPS) and brefeldin A (BFA). The signaling dynamics induced by LPS have been well studied, and hence, a previously published model was used as the nominal (mechanistic) model [11]. Since the dynamics initiated by BFA are less characterized, the nominal model could not capture the signaling dynamics induced by both BFA and LPS well. By implementing the proposed methodology, the developed hybrid model was able to predict the NFκB signaling dynamics induced by both LPS and BFA accurately.

References

[1] Hangos, K. M.; Cameron, I.T. Process modelling and model analysis. Academic Press: London, 2001.

[2] Cho, K.-H.; Choo, S.-M.; Jung, S.H.; Kim, J.-R.; Choi, H.-S.; Kim, J. Reverse engineering of gene regulatory networks, IET Systems Biology 2007, 1, 149 - 163.

[3] Willis, M.J.; von Stosch, M. Inference of chemical reaction networks using mixed integer linear programming, Computers and Chemical Engineering 2016, 90, 31-43.

[4] Lee, D.; Jayaraman, A.; Kwon, J.S. Identification of a time-varying intracellular signalling model through data clustering and parameter selection: application to NF-κB signalling pathway induced by LPS in the presence of BFA, IET Systems Biology 2019, 13, 169-179.

[5] Thompson, M.L.; Kramer, M.A. Modeling chemical processes using prior knowledge and neural networks, AIChE Journal 1994, 40, 1328-1340

[6] Narasingam,A.; Kwon, J.S. Development of local dynamic mode decomposition with control: Application to model predictive control of hydraulic fracturing, Computers & Chemical Engineering 2017, 106, 501-511.

[7] von Stosch, M.; Oliveira, R.; Joana Peres, J.; de Azevedo, S.F. Hybrid semi-parametric modeling in process systems engineering: Past, present and future. Computers & Chemical Engineering 2014, 60, 86-101.

[8] Faizan Bangi, M.S.; Kwon, J.S. Deep hybrid modeling of chemical process: Application to hydraulic fracturing, Computers & Chemical Engineering 2020, 134, 106696.

[9] Engelhardt, B.; Fröhlich H.; Kschischo, M. Learning (from) the errors of a systems biology model, Scientific Reports 2016, 6, 20772.

[10] Howsmon, D.P.; Hahn, J. Regularization Techniques to Overcome Overparameterization of Complex Biochemical Reaction Networks, IEEE Life Sciences Letters 2016, 2, 31 – 34.

[11] Lee, D.; Ding, Y.; Jayaraman, A.; Kwon, J.S. Mathematical modeling and parameter estimation of intracellular signaling pathway: application to LPS-induced NFκB activation and TNFα production in macrophages, Processes 2018, 6, 21.