Concurrency-Aware Process Model Forecasting with Causal Nets

Yongbo Yu; Jari Peeperkorn; Johannes De Smedt; Jochen De Weerdt

cs.LGSep 18, 2026

Concurrency-Aware Process Model Forecasting with Causal Nets

Authors: Yongbo Yu, Jari Peeperkorn, Johannes De Smedt, Jochen De Weerdt

Organizations: Research Center for Information Systems Engineering (LIRIS), KU Leuven, Leuven, Belgium

Abstract

Process model forecasting (PMF) aims to predict the process model that will characterize a future period, thereby providing a process-level view of how behavior is expected to evolve. Existing PMF methods, however, forecast directly-follows graphs, which cannot explicitly represent concurrency. We extend PMF to causal nets by forecasting time series of relation and binding counts and using these forecasts to reconstruct future process models with AND/XOR semantics. To evaluate the resulting models, we introduce a protocol that accounts for partial traces and constructs the workflow nets required for conformance checking. Experiments on four event logs show that the forecasted models achieve conformance levels close to those of models re-mined from observations in the corresponding future windows. They also outperform static discovery baselines, which retain high precision on the structurally stable log but exhibit substantial precision losses on the other three logs. Filtering infrequent bindings improves most conformance metrics, although it also removes much of the concurrent behavior captured by the models.

Figures & tables

Panel of Figure 1 — Figure 1. The pipeline extracts daily counts of activities, direct successions, length-two loops, and input and output bindings. Each series is forecast by Chronos-2, and the predicted window totals are used to reconstruct a causal net following Fodina’s construction rules. The net represents concurrency and choice through bindings and is converted to a workflow net for evaluation. The dashed path shows reference models constructed from observed counts or mined directly from event logs.

	Log					Daily counts, by relation family					Eval. windows ( $h=7$ d, 1-d stride)
	Cases	Events	Act.	Var.	Med. (d)	$A$	$AB$	$ABA$	$\mathit{IB}$	$\mathit{OB}$	$N$	Cases/win	Compl. %	Pref.-tr. %	Suf.-tr. %	Mid.-cr. %
BPI2017	40,229	248,236	10	29	13.9	10	21	0	22	29	58	1,882	12.4	44.2	32.4	10.9
BPI2019	197,521	1,298,887	32	741	57.1	32	149	11	219	249	55	14,855	0 6.1	47.3	19.9	26.7
Sepsis	999	16,009	18	790	0 5.1	18	137	21	252	280	64	17	18.0	43.4	22.5	16.2
Hosp. Bill.	78,848	439,278	17	301	50.1	17	71	8	87	87	139	1,707	23.1	35.1	12.5	29.4

Table 1. Characteristics of the four preprocessed event logs, their daily relation and binding count series, and the composition of their 7-day evaluation windows. A case is active in a window if it has at least one event in the window, and the four life-cycle shares are computed over active cases and sum to approximately

100\%

per column (due to rounding).

Figure 2. Forecast workflow net for BPI2017, window 1, with the binding filter disabled (

\tau_{\mathrm{PAT}}=-1.0

), as constructed (a) and after

\tau

-reduction (b). Circles are places, with the source in green and the sink in pink. Rounded rectangles are visible transitions, black bars are the silent transitions that carry an input (green) or output (blue) binding, and the labels show the forecast frequencies.

			Structure	Token replay				Alignment			Entropic relevance
Log	Model	$\boldsymbol{\tau_{\mathrm{PAT}}}$	AND bind. %	fitness	precision	no-miss. %	ETC cov.	fitness	precision	zero-cost %	bits/trace	fit. ratio	coverage
BPI2017	Forecast	$-1.0$	$10.9_{\pm 0.6\phantom{0}}$	$0.915_{\pm 0.015}$	$0.880_{\pm 0.014}$	$\phantom{0}99.6_{\pm 0.2\phantom{0}}$	$100.0_{\pm 0.0\phantom{0}}$	$0.979_{\pm 0.024}$	$0.841_{\pm 0.017}$	$\phantom{0}87.8_{\pm 13.2}$	$\phantom{0}0.663_{\pm 0.07\phantom{0}}$	$0.9996_{\pm 0.000}$	$58/58$
	Forecast	$0.0$	$\phantom{0}0.0_{\pm 0.0\phantom{0}}$	$0.985_{\pm 0.018}$	$0.999_{\pm 0.007}$	$\phantom{0}99.6_{\pm 0.2\phantom{0}}$	$100.0_{\pm 0.0\phantom{0}}$	$0.979_{\pm 0.024}$	$0.999_{\pm 0.007}$	$\phantom{0}87.8_{\pm 13.2}$	$\phantom{0}0.663_{\pm 0.07\phantom{0}}$	$0.9996_{\pm 0.000}$	$58/58$
	Re-mined	$-1.0$	$\phantom{0}3.1_{\pm 1.7\phantom{0}}$	$0.937_{\pm 0.019}$	$0.897_{\pm 0.025}$	$\phantom{0}99.9_{\pm 0.1\phantom{0}}$	$100.0_{\pm 0.0\phantom{0}}$	$0.988_{\pm 0.014}$	$0.893_{\pm 0.030}$	$\phantom{0}88.2_{\pm 13.2}$	$\phantom{0}0.691_{\pm 0.07\phantom{0}}$	$1.0000_{\pm 0.000}$	$58/58$
	Re-mined	$0.0$	$\phantom{0}0.0_{\pm 0.0\phantom{0}}$	$0.985_{\pm 0.017}$	$0.999_{\pm 0.001}$	$\phantom{0}99.9_{\pm 0.1\phantom{0}}$	$100.0_{\pm 0.0\phantom{0}}$	$0.988_{\pm 0.014}$	$0.999_{\pm 0.001}$	$\phantom{0}88.2_{\pm 13.2}$	$\phantom{0}0.691_{\pm 0.07\phantom{0}}$	$1.0000_{\pm 0.000}$	$58/58$
	Direct-mined	$0.0$	$\phantom{0}0.0_{\pm 0.0\phantom{0}}$	$0.972_{\pm 0.035}$	$0.997_{\pm 0.006}$	$\phantom{0}88.5_{\pm 29.9}$	$\phantom{0}96.7_{\pm 8.7\phantom{0}}$	$0.971_{\pm 0.045}$	$0.997_{\pm 0.006}$	$\phantom{0}76.9_{\pm 29.6}$	$\phantom{0}0.798_{\pm 0.32\phantom{0}}$	$0.9955_{\pm 0.012}$	$58/58$

Table 2. Binding structure and case-complete conformance. Conformance uses

\tau

-reduced workflow nets and is reported as

\mathrm{mean}_{\pm\sigma}

over tractable units. AND bind. is the mean per-window percentage of retained input and output bindings with multiple members. Forecast and Re-mined use both thresholds; Direct-mined and Static use

\tau_{\mathrm{PAT}}=0.0

. Lower ER bits/trace is better. ETC cov. is fit-prefix mass. fit. ratio is the automaton-accepted trace share. no-miss. ignores remaining tokens. zero-cost requires completion to the final marking without deviations. coverage is completed/attempted ER units. † marks fewer than two ER values.

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Time Series Foundation Models for Process Model Forecasting

Yongbo Yu, Jari Peeperkorn, Johannes De Smedt, Jochen De Weerdt

Research Center for Information Systems Engineering (LIRIS), KU Leuven, Belgium

Zero-Shot Time Series Forecasting Process Mining Time Series Forecasting Time-Series Foundation Models

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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.

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