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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Exploiting and Predicting System-Wide Behaviors for Predictive Process Monitoring</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Xiaomeng He</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Research Center for Information Systems Engineering (LIRIS), KU Leuven</institution>
          ,
          <addr-line>Naamsestraat 69, 3000 Leuven</addr-line>
          ,
          <country country="BE">Belgium</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Predictive Process Monitoring (PPM) focuses on forecasting the future progression of ongoing business process instances (cases). Despite growing interest in alternative viewpoints, many PPM approaches still tend to adopt a case-centric perspective inherited from traditional process mining, using an incomplete trace of a single case to generate case-specific predictions. However, this perspective overlooks system-level dynamics in both the input and output dimensions. Specifically, the exclusive reliance on intra-case data as inputs limits predictive accuracy by neglecting valuable contextual information from other concurrently running cases. Similarly, the ifeld's predominant focus on case-level predictions has constrained the exploration of system-level predictions, such as system-wide event stream modeling or system load forecasting, which may enable applications including anomaly detection and resource allocation. This proposal aims to address these limitations by enhancing caselevel prediction through the automated extraction of inter-case dynamics from event logs, and extending PPM to support system-level prediction tasks. Ultimately, we propose to integrate these two research directions into a unified modeling framework that enhances predictions at both the case and system levels, and supports data-driven decision-making and interventions to improve overall system performance.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Predictive Process Monitoring</kwd>
        <kwd>Suxfi Prediction</kwd>
        <kwd>Event Log Prediction</kwd>
        <kwd>Inter-Case Dependencies</kwd>
        <kwd>Deep Learning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Background and Motivation</title>
      <p>
        Business processes supported and executed by information systems generate event data that serve
as the foundation for process mining, a data-driven approach to analyzing and optimizing business
processes [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Predictive Process Monitoring (PPM) is a subfield of process mining that focuses on
developing predictive models to forecast the future progression of ongoing cases [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Accurate PPM
models can ofer valuable operational support by, for example, alerting staf of potential delays or
recommending actions based on predicted outcomes.
      </p>
      <p>
        Within PPM research, an instance of a process execution is referred to as a case, which comprises a
series of events, each reflecting an executed activity with a timestamp. Events belonging to the same
case are typically temporally ordered to form a trace. The case ID, activity label, and timestamp are
three attributes required to define an event and capture the control-flow perspective of a process. Other
perspectives can be reflected by optional event attributes (e.g., resources) or case attributes (e.g., product
types), forming the basis for the growing interest in data-aware PPM models [
        <xref ref-type="bibr" rid="ref3 ref4 ref5">3, 4, 5</xref>
        ].
      </p>
      <p>
        Inheriting the case-centric view from traditional process mining, PPM approaches conventionally
use the incomplete trace of a single case (trace prefix ) as input, and generate predictions concerning
specific aspects of this given case. The main categories of predictions include next event prediction [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ],
sufix prediction [
        <xref ref-type="bibr" rid="ref4 ref7">4, 7</xref>
        ], remaining time prediction [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ], and outcome prediction [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>However, each case is executed within the broader context of a system, and a strictly case-centric
approach is inherently limited as it overlooks system-level dynamics in both the inputs it considers and
the outputs it seeks to predict.</p>
      <p>
        With respect to input data, the exclusive use of intra-case data has been increasingly identified
as a key limitation [
        <xref ref-type="bibr" rid="ref10 ref11 ref12">10, 11, 12</xref>
        ]. In response, inter-case approaches have emerged that incorporate
dependencies among cases as additional features [
        <xref ref-type="bibr" rid="ref13 ref14 ref15">13, 14, 15</xref>
        ], grounded in the observation that cases
often influence one another or are jointly afected by overarching system conditions. Other lines of work
enrich event logs with external contextual data [
        <xref ref-type="bibr" rid="ref16 ref17">16, 17, 18</xref>
        ] or with the interactions between objects and
events [19, 20]. Our first research objective builds on inter-case PPM by addressing major shortcomings
of existing solutions—reliance on manually selected and engineered features and a predominant focus on
remaining time prediction. We aim to develop methods that automatically capture inter-case dynamics
from event logs for a wider range of predictive tasks.
