Soft sensors estimate process variables that are difficult or impossible to measure directly by using mathematical models and available sensor data, e.g., product concentrations. Machine learning-based approaches have become popular for soft sensing tasks. These approaches offer automatic modeling using historical process data but lack basic process information, such as the process topology. This can lead to (1) modeling of correlations instead of causation between process measurements, (2) model deterioration in deployment due to unseen process scenarios, and (3) large data requirements. To overcome these shortcomings, we propose a novel ML modeling approach incorporating the process topology into soft sensor models for improved spatio-temporal modeling. For this, we propose process topology-aware graph neural networks. We combine process topology and sensor data by representing process data in a directed graph and leverage these process graphs to train graph neural networks. Our method demonstrates enhanced model robustness, reduced data requirements, and more intuitive data representations compared to standard black-box machine learning modeling approaches. Overall, this work introduces a new paradigm for soft sensing by directly embedding process information into the data, paving the way for more efficient and reliable digital twin applications.

Reinforcement learning has shown some success in automating process design by integrating data-driven models that interact with process simulators to learn to build process flowsheets iteratively. However, one major challenge in the learning process is that the reinforcement learning agent demands numerous process simulations in rigorous process simulators, thereby requiring long simulation times and expensive computational power. We propose employing transfer learning to enhance the reinforcement learning process in process design. This study examines two transfer learning strategies: (i) transferring knowledge from shortcut process simulators to rigorous simulators, and (ii) transferring knowledge from process variational autoencoders (VAEs). Our findings reveal that appropriate transfer learning can significantly improve both learning efficiency and convergence scores. However, transfer learning can also negatively impact the learning process when there are substantial discrepancies in decision range and reward function. This suggests that pre-trained process data should match the complexity of the fine-tuning task.

Multiscale modeling of catalytical chemical reactors typically results in solving a system of partial differential equations (PDEs) or ordinary differential equations (ODEs). Despite significant progress, the numerical solution of such PDE or ODE systems is still a computational bottleneck. In the past, deep learning techniques have gained attention for developing surrogate models in chemical engineering. Also, hybrid models and physics-informed neural networks (PINNs) have been developed to integrate physical knowledge and data-driven approaches. However, it is often unclear how such modeling approaches compare for specific case studies. In this study, we investigate and compare state-of-the-art surrogate and hybrid models for the spatial evolution of the state variables in a packetbed reactor for methanol production. Firstly, we develop a tailored hybrid model based on PINNs, thereby seamlessly integrating physical knowledge and data. Secondly, we investigate a recently-developed time-series transformer model to learn the spatial evolution of the state variables. As a benchmark model, we train a traditional multilayer perceptron (MLP) and compare the models to a standard numerical integration technique. We achieve orders of magnitude in speedup using MLPs and PINNs when compared to classical ODE solvers, while maintaining high levels of accuracy in modeling the underlying system.