Wasserstein Weight Estimation for Stochastic Petri Nets

Traditional process models like Petri nets effectively describe the control flow of processes but fail to capture stochastic information such as choice likelihoods. To address this, Stochastic Labeled Petri Nets (SPNs) have recently gained attention, extending Petri nets with transition weights that allow to associate executions with probabilities. The language of an SPN thereby becomes a probability distribution over traces (i.e., sequences of activities). To assess an SPN's quality, Earth Mover's Stochastic Conformance (EMSC) emerged as a natural metric that measures the similarity of the SPN's trace distribution to the observed real-world distribution. In this paper, we propose a locally optimal approach for fine-tuning (or finding) transitions weights to maximize an SPN's EMSC. Leveraging the relationship between EMSC and the Wasserstein distance, which recently gained attention as a loss function in machine learning, we compute subgradients for EMSC to optimize transition weights via subgradient descent. Besides, we propose a straightforward solution to handle models that allow for infinitely many traces. Our optimization approach is broadly applicable for EMSC that is, for EMSC using arbitrary trace-to-trace distances-unlike existing works that either to not explicitly consider EMSC or only special variants. We demonstrate the applicability of our approach on several real-life event logs and discovery algorithms, comparing it to state-of-the-art stochastic process discovery methods and a recent full automated simulation approach.