      </p>
      <p>With respect to model outputs, the case-centric focus is even more pronounced, as case-level
predictions dominate the PPM literature. Few exceptions exist, such as process model forecasting [21]
or Work-In-Progress prediction [22]. Notably, a recent study [23] represents event logs as a single
"traceless" event sequence ordered as being executed, and estimates entropy rates to assess its
predictability. The findings suggest that system-level event sequences exhibit learnable structure, laying
the groundwork for modeling system behavior. In a related line of work, streaming process mining
also treats event streams as an infinite sequence of events [ 24, 25] . System-level predictions, such as
"traceless" event stream modeling or system load forecasting, can enable applications like anomaly
detection and dynamic resource allocation. Our second research objective addresses the current gap in
system-level prediction by developing models capable of forecasting future system behavior.</p>
      <p>Building from the first two objectives, the third research objective aims to enhance decision-making by
integrating system behavior modeling with Prescriptive Process Monitoring (PresPM). PresPM prescribes
interventions (treatment) to optimize process outcomes or eficiency [ 26]. A growing trend in this area is
the application of causal inference to estimate treatment efects by comparing potential outcomes (with
and without treatment) conditioned on features characterizing a case’s current state [27, 28]. Although
most research assumes that treatments afect only the targeted case, this assumption is challenged in
dynamic environments where concurrently running cases may interact. For instance, as noted by [26],
assigning a resource to a delayed case at the expense of others can lead to increased overall delays.
Such inter-case dependencies should be considered to maximize the total net benefit of interventions.
Furthermore, most existing approaches focus on case-level treatments, such as prescribing the next
task or assigning a resource for a case [26]. Cross-case or system-level interventions, like reprioritizing
or reordering cases, have received limited attention, despite their practical importance in real-world
process management. Our third research objective focuses on developing PresPM approaches that
account for inter-case dependencies and enable system-level interventions.</p>
      <p>Based on the background and research objectives, the following three Research Questions (RQs) are
formulated:
• RQ1: What approaches can be developed to automatically extract and utilize inter-case
dependencies from prior process executions to improve case-level predictions?
• RQ2: What approaches can be developed to predict system-level behavior using historical event
data?
• RQ3: How can inter-case dependency mining and system-level prediction be integrated and
extended to support decision-making?</p>
    </sec>
    <sec id="sec-2">
      <title>2. Research Methodology</title>
      <p>This doctoral project is primarily guided by the Design Science Research (DSR) methodology in
information systems [29]. The research process involves identifying the research problem and motivation,
designing a suitable artifact (in this case, a deep learning technique), and demonstrating and evaluating
its utility in addressing the problem.</p>
      <p>This section outlines the planned methodological approach for each research question, along with
the proposed solutions. An overview of the proposed solutions is presented in Figure 1.</p>
      <sec id="sec-2-1">
        <title>2.1. RQ1: What approaches can be developed to automatically extract and utilize inter-case dependencies from prior process executions to improve case-level predictions?</title>
        <p>Motivated by advances in Natural Language Processing (NLP) and the observed similarities between
event logs and natural language text [30], sequential deep learning models have been adopted as efective
tools for PPM [31]. In this context, a trace is modeled as a sequence of events. Following the same
principle, to incorporate inter-case dynamics, we propose representing events from multiple cases as a
single, temporally ordered sequence that reflects the global execution flow of the system, and using this
system-level sequence as an additional input to the model, alongside the trace prefix.</p>
        <p>
          One key challenge is designing a model that can automatically identify relevant inter-case patterns
from this additional input sequence, while efectively filtering noise from the massive information in
preceding events. We will address this by evaluating various deep learning architectures as base models
and designing customized neural network structures to handle the multi-input characteristics of the
tasks. Candidate base architectures include Long Short-Term Memory (LSTM) networks, which are
widely used for PPM tasks [
          <xref ref-type="bibr" rid="ref6">6, 30, 31</xref>
          ], while LSTM with attention [32], Transformer-based models [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]
and the more recent Extended Long Short-Term Memory (xLSTM) [33] will also be investigated for
their superior performance in modeling long sequence.
