Learnable Petri Net Neural Network Using Max-Plus Algebra

Interpretable decision-making algorithms are important when used in the context of production optimization. While concepts like Petri nets are inherently interpretable, they are not straightforwardly learnable. This paper presents a novel approach to transform the Petri net model into a learnable entity. This is accomplished by establishing a relationship between the Petri net description in the event domain, its representation in the max-plus algebra, and a one-layer perceptron neural network. This allows us to apply standard supervised learning methods adapted to the max-plus domain to infer the parameters of the Petri net. To this end, the feed-forward and back-propagation paths are modified to accommodate the differing mathematical operations in the context of max-plus algebra. We apply our approach to a multi-robot handling system with potentially varying processing and operation times. The results show that essential timing parameters can be inferred from data with high precision.