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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>A Framework for Multidimensional Business Process Forecasting</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Aurélie Leribaux</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Research Centre for Information Systems Engineering</institution>
          ,
          <addr-line>KU Leuven</addr-line>
          ,
          <country country="BE">Belgium</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Accurate forecasting of business process models is essential for efective process management and decisionmaking. However, existing techniques often focus narrowly on predicting control flow, overlooking the rich, multidimensional nature of real-world processes. This research addresses this gap by proposing a comprehensive framework that forecasts interactions between control flow and critical process dimensions, including resources, data objects, decision logic, and performance metrics. Leveraging recent advances in process knowledge graphs and graph neural networks, the proposed approach represents event data as multiple time series, each capturing a distinct behavioral aspect of the process. This multidimensional perspective enables the development of neural network-based models that predict the evolution of complex process structures rather than isolated outcomes. The research agenda is organized into four key pillars: enhancing process representations and predictive models, integrating simulation for process optimization, ensuring model explainability, and validating ifndings through real-life case studies. By uniting these elements, this work aims to advance the field of predictive process monitoring, ofering more accurate, scalable, and interpretable forecasting solutions for business process management.</p>
      </abstract>
      <kwd-group>
        <kwd>Predictive Process Monitoring</kwd>
        <kwd>Multidimensional Process Models</kwd>
        <kwd>Graph Neural Networks</kwd>
        <kwd>Simulation</kwd>
        <kwd>Explainable AI</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Motivation and Background</title>
      <p>Predictive Process Monitoring (PPM) has emerged as a key component of Business Process Management
(BPM), enabling organizations to make proactive decisions by predicting the future states of ongoing
process instances. Traditional PPM techniques typically focus on predicting specific outcomes, such as
the remaining time of a case or the next activity to be executed, often using classification or regression
models trained on historical event logs. While efective in predicting instance-level outcomes, most
PPM approaches rely on control-flow-centric models, which focus on the sequence of activities but often
neglect other important process dimensions, such as resource usage, data interactions, and decision
logic. Even so, there are alternative solutions that take into consideration the data-flow of processes,
although there is no common agreement on how to address the problem, given the particular nature of
each problem domain. Consequently, these approaches fail to capture the complex, multidimensional
nature of real-world business processes generically.</p>
      <p>
        Process Model Forecasting (PMF) was introduced to address some of the limitations of PPM [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
Instead of predicting individual outcomes, PMF aims to forecast the evolution of the entire process
model over time, enabling organizations to anticipate structural process changes. Early PMF work
primarily focused on forecasting Directly-Follows Graphs (DFGs) as time series, providing insights into
control-flow-level dynamics. However, even these approaches often remain limited to univariate time
series forecasting, lacking the integration of additional dimensions, such as resources, data, decision
points, and performance metrics, that are crucial for understanding complex process behaviors.
      </p>
      <p>
        Recent research has begun to address this research gap by extending PMF beyond simple control
lfow predictions. For example, a time-series-based approach for forecasting process models based
on sequence data was introduced [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], yet primarily focused on predicting Directly-Follows relations
without integrating other process dimensions. Similarly, a recurrent neural network approach for
predicting process constraints was proposed [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], but without accounting for resources or data
perspectives. Additionally, a data model to enable multidimensional process mining was presented, including
dimensions such as material flow and information flow, demonstrating the feasibility of a
comprehensive representation of process dynamics [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Moreover, recent advancements in object-centric process
mining emphasize the need to model event data that includes interactions between diferent objects
within processes, enabling a more comprehensive representation of process behavior [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ].
      </p>
      <p>Building upon these foundations, this research project aims to advance predictive business process
modeling by developing neural network-based forecasting models that capture the multidimensional
nature of real-world processes. Unlike traditional methods that focus solely on control-flow, our
approach extends to predicting interactions between and among four key dimensions: (1) resources, (2)
data objects, (3) decision logic, and (4) performance metrics. This work is grounded in representing
event data as multiple time series, each encapsulating a distinct behavioral aspect of the process.
This multidimensional approach leverages advances in both process knowledge graphs (PKGs), event
knowledge graphs (EKGs), and graph neural networks (GNNs), facilitating the prediction of process
dynamics at the process level rather than merely predicting individual outcomes at the instance level.
By integrating these dimensions into a cohesive forecasting framework, this research aims to deliver
more accurate, actionable, and explainable insights for BPM.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Research Agenda</title>
      <p>To realize the vision of multidimensional process forecasting, this research is structured around four
key pillars: (1) Enhancing process representations and predictive models, (2) Integrating simulation for
process optimization, (3) Ensuring the explainability of predictive models, and (4) Validating findings
through real-life case studies. Figure 1 summarizes the methodology. Each pillar contributes to
overcoming the limitations of current predictive approaches, enabling more accurate and comprehensive
forecasts. In the remainder, each of the pillars is outlined in more detail, including recent research,
research gaps, and proposed contributions and methodology.</p>
      <sec id="sec-2-1">
        <title>2.1. Pillar 1: Enhancing Process Representations and Predictive Models</title>
        <p>A fundamental challenge in process forecasting is developing predictive models that accurately capture
the multi-dimensional nature of real-world business processes. This challenge motivates the following
guiding research question:
• RQ1: How can a multi-dimensional process representation and deep learning models be designed
to enhance the accuracy, scalability, and interpretability of long-term business process forecasting?