        </p>
        <p>Integrating heterogeneous input sources including intra- and inter-case information poses another
challenge. Inspired by multimodal deep learning [34], which seeks to integrate data from diverse
sources, distributions, and modalities into a unified representation space, we will explore various data
fusion strategies, ranging from simple concatenation to more sophisticated hierarchical feature fusion
methods [35].</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. RQ2: What approaches can be developed to predict system-level behavior using historical event data?</title>
        <p>As system-level prediction remains a largely underexplored area in business process research, the first
key challenge is defining meaningful prediction targets and establishing robust baselines and evaluation
methods. Following the research on traceless event sequencing [23], we propose representing system
behavior as an (infinite) temporally ordered event sequence, aiming to forecast the sequence of future
events and their timestamps within a specified horizon, based on the sequence of observed consecutive
events. Additionally, predicting system load (measured by the number of active cases over time) is also
of practical relevance (e.g., for resource allocation) and can be formulated as a time series forecasting
problem. Related works include research on Work-In-Progress (WIP) prediction which applies time
series models to estimate future WIP levels with LSTM [36] or Temporal Convolutional Networks [22].</p>
        <p>Modeling the complexity and stochastic behavior of the underlying system is inherently challenging,
particularly when processing and generating exceptionally long and variable-length event sequences.
Recent advances in architectures capable of capturing long-range dependencies in Large Language
Models (LLMs) field, such as Transformer [ 37] and Mamba [38], or difusion models [ 39] as an alternative
to autoregressive generation approaches, provide valuable inspiration and opportunities. Nevertheless,
despite their similarities, event data difers from natural language due to its strong temporal dependencies
and complex interaction patterns embedded in additional case attributes and event attributes, such as
interactions between resources. To efectively capture these characteristics, we aim to adapt modern
neural architectures and develop specialized neural network architectures explicitly tailored to the
structural and temporal nature of event data.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. RQ3: How can inter-case dependency mining and system-level prediction be integrated and extended to support decision-making?</title>
        <p>Building on the findings of RQ1 and RQ2, RQ3 investigates how to integrate case-level predictions
(enriched with inter-case dependencies) and system-level predictions into a unified framework, and
extend system behavior modeling to support decision-making.</p>
        <p>We first aim to develop a unified modeling approach capable of generating both case-level and
system-level predictions. This will be pursued through a Multi-Task Learning (MTL) framework, where
both tasks share representations and parameters. MTL is expected to enhance generalization by allowing
the model to leverage commonalities across related tasks.</p>
        <p>To bridge the gap between prediction and proactive decision-making, we aim to extend system
behavior modeling techniques into a PresPM framework. Inter-case dynamics relate closely to the
broader notion of interference in the causal inference literature. A widely studied approach to handling
interference is network interference [40, 41], where units are connected through a network structure,
and causal inference is conditioned on features extracted from this network.</p>
        <p>In our context, to incorporate inter-case interactions when optimizing case-level metrics, we propose
grounding causal inference on a combination of intra-case features and inter-case features, which are
extracted, for example, from system-level event sequences using neural networks. This approach allows
treatment efect estimation to account for the broader inter-case context in which a case operates.</p>
        <p>To optimize global system-level metrics while considering interactions among cases, we further
propose conditioning treatment efect estimates on representations of the overall system state, such as
system-level event sequences or interaction networks derived from observed event logs. In this setting,
treatments could be prescribed event sequences, including interventions for specific cases (e.g., the next
task to perform) or cross-case interventions (e.g., altering the execution order of multiple cases). The
efects of such interventions will then be estimated by comparing predicted system trajectories, with
and without the prescribed treatment, based on the system behavior model.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Research Progress and Intermediate Results</title>
      <p>For RQ1, an initial artifact has been designed and evaluated, which is an multi-input encoder-decoder
model for the task of sufix prediction. Work is ongoing to refine and extend this artifact. The research
related to RQ2 and RQ3 is currently in the literature review and conceptualization phase.</p>
      <p>The first technique designed for RQ1 adopts an LSTM-based encoder-decoder architecture (Seq2Seq
model). The model takes both trace prefixes and log prefixes as input. The trace prefix captures the
intra-case behavior of the case under prediction, while the log prefix represents a temporally ordered
sequence of events from multiple cases across the entire system. The integration of the log prefix
constitutes the primary novelty of this approach, as it allows the model to learn inter-case dependencies
and system-level patterns in addition to case-specific information. The model architecture employs two
separate LSTM encoders: one for the trace prefix and one for the log prefix. The final hidden states
Model
Trace-based
Seq2Seq model
Integrated</p>
      <p>Seq2Seq model</p>
    </sec>
    <sec id="sec-4">
      <title>4. Future Plan</title>
      <p>from both encoders are concatenated to form a joint context vector. A dual-decoder mechanism is then
used to simultaneously predict the sufix of activity labels and the sufix of timestamps.</p>
      <p>The proposed model has been evaluated on three real-life event logs: BPIC2017, BPIC2019, and BAC.
