(386c) Predictive Control of Chemical Processes Using Physics-Informed Neural Network Models

Data-driven modeling methods in model predictive control (MPC) have recently gained much interest from chemical engineering (Bangi and Kwon (2020), Shah et al. (2022)). Purely data-driven models usually require a large amount of high-quality data, which is often expensive or time-consuming to collect. When there is insufficient data, machine learning (ML) models lack robustness and could potentially overfit, leading to poor generalizability and inaccurate predictions. This could potentially hinder the applicability of ML models in MPC, especially in performance critical applications. To address this issue, physics-informed modeling approaches can be developed to improve the generalization performance of machine learning models by embedding the knowledge of physical laws in the learning process. In view of the favorable results engendered by implementing regularization techniques in ML tasks, and in addition to constraining the magnitude of the network weights, it is proposed to supplement the training process by harnessing and embedding a priori mechanistic knowledge expressed in the form of ordinary differential equation (ODE) or partial differential equation (PDE) directly into the loss function as soft penalty constraints, thereby making the learning algorithm physics-informed (PI).

In this work, we propose to utilize physics-informed recurrent neural networks (PIRNNs) originally proposed by Raissi et al. (2019) for model predictive control (MPC). This involves incorporating prior knowledge of the chemical process (e.g., governing equations) into the loss function during training, effectively imposing a soft-penalty constraint (termed the forward problem of PIRNN). This will prevent trained PIRNN from making physical infeasible predictions and improve its generalization performance. In the low-data regime, this will also amplify the information content of the data because the hypothesis space is significantly constrained to those consistent with the physics of the process. In this work, we develop the methodology of forward PIRNN, and provide a theoretical analysis on its generalization performance. Furthermore, in solving forward problems, the process parameters are usually well-defined and are known precisely. However, in many real-world processes, the values of the process parameters are often unknown and evolve constantly over time (Wu et al. (2019), Mainworm et al. (2021)). Motivated by this consideration, we further develop an inverse PIRNN modeling method and incorporate it with online machine learning to estimate unknown process parameters for nonlinear systems in real time. Specifically, we estimate unknown parameters using most recently acquired data and the PIRNN model is updated online to better conform to evolving process dynamics. Finally, the proposed PIRNN modeling method is applied to a batch crystallization process to demonstrate its superiority compared to purely data-driven ML models.

References

Bangi, M.S.F., Kwon, J.S.I., 2020. Deep hybrid modeling of chemical process: Application to hydraulic fracturing. Computers & Chemical Engineering 134, 106696.

Maiworm, M., Limon, D., Findeisen, R., 2021. Online learning-based model predictive control with gaussian process models and stability guarantees. International Journal of Robust and Nonlinear Control 31, 8785–8812

Raissi, M., Perdikaris, P., Karniadakis, G.E., 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics 378, 686–707

Shah, P., Sheriff, M.Z., Bangi, M.S.F., Kravaris, C., Kwon, J.S.I., Botre, C., Hirota, J., 2022. Deep neural network-based hybrid modeling and experimental validation for an industry-scale fermentation process: Identification of time-varying dependencies among parameters. Chemical Engineering Journal 441, 135643

Wu, Z., Rincon, D., Christofides, P.D., 2019. Real-time adaptive machine-learning-based predictive control of nonlinear processes. Industrial & Engineering Chemistry Research 59, 2275–2290