(457g) Graph-Based Symmetry Detection and Elimination for Optimal Process Control of Numbered-up Modular Facilities

As the demand for dynamic flexibility in renewable energy resource allocation and chemical production facilities is increasing, distributed modular manufacturing has become more and more popular due to its advantages of reduced transportation costs, increased resiliency, and improved agile response to sudden changes. Modular production units[1], which are small-scale, standardized process units, are a pivotal technology for distributed manufacturing because of easy assemblability and mobility. To achieve a desired facility throughput, modules need to be numbered-up. Real-time model predictive control of numbered-up modular systems is challenging due to the increased computing cost resulting from changes in the optimization problem structure. One such challenge is associated with the inherent symmetries appearing in the nonlinear optimal control problem. Our group recently defined theoretical criteria for the presence of symmetry in modular systems[2]. However, at present applying these criteria for symmetry breaking must either be done manually or make use of computationally expensive automorphism detection tools.

In this work, we present an automated approach to detect symmetric structure of complex numbered-up modular systems using network theory and graph neural networks (GNN)[3]. We convert the original optimal control problem into a graph structure by defining the nodes or node features as control input, states, and outputs, and the edges or edge features based on their physical relationships, such as heat and mass balances. Training datasets are obtained by applying the symmetry criteria to a wide variety of different set points, disturbances, and initial conditions. After training the GNN model, we obtain the learned node embedding and grouping which represent the elements in the problem space are likely to be symmetrical. Through classifying and labeling the embedding groups based on the symmetry detection from GNN model, we propose one symmetry-breaking approach which removes variables corresponding to nodes that are members of the grouping set from the original optimal control problem formulation.

To demonstrate the efficacy of the proposed approach, we present the control performance of two benchmark systems: the first with three modular nonisothermal CSTR's operating in parallel configurations[2] and the second with two modular CSTRs followed by two separators. Results demonstrate that the trained GNN model efficiently reveals a symmetric automorphism in the graph structure, reflecting that the nodes associated with each undisturbed reactor in both benchmark systems exhibit identical connectivity patterns. Following the symmetry-breaking approach, the number of variables in the optimal control problem decreases significantly, resulting in faster model predictive control solutions. Moreover, the refined GNN demonstrates the capacity to discriminate among various types of modular units by summarizing the characteristics inherent in the embedded grouping, which is beneficial to further study, such as decomposition of multiple modular units with different functions.

[1] M. Baldea, T. F. Edgar, B. L. Stanley, and A. A. Kiss, “Modular manufacturing processes: Status, challenges, and opportunities,” AIChE journal, vol. 63, no. 10, pp. 4262–4272, 2017.

[2] Y. Dai, S. Fay, and A. Allman, “Analysis of model predictive control in numbered-up modular facilities,” Digital Chemical Engineering, vol. 7, p. 100088, 2023.