To assess its efectiveness, the integrated Seq2Seq model is compared against several benchmark models.
A key baseline among them is a trace-based Seq2Seq model, which shares the same encoder-decoder
architecture but uses only the trace prefix as input. Table 1 presents the performance comparison
between the proposed integrated Seq2Seq model and the trace-based baseline across all three datasets.
The integrated model consistently outperforms the trace-based model in activity label sufix prediction.
For timestamp sufix prediction, the integrated model also achieves superior performance in most cases.
It outperforms the baseline on all datasets except BPIC2017 when evaluated using MAE.</p>
    </sec>
    <sec id="sec-5">
      <title>Acknowledgments</title>
      <p>This Ph.D. project is supervised by Prof. dr. Jochen De Weerdt and Prof. dr. Johannes De Smedt from
KU Leuven, and Prof. dr. Seppe vanden Broucke from Ghent University.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author used ChatGPT-4o for grammar and spelling check.
After using this tool, the author reviewed and edited the content as needed and takes full responsibility
for the publication’s content.
future: Leveraging a-priori knowledge in predictive business process monitoring, in: J. Carmona,
G. Engels, A. Kumar (Eds.), Business Process Management, Springer, Cham, 2017, pp. 252–268.
doi:10.1007/978-3-319-65000-5_15.
[18] A. Yeshchenko, F. Durier, K. Revoredo, J. Mendling, F. Santoro, Context-aware predictive process
monitoring: The impact of news sentiment, in: H. Panetto, C. Debruyne, H. A. Proper, C. A.
Ardagna, D. Roman, R. Meersman (Eds.), On the Move to Meaningful Internet Systems. OTM 2018
Conferences, Springer, Cham, 2018, pp. 586–603. doi:10.1007/978-3-030-02610-3_33.
[19] R. Galanti, M. de Leoni, N. Navarin, A. Marazzi, Object-centric process predictive analytics, Expert</p>
      <p>Systems with Applications 213 (2023) 119173. doi:10.1016/j.eswa.2022.119173.
[20] T. K. Smit, H. A. Reijers, X. Lu, HOEG: A new approach for object-centric predictive process
monitoring, in: G. Guizzardi, F. Santoro, H. Mouratidis, P. Sofer (Eds.), Advanced Information
Systems Engineering, Springer, Cham, 2024, pp. 231–247. doi:10.1007/978-3-031-61057-8_
14.
[21] J. De Smedt, A. Yeshchenko, A. Polyvyanyy, J. De Weerdt, J. Mendling, Process model forecasting
and change exploration using time series analysis of event sequence data, Data Knowledge
Engineering 145 (2023) 102145. doi:10.1016/j.datak.2023.102145.
[22] Y. Mehrdad Bibalan, B. Far, F. Eshragh, B. Ghiyasian, Work in progress prediction for business
processes using temporal convolutional networks, in: H. Fujita, R. Cimler, A. Hernandez-Matamoros,
M. Ali (Eds.), Advances and Trends in Artificial Intelligence. Theory and Applications, Springer,
Singapore, 2024, pp. 109–121. doi:10.1007/978-981-97-4677-4_10.
