The early detection of delayed cases in business processes is a critical capability for organizations. Predictive process monitoring (PPM) supports this task by using historical event logs to predict the remaining time of ongoing cases, enabling timely interventions to avoid missed deadlines and service level violations. Although remaining time prediction has advanced considerably through sophisticated deep learning architectures, little is known about the intrinsic difficulty of delay detection itself. Since performance is typically assessed using aggregate metrics, prior work provides limited insight into how models perform across the target distribution, especially on the operationally most critical cases with large delays. In this paper, we address this gap by analyzing the difficulty of delay detection. Across 14 event logs, we show that remaining times are typically strongly right-skewed, with only a small fraction of cases exhibiting large delays. Existing models capture the mode of this distribution well but perform poorly on high-delay cases. We further uncover pronounced heteroscedasticity, showing that predictive uncertainty increases with delay magnitude. Based on these findings, we evaluate approaches to mitigate the imbalance problem, but find only limited benefits, suggesting that the key underlying problem may not be imbalance but higher uncertainty associated with delayed cases. We show that this correlation can be exploited to substantially improve the identification of delayed cases. Overall, our work provides new insights into the sources of difficulty in delay detection and identifies uncertainty-aware modeling as a promising direction for future PPM research.
Figures & tables
Figure 1: BPIC20PTC distribution of ground-truth and predicted remaining times (in days), with average error and heteroscedastic uncertainty per target range.
Case duration
Case duration
Event log
Cases
Events
Avg.
Max
γ
Event log
Cases
Events
Avg.
Max
γ
P2P
608
9119
21.5
109.4
2.8
Helpdesk
4580
21348
40.9
60.0
-0.1
BPIC17W
30276
240854
12.7
288.9
4.2
Sepsis
1050
15214
28.5
422.3
3.0
BPIC15-1
1199
52217
95.9
1486.0
5.2
BPIC20ID
6449
72151
86.5
742.0
3.5
BPIC15-2
832
44354
160.3
1326.0
3.2
BPIC20DD
10500
56437
11.5
469.2
11.5
BPIC15-3
1409
59681
62.2
1512.0
10.0
BPIC20PTC
2099
18246
36.8
328.2
4.0
Table 1: Characteristics of the 14 event logs used for evaluation. Case duration is in days. γ denotes the skewness of the remaining-time distribution.
Dataset
ρ(y,∣e∣)
ρ(y,PISurv)
Dataset
ρ(y,∣e∣)
ρ(y,PISurv)
P2P
0.89
0.46
Helpdesk
−0.41
−0.53
BPIC17W
0.38
−0.43
Sepsis
0.51
0.39
BPIC15-1
0.30
0.55
BPIC20ID
0.64
0.80
BPIC15-2
−0.20
−0.22
BPIC20DD
0.47
0.21
BPIC15-3
0.68
0.64
BPIC20PTC
0.56
0.67
BPIC15-4
−0.69
0.09
BPIC20TPD
0.61
0.68
Table 2: Spearman correlation between ground-truth remaining time y and (i) absolute prediction error ∣e∣ and (ii) prediction interval (PI) width produced by the survival model (Surv).
Figure 2: BPIC20PTC target distribution for various configurations of SMOGN.
Mode
Average Ranks (lower is better)
Significant Performance Differences (Wilcoxon signed-rank test p−values )
Many
Vanilla (1.64), CSW (2.14), EAL (2.36), BMSE (3.86), SERA (5.00)
Vanilla > SERA (0.001); CSW > SERA (0.006); EAL > SERA (0.015)
Medium
CSW (2.21), BMSE (2.36), EAL (2.64), Vanilla (2.86), SERA (4.93)
CSW > SERA (0.012); BMSE > SERA (0.020)
Few
SERA (1.00), BMSE (2.14), CSW (3.57), EAL (3.79), Vanilla (4.50)
Vanilla vs BMSE (0.042); SERA > Vanilla (0.000); SERA > CSW (0.020); SERA > EAL (0.009)
All
EAL (1.93), CSW (2.00), Vanilla (2.36), BMSE (3.71), SERA (5.00)
Vanilla > SERA (0.015); CSW > SERA (0.004); EAL > SERA (0.003)
Table 3: Comparison of algorithm-level approaches using average ranks (lower is better) and significant pairwise differences identified by the Wilcoxon signed-rank test. Results are reported for nMAE across target regions.
Figure 3: Distribution of nMAE across datasets for algorithm-level imbalanced regression approaches, analyzed across different target-frequency regions.
Figure 4: Uncertainty-aware delay detection pipeline using survival-based predictions and a tabular classifier.