To address this question, this pillar focuses on building a strong foundation for forecasting by
emphasizing three key subtopics:
Existing forecasting models in BPM often focus narrowly on the control flow of processes, overlooking
critical aspects such as resource interactions, data dependencies, and decision logic. To address this
limitation, this research aims to develop and advance PKGs and EKGs to build a unified, multidimensional
process representation for predictive forecasting.</p>
        <p>
          PKGs and EKGs are both specialized forms of knowledge graphs that capture diferent facets of process
knowledge. PKGs, as applied in several domains such as manufacturing process planning, integrate
structured process knowledge from various sources (i.e. process steps, resources, and attributes) and
model relationships among them [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ]. PKGs can also represent performance metrics and decision
logic as attributes or linked entities, enabling comprehensive modeling of process dependencies and
requirements. However, these representations are typically static, focusing on structural knowledge
rather than modeling dynamic process behavior over time.
        </p>
        <p>
          EKGs, on the other hand, focus on modeling event-centric knowledge by capturing rich,
multidimensional relationships between events and entities, such as temporal event relations, event-entity
relations, and entity-entity relations [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]. This makes EKGs highly valuable for representing sequential
process dynamics and multi-dimensional interactions. However, EKGs are often designed for descriptive
analysis, focusing on knowledge extraction and event relations rather than dynamic process forecasting.
Moreover, they typically do not explicitly integrate performance metrics or decision logic that are
critical in BPM forecasting.
        </p>
        <p>Building on these foundations, this research proposes to enrich and extend KGs into an unified
semantic graph. This approach aims to capture both the sequential dynamics of events and the relational
dependencies among process elements, such as resources, data objects, and decision logic. By integrating
the strengths of both PKGs and EKGs, this research seeks to create a holistic, actionable, and explainable
framework for process forecasting that overcomes the limitations of existing models.</p>
        <sec id="sec-2-1-1">
          <title>2.1.2. Designing GNNs for Process Forecasting</title>
          <p>Accurately forecasting business processes requires models that can efectively learn both temporal
dependencies and complex structural relationships given their graph-based structures. Hence, this
research will design and implement GNNs that leverage PKGs to capture interactions between activities,
resources, and data elements while maintaining temporal consistency. These GNNs will be specifically
tailored to the characteristics of PKGs, ensuring that the models learn from both the sequential and
relational aspects of process data.</p>
        </sec>
        <sec id="sec-2-1-2">
          <title>2.1.3. Adapting GNNs from Other Domains</title>
          <p>
            In addition to developing GNNs specifically designed for PKGs in process mining, this research will also
draw inspiration from recent advances. For example, spatio-temporal graph neural networks (ST-GNNs)
[
            <xref ref-type="bibr" rid="ref8 ref9">8, 9</xref>
            ] have shown potential. These models, successfully applied in domains such as trafic forecasting and
ifnancial analysis, efectively integrate temporal dynamics with relational structures. This research will
investigate how to adapt these techniques for event-driven business processes, ensuring compatibility
with the discrete and evolving nature of process event data.
          </p>
        </sec>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Pillar 2: Integrating Simulation for Process Optimization</title>
        <p>Building upon forecasting in Pillar 1, an essential aspect of this research is simulating and optimizing
future process states. While forecasting provides valuable insights into potential future process behaviors,
simulation enables stakeholders to evaluate and optimize these behaviors under various scenarios.</p>
        <p>
          Existing research has explored the integration of process mining and simulation, particularly through
discrete-event simulation (DES) engines that utilize static process models extracted from event logs
[
          <xref ref-type="bibr" rid="ref10 ref11 ref12">10, 11, 12</xref>
          ]. However, these simulation engines often operate on static models, which limits their
ability to incorporate dynamic process changes or to simulate complex multi-dimensional process
dynamics. They typically do not integrate predictive models that capture how processes evolve over
time, especially across multiple process dimensions.
        </p>
        <p>
          Notable recent developments focus on user perspectives to perform ‘what-if’ analyses. For example,
SIMPT [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] leverages time-aware process trees to enable interactive simulations, allowing process
owners to explore process improvement scenarios dynamically. However, even these developments
remain limited in their capacity to integrate predictive, multi-dimensional process models
        </p>
        <p>
          This research pillar aims to bridge these gaps by integrating the predictive models established in Pillar
1 into a comprehensive simulation engine. By transforming PKGs into data-aware, executable process
models, this simulation engine will support both AS-IS and TO-BE analyses, empowering stakeholders
to assess potential improvements, anticipate dynamic process changes, and mitigate bottlenecks more
efectively. The approach aligns with recent calls for more flexible, knowledge-driven simulation
frameworks that can dynamically incorporate forecasted process states [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ]. This leads to the guiding
research question for this pillar:
• RQ2: How can simulation and predictive