[23] P. Pfeifer, P. Fettke, Trace vs. time: Entropy analysis and event predictability of traceless event
sequencing, in: A. Marrella, M. Resinas, M. Jans, M. Rosemann (Eds.), Business Process Management
Forum, Springer, Cham, 2024, pp. 72–89. doi:10.1007/978-3-031-70418-5_5.
[24] A. Burattin, Streaming process mining, in: W. M. P. van der Aalst, J. Carmona (Eds.), Process</p>
      <p>Mining Handbook, Springer, Cham, 2022, pp. 349–372. doi:10.1007/978-3-031-08848-3_11.
[25] T. Verbeek, M. Hassani, Handling catastrophic forgetting: Online continual learning for next
activity prediction, in: M. Comuzzi, D. Grigori, M. Sellami, Z. Zhou (Eds.), Cooperative Information
Systems, Springer, Cham, 2025, pp. 225–242. doi:10.1007/978-3-031-81375-7_13.
[26] K. Kubrak, F. Milani, A. Nolte, M. Dumas, Prescriptive process monitoring: Quo vadis?, PeerJ</p>
      <p>Computer Science 8 (2022) e1097. URL: https://doi.org/10.7717/peerj-cs.1097.
[27] M. Shoush, M. Dumas, Prescriptive process monitoring under resource constraints: A causal
inference approach, in: J. Munoz-Gama, X. Lu (Eds.), Process Mining Workshops, Springer, Cham,
2022, pp. 180–193. doi:10.1007/978-3-030-98581-3_14.
[28] Z. Dasht Bozorgi, I. Teinemaa, M. Dumas, M. La Rosa, A. Polyvyanyy, Prescriptive process
monitoring based on causal efect estimation, Information Systems 116 (2023) 102198. doi: 10.
1016/j.is.2023.102198.
[29] K. Pefers, T. Tuunanen, M. A. Rothenberger, S. C. and, A design science research methodology
for information systems research, Journal of Management Information Systems 24 (2007) 45–77.
doi:10.2753/MIS0742-1222240302.
[30] J. Evermann, J.-R. Rehse, P. Fettke, Predicting process behaviour using deep learning, Decision</p>
      <p>Support Systems 100 (2017) 129–140. doi:10.1016/j.dss.2017.04.003.
[31] E. Rama-Maneiro, J. C. Vidal, M. Lama, Deep learning for predictive business process monitoring:
Review and benchmark, IEEE Transactions on Services Computing 16 (2023) 739–756. doi:10.
1109/TSC.2021.3139807.
[32] H. Weytjens, J. De Weerdt, Process outcome prediction: CNN vs. LSTM (with attention), in: A. Del
Río Ortega, H. Leopold, F. M. Santoro (Eds.), Business Process Management Workshops, Springer,
Cham, 2020, pp. 321–333. doi:10.1007/978-3-030-66498-5_24.
[33] M. Beck, K. Pöppel, M. Spanring, A. Auer, O. Prudnikova, M. Kopp, G. Klambauer, J. Brandstetter,
S. Hochreiter, xlstm: Extended long short-term memory, in: A. Globerson, L. Mackey, D. Belgrave,
A. Fan, U. Paquet, J. Tomczak, C. Zhang (Eds.), Advances in Neural Information Processing Systems,
volume 37, Curran Associates, Inc., 2024, pp. 107547–107603. URL: https://proceedings.neurips.cc/
paper_files/paper/2024/file/c2ce2f2701c10a2b2f2ea0bfa43cfaa3-Paper-Conference.pdf.
[34] J. Gao, P. Li, Z. Chen, J. Zhang, A survey on deep learning for multimodal data fusion, Neural</p>
      <p>Computation 32 (2020) 829–864. doi:10.1162/neco_a_01273.
[35] F. Zhao, C. Zhang, B. Geng, Deep multimodal data fusion, ACM Computing Surveys 56 (2024).</p>
      <p>doi:10.1145/3649447.
[36] V. Gallina, L. Lingitz, J. Breitschopf, E. Zudor, W. Sihn, Work in progress level prediction with
long short-term memory recurrent neural network, Procedia Manufacturing 54 (2021) 136–141.
doi:10.1016/j.promfg.2021.07.047.
