Another form of domain knowledge that has been rarely utilized is the process structure. Process structure, i.e., the arrangement of operating units within a production plant, is a valuable piece of information as the plant configuration is known to influence the behavior of the entire plant and the individual operating units [5]. In [6, 7], the authors designed the structures of their data-driven models to reflect the configuration of the process networks. They used an NN to represent each operating unit and joined the NNs based on the physical connections within the system. Despite the improvement in modelling accuracy, the proposed frameworks in [6, 7] assume a unidirectional flow of materials, i.e., from upstream to downstream, and therefore may not work well for systems with recycles.
To handle the presence of recycle streams, we propose to represent the system as a process variable digraph and use graph neural networks — namely, Graph Convolutional Network (GCN), a special type of NN tailored for graph data, for modelling. Specifically, we developed a spatial temporal graph neural network (STGNN), comprising a GCN and Long Short-Term Memory (LSTM) network, termed ‘GCN-LSTM’, to capture the spatial-temporal dependencies in a chemical process network with recycles. The GCN-LSTM models, compared to their LSTM counterparts, demonstrated improved accuracy of up to 64%, especially when given limited training data. Furthermore, to improve the computational efficiency of the training process, the graph structure was refined using the transitive reduction method to reduce its complexity. A reduction of 29.6% in training time was observed when the transitively reduced graph was used. Our study demonstrated the feasibility of using STGNNs to model complex chemical processes. The improved performance of the proposed GCN-LSTM model in small-data regimes provides an alternative to address the issue of data scarcity in the practical implementation of data-driven models.
References:
[1] Z. Wu et al., "A tutorial review of machine learning-based model predictive control methods," Reviews in Chemical Engineering, early access, doi: 10.1515/revce-2024-0055.
[2] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, "Physics-informed machine learning," Nature Reviews Physics, vol. 3, no. 6, pp. 422-440, 2021.
[3] M. Raissi, P. Perdikaris, and G. E. Karniadakis, "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, vol. 378, pp. 686-707, 2019.
[4] Y. Zheng, C. Hu, X. Wang, and Z. Wu, "Physics-informed recurrent neural network modeling for predictive control of nonlinear processes," Journal of Process Control, vol. 128, p. 103005, 2023.
[5] R. Turton, Analysis, Synthesis, and Design of Chemical Processes (no. v. 1). Prentice Hall, 2003.
[6] Z. Wu, D. Rincon, and P. D. Christofides, "Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes," Journal of Process Control, vol. 89, pp. 74-84, 2020.
[7] L. B. d. Giuli, A. L. Bella, and R. Scattolini, "Physics-Informed Neural Network Modeling and Predictive Control of District Heating Systems," IEEE Transactions on Control Systems Technology, vol. 32, no. 4, pp. 1182-1195, 2024.