Baseline Classifier
Uncertainty-Aware Model
Dataset
Recall
Precision
F1-Score
PRAUC
Recall
Precision
F1-Score
PRAUC
P2P
0.11
0.99
0.20
0.74
0.83
0.95
0.89
0.91
BPIC17W
0.34
0.48
0.40
0.38
0.59
0.77
0.67
0.59
BPIC15-1
0.49
0.34
0.39
0.23
0.66
0.40
0.49
0.30
BPIC15-2
0.38
0.11
0.17
0.07
0.75
0.12
0.21
0.10
BPIC15-3
0.31
0.39
0.34
0.23
0.65
0.65
0.65
0.48
Table 4: Delay detection performance (threshold q=0.8 ). Average Recall, Precision, F1-score, and PR-AUC over five random seeds for baseline and uncertainty-aware models.
Predictive Process Monitoring (PPM) forecasts how ongoing organizational processes unfold, enabling information systems to move beyond execution support toward proactive analysis and monitoring. Although deep learning has improved prediction accuracy in PPM, most approaches follow a single-task learning (STL) setup, training a separate model per task. This increases maintenance effort and overlooks potential synergies. Multi-task learning (MTL), which jointly learns multiple prediction targets in one model, offers a promising alternative, yet its effectiveness in PPM remains underexplored. It remains unclear whether and under which settings MTL improves upon STL, which prediction tasks benefit most from joint learning, which task combinations are particularly synergistic, and if and how tasks should be balanced. To fill this gap, we present the first comprehensive empirical study of MTL for PPM, evaluating a variety of task combinations, neural architectures, and optimization methods. Overall, our results position MTL as a strong paradigm for PPM: we see substantial improvements in next-activity prediction and inherent mitigation of class imbalance using MTL, while task balancing is especially critical under low-capacity models.
Lukas Kirchdorfer, Keyvan Amiri Elyasi, Heiner Stuckenschmidt
Predictive Process Monitoring (PPM) enables organizations to forecast future process behavior, such as the next activity and remaining time of ongoing cases. In practice, three conditions cause existing methods to degrade, namely data scarcity, high process entropy and distributional shift. While Foundation Models (FMs), especially Large Language Models (LLMs), offer a new paradigm through broad sequential reasoning, adapting them to multi-task PPM under these conditions remains an open challenge. Existing FM-based approaches either lack mechanisms for handling distributional shift or rely on direct regression heads that can be structurally misaligned with continuous time prediction tasks. This paper introduces D-TAIA (Domain-aware Training and Attention-based Inference Architecture), a framework for a joint next activity and remaining time prediction task via parameter-efficient fine-tuning of an FM backbone. Our approach combines domain-aware triplet loss (DATL) pre-training with FAISS-based nearest neighbor retrieval for remaining time prediction, and adopts the TAIA inference strategy to preserve pre-trained sequential reasoning during fine-tuning. Evaluated across four real-world event logs, D-TAIA consistently shows SOTA or competitive performance compared to a fine-tuned LLM and a recurrent neural network baseline. Ablation studies confirm that techniques from NLP and computer vision can be transferred effectively to PPM with only a 10M-parameter backbone, though component contributions vary by dataset entropy.
Sjoerd van Straten, Christine Jacob, Marwan Hassani
Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands · Department of Mathematics and Computer Science, University of Wuppertal, Germany
Accurate delivery delay prediction is critical for maintaining operational efficiency and customer satisfaction across modern supply chains. Yet the increasing complexity of logistics networks, spanning multimodal transportation, cross-country routing, and pronounced regional variability, makes this prediction task inherently challenging. This paper introduces a multi-task deep learning model for delivery delay duration prediction in the presence of significant imbalanced data, where delayed shipments are rare but operationally consequential. The model embeds high-dimensional shipment features with dedicated embedding layers for tabular data, and then uses a classification-then-regression strategy to predict the delivery delay duration for on-time and delayed shipments. Unlike sequential pipelines, this approach enables end-to-end training, improves the detection of delayed cases, and supports probabilistic forecasting for uncertainty-aware decision making. The proposed approach is evaluated on a large-scale real-world dataset from an industrial partner, comprising more than 10 million historical shipment records across four major source locations with distinct regional characteristics. The proposed model is compared with traditional machine learning methods. Experimental results show that the proposed method achieves a mean absolute error of 0.67-0.91 days for delayed-shipment predictions, outperforming single-step tree-based regression baselines by 41-64% and two-step classify-then-regress tree-based models by 15-35%. These gains demonstrate the effectiveness of the proposed model in operational delivery delay forecasting under highly imbalanced and heterogeneous conditions.
Stefan Faulkner, Reza Zandehshahvar, Vahid Eghbal Akhlaghi +3
NSF Artificial Intelligence Institute for Advances in Optimization, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA · Kinaxis