[37] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, I. Polosukhin,
Attention is all you need, in: I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S.
Vishwanathan, R. Garnett (Eds.), Advances in Neural Information Processing Systems, volume 30,
Curran Associates, Inc., 2017. URL: https://proceedings.neurips.cc/paper_files/paper/2017/file/
3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf.
[38] A. Gu, T. Dao, Mamba: Linear-time sequence modeling with selective state spaces, 2024. URL:
https://arxiv.org/abs/2312.00752. arXiv:2312.00752.
[39] M. Zeng, F. Regol, M. Coates, Interacting difusion processes for event sequence forecasting, in:</p>
      <p>Proceedings of the 41st International Conference on Machine Learning, ICML’24, JMLR.org, 2024.
[40] R. Bhattacharya, D. Malinsky, I. Shpitser, Causal inference under interference and network
uncertainty, in: R. P. Adams, V. Gogate (Eds.), Proceedings of The 35th Uncertainty in Artificial
Intelligence Conference, volume 115 of Proceedings of Machine Learning Research, PMLR, 2020, pp.
1028–1038. URL: https://proceedings.mlr.press/v115/bhattacharya20a.html.
[41] Y. Ma, V. Tresp, Causal inference under networked interference and intervention policy
enhancement, in: A. Banerjee, K. Fukumizu (Eds.), Proceedings of The 24th International Conference
on Artificial Intelligence and Statistics, volume 130 of Proceedings of Machine Learning Research,
PMLR, 2021, pp. 3700–3708. URL: https://proceedings.mlr.press/v130/ma21c.html.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <surname>W. M. P. van der Aalst</surname>
          </string-name>
          ,
          <article-title>Process mining: A 360 degree overview</article-title>
          , in: W.
          <string-name>
            <surname>M. P. van der Aalst</surname>
          </string-name>
          , J. Carmona (Eds.),
          <source>Process Mining Handbook</source>
          , Springer, Cham,
          <year>2022</year>
          , pp.
          <fpage>3</fpage>
          -
          <lpage>34</lpage>
          . doi:
          <volume>10</volume>
          .1007/ 978-3-
          <fpage>031</fpage>
          -08848-
          <issue>3</issue>
          _
          <fpage>1</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>P.</given-names>
            <surname>Ceravolo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Comuzzi</surname>
          </string-name>
          ,
          <string-name>
            <surname>J. De Weerdt</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          <string-name>
            <surname>Di Francescomarino</surname>
            ,
            <given-names>F. M.</given-names>
          </string-name>
          <string-name>
            <surname>Maggi</surname>
          </string-name>
          ,
          <article-title>Predictive process monitoring: concepts, challenges, and future research directions</article-title>
          ,
          <source>Process Science</source>
          <volume>1</volume>
          (
          <year>2024</year>
          )
          <article-title>2</article-title>
          . doi:
          <volume>10</volume>
          .1007/s44311-024-00002-4.
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>N.</given-names>
            <surname>Navarin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Vincenzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Polato</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Sperduti</surname>
          </string-name>
          ,
          <article-title>LSTM networks for data-aware remaining time prediction of business process instances</article-title>
          ,
          <source>in: 2017 IEEE Symposium Series on Computational Intelligence (SSCI)</source>
          ,
          <year>2017</year>
          , pp.
          <fpage>1</fpage>
          -
          <lpage>7</lpage>
          . doi:
          <volume>10</volume>
          .1109/SSCI.
          <year>2017</year>
          .
          <volume>8285184</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>B. R.</given-names>
            <surname>Gunnarsson</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. v.</given-names>
            <surname>Broucke</surname>
          </string-name>
          ,
          <string-name>
            <surname>J. De Weerdt</surname>
          </string-name>
          ,
          <article-title>A direct data aware LSTM neural network architecture for complete remaining trace and runtime prediction</article-title>
          ,
          <source>IEEE Transactions on Services Computing</source>
          <volume>16</volume>
          (
          <year>2023</year>
          )
          <fpage>2330</fpage>
          -
          <lpage>2342</lpage>
          . doi:
          <volume>10</volume>
          .1109/TSC.
