Tai Xuan Tan

Tai Xuan Tan, Alexander Mitsos, Eike Cramer

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.

Jan Pavšek, Alexander Mitsos, Manuel Dahmen et al.

We propose a machine learning (ML) architecture to better capture the dependency of thermodynamic properties on the independent states. When predicting state-dependent thermodynamic properties, ML models need to account for both molecular structure and the thermodynamic state, described by independent variables, typically temperature, pressure, and composition. Modern molecular ML models typically include state information by adding it to molecular fingerprint vectors or by embedding explicit (semi-empirical) thermodynamic relations. Here, we propose to rather split the information processing on the molecular structure and the dependency on states into two separate network channels: a graph neural network and a multilayer perceptron, whose output is combined by a dot product. We refer to our approach as DeepEOSNet, as this idea is based on the DeepONet architecture [Lu et al. (2021), Nat. Mach. Intell.]: instead of operators, we learn state dependencies, with the possibility to predict equation of states (EOS). We investigate the predictive performance of DeepEOSNet by means of three case studies, which include the prediction of vapor pressure as a function of temperature, and mixture molar volume as a function of composition, temperature, and pressure. Our results show superior performance of DeepEOSNet for predicting vapor pressure and comparable performance for predicting mixture molar volume compared to state-of-research graph-based thermodynamic prediction models from our earlier works. In fact, we see large potential of DeepEOSNet in cases where data is sparse in the state domain and the output function is structurally similar across different molecules. The concept of DeepEOSNet can easily be transferred to other ML architectures in molecular context, and thus provides a viable option for property prediction.