Concurrency-Aware Process Model Forecasting with Causal Nets

Process Model Forecasting (PMF) aims to predict how the control-flow structure of a process evolves over time by modeling the temporal dynamics of directly-follows (DF) relations, complementing predictive process monitoring that focuses on single-case prefixes. Prior benchmarks show that machine learning and deep learning models provide only modest gains over statistical baselines, mainly due to the sparsity and heterogeneity of the DF time series. We investigate Time Series Foundation Models (TSFMs), large pre-trained models for generic time series, as an alternative for PMF. Using DF time series derived from real-life event logs, we compare zero-shot use of TSFMs, without additional training, with fine-tuned variants adapted on PMF-specific data. TSFMs generally achieve lower forecasting errors (MAE and RMSE) than traditional and specialized models trained from scratch on the same logs, indicating effective transfer of temporal structure from non-process domains. While fine-tuning can further improve accuracy, the gains are often small and may disappear on smaller or more complex datasets, so zero-shot use remains a strong default. Our study highlights the generalization capability and data efficiency of TSFMs for process-related time series and, to the best of our knowledge, provides the first systematic evaluation of temporal foundation models for PMF.

Operators of service-based systems act on forecasts of how a running execution will continue, and such a forecast is actionable only if its reliability is known. Mainstream deep-learning models for this task are discriminative and deterministic: they emit a single next activity and a single remaining-time estimate, without a distribution to reason over. We instead cast the problem as generative sequence modelling with marked temporal point processes, which define a joint density over the next mark and its inter-event time and therefore deliver predictive distributions by construction. Real event logs violate the simple-point-process assumption these models rest on, since consecutive events frequently carry identical timestamps; we handle such ties explicitly and combine a transformer encoder with a mixture decoder over inter-event times, trained by exact log-likelihood. On ten public logs, the resulting model matches discriminative baselines on point accuracy, dominates them on the calibration and sharpness of remaining-time distributions, and is the cheapest at inference, since a full predictive distribution is obtained in a single forward pass without sampling.

Evaluating the quality of process models discovered from event logs is a fundamental challenge in process mining. Traditional evaluation relies on conformance metrics such as fitness and precision, which are highly sensitive to noise and deviations in event logs and therefore often fail to give a consistent assessment of discovery algorithms. We introduce a model-centric evaluation framework that combines node embeddings with Procrustes alignment to enable cross-graph comparability, since embeddings derived from different graphs reside in distinct vector spaces. The proposed PetriNetGraph method transforms Petri net process models into graph representations compatible with embedding algorithms. Comparing the node embeddings of ground-truth and discovered models through a parameterized cosine distance yields a unified and bounded metric for evaluating process discovery across datasets and methods. We evaluate the framework under static and context-aware scenarios to examine how prior knowledge of activity existence influences the assessment of structural similarity. The framework also integrates a compliance checking mechanism that localizes deviations at the activity level and an entropy-regularized node distance aggregation function that quantifies global deviations across the model. Experiments on nine publicly available event logs show that the approach provides a reliable embedding-based conformance indicator that reflects the behavior of fitness and precision. Experiments on synthetic logs with controlled noise levels confirm that it is substantially more robust to log deviations than traditional conformance metrics, PetriNet2Vec, and its dynamic-window and Procrustes-aligned variants, while remaining sensitive to process model degradation. All implementation details and datasets are publicly available.