          <year>2023</year>
          .
          <volume>3245726</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>J.</given-names>
            <surname>Roider</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Zanca</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B. M.</given-names>
            <surname>Eskofier</surname>
          </string-name>
          ,
          <article-title>Eficient training of recurrent neural networks for remaining time prediction in predictive process monitoring</article-title>
          , in: A.
          <string-name>
            <surname>Marrella</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Resinas</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          <string-name>
            <surname>Jans</surname>
          </string-name>
          , M. Rosemann (Eds.),
          <source>Business Process Management</source>
          , Springer, Cham,
          <year>2024</year>
          , pp.
          <fpage>238</fpage>
          -
          <lpage>255</lpage>
          . doi:
          <volume>10</volume>
          .1007/ 978-3-
          <fpage>031</fpage>
          -70396-6_
          <fpage>14</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>N.</given-names>
            <surname>Tax</surname>
          </string-name>
          , I. Verenich,
          <string-name>
            <given-names>M. La</given-names>
            <surname>Rosa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Dumas</surname>
          </string-name>
          ,
          <article-title>Predictive business process monitoring with LSTM neural networks</article-title>
          , in: E. Dubois,
          <string-name>
            <surname>K.</surname>
          </string-name>
          Pohl (Eds.),
          <source>Advanced Information Systems Engineering</source>
          , Springer, Cham,
          <year>2017</year>
          , pp.
          <fpage>477</fpage>
          -
          <lpage>492</lpage>
          . doi:
          <volume>10</volume>
          .1007/978-3-
          <fpage>319</fpage>
          -59536-8_
          <fpage>30</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>B.</given-names>
            <surname>Wuyts</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S. Vanden</given-names>
            <surname>Broucke</surname>
          </string-name>
          , J. De Weerdt,
          <article-title>SuTraN: an encoder-decoder transformer for fullcontext-aware sufix prediction of business processes</article-title>
          ,
          <source>in: 2024 6th International Conference on Process Mining (ICPM)</source>
          ,
          <year>2024</year>
          . doi:
          <volume>10</volume>
          .1109/ICPM63005.
          <year>2024</year>
          .
          <volume>10680671</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>I.</given-names>
            <surname>Verenich</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Dumas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. L.</given-names>
            <surname>Rosa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. M.</given-names>
            <surname>Maggi</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Teinemaa</surname>
          </string-name>
          ,
          <article-title>Survey and cross-benchmark comparison of remaining time prediction methods in business process monitoring</article-title>
          ,
          <source>ACM Transactions on Intelligent Systems and Technology</source>
          <volume>10</volume>
          (
          <year>2019</year>
          ). doi:
          <volume>10</volume>
          .1145/3331449.
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>I.</given-names>
            <surname>Teinemaa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Dumas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. L.</given-names>
            <surname>Rosa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. M.</given-names>
            <surname>Maggi</surname>
          </string-name>
          ,
          <article-title>Outcome-oriented predictive process monitoring: Review and benchmark</article-title>
          ,
          <source>ACM Trans. Knowl. Discov. Data</source>
          <volume>13</volume>
          (
          <year>2019</year>
          ). doi:
          <volume>10</volume>
          .1145/3301300.
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>C.</given-names>
            <surname>Di Francescomarino</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Ghidini</surname>
          </string-name>
          ,
          <article-title>Predictive process monitoring</article-title>
          , in: W.
          <string-name>
            <surname>M. P. van der Aalst</surname>
          </string-name>
          , J. Carmona (Eds.),
          <source>Process Mining Handbook</source>
          , Springer, Cham,
          <year>2022</year>
          , pp.
          <fpage>320</fpage>
          -
          <lpage>346</lpage>
          . doi:
          <volume>10</volume>
          .1007/ 978-3-
          <fpage>031</fpage>
          -08848-3_
          <fpage>10</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>A.</given-names>
            <surname>Grinvald</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Sofer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>Mokryn</surname>
          </string-name>
          ,
          <article-title>Inter-case properties and process variant considerations in time prediction: A conceptual framework</article-title>
          , in: A.
