Deep Neural Networks, Cellular Automata and Petri Nets: Useful Hybrids for Smart Manufacturing

In the era of Industry 4.0 and beyond, intelligent and reliable models are vital for processes and assets. Models in smart manufacturing involve combining knowledge-based and data-driven methods with discrete and continuous modelling components. Formalism choice determines models' strengths and weaknesses in accuracy, efficiency, robustness, and explainability. Hybrid models seem to be the only way to address the complexity of modern industrial systems with respect to different and conflicting quality criteria. This study focuses on three paradigms: Petri nets, cellular automata, and neural network driven deep learning. We create four hybrids: Petri nets controlling deep neural networks, and vice versa; cellular automata controlling deep neural networks, and vice versa. These hybrids combine explainable discrete models with continuous black-box models, enhancing either explainability with robustness or elevating accuracy with efficiency. The flexibility of these and similar hybrids enable enhancement of the scope and quality of modeling and simulation in smart manufacturing.