          <string-name>
            <surname>Augusto</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Gill</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Nurcan</surname>
            ,
            <given-names>I.</given-names>
          </string-name>
          <string-name>
            <surname>Reinhartz-Berger</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          <string-name>
            <surname>Schmidt</surname>
          </string-name>
          , J. Zdravkovic (Eds.), Enterprise,
          <source>Business-Process and Information Systems Modeling</source>
          , Springer, Cham,
          <year>2021</year>
          , pp.
          <fpage>96</fpage>
          -
          <lpage>111</lpage>
          . doi:
          <volume>10</volume>
          .1007/978-3-
          <fpage>030</fpage>
          -79186-
          <issue>5</issue>
          _
          <fpage>7</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Dubinsky</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Sofer</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Hadar</surname>
          </string-name>
          ,
          <article-title>Detecting cross-case associations in an event log: toward a pattern-based detection</article-title>
          ,
          <source>Software and Systems Modeling</source>
          <volume>22</volume>
          (
          <year>2023</year>
          )
          <fpage>1755</fpage>
          -
          <lpage>1777</lpage>
          . doi:
          <volume>10</volume>
          .1007/ s10270-023-01100-w.
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>A.</given-names>
            <surname>Senderovich</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C. D.</given-names>
            <surname>Francescomarino</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. M.</given-names>
            <surname>Maggi</surname>
          </string-name>
          ,
          <article-title>From knowledge-driven to data-driven inter-case feature encoding in predictive process monitoring</article-title>
          ,
          <source>Information Systems</source>
          <volume>84</volume>
          (
          <year>2019</year>
          )
          <fpage>255</fpage>
          -
          <lpage>264</lpage>
          . doi:
          <volume>10</volume>
          .1016/j.is.
          <year>2019</year>
          .
          <volume>01</volume>
          .007.
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>E. L.</given-names>
            <surname>Klijn</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Fahland</surname>
          </string-name>
          ,
          <article-title>Identifying and reducing errors in remaining time prediction due to inter-case dynamics</article-title>
          ,
          <source>in: 2020 2nd International Conference on Process Mining (ICPM)</source>
          ,
          <year>2020</year>
          , pp.
          <fpage>25</fpage>
          -
          <lpage>32</lpage>
          . doi:
          <volume>10</volume>
          .1109/ICPM49681.
          <year>2020</year>
          .
          <volume>00015</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>B. R.</given-names>
            <surname>Gunnarsson</surname>
          </string-name>
          , S. vanden Broucke, J. De Weerdt,
          <article-title>LS-ICE: A load state intercase encoding framework for improved predictive monitoring of business processes</article-title>
          ,
          <source>Information Systems</source>
          <volume>125</volume>
          (
          <year>2024</year>
          )
          <article-title>102432</article-title>
          . doi:
          <volume>10</volume>
          .1016/j.is.
          <year>2024</year>
          .
          <volume>102432</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>I.</given-names>
            <surname>Teinemaa</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Dumas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. M.</given-names>
            <surname>Maggi</surname>
          </string-name>
          ,
          <string-name>
            <surname>C.</surname>
          </string-name>
          <article-title>Di Francescomarino, Predictive business process monitoring with structured and unstructured data</article-title>
          , in: M. La Rosa,
          <string-name>
            <given-names>P.</given-names>
            <surname>Loos</surname>
          </string-name>
          ,
          <string-name>
            <surname>O.</surname>
          </string-name>
          Pastor (Eds.),
          <source>Business Process Management</source>
          , Springer, Cham,
          <year>2016</year>
          , pp.
          <fpage>401</fpage>
          -
          <lpage>417</lpage>
          . doi:
          <volume>10</volume>
          .1007/978-3-
          <fpage>319</fpage>
          -45348-4_
          <fpage>23</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>C.</given-names>
            <surname>Di Francescomarino</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Ghidini</surname>
          </string-name>
          ,
          <string-name>
            <given-names>F. M.</given-names>
            <surname>Maggi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Petrucci</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Yeshchenko</surname>
          </string-name>
          ,
          <article-title>An eye into the</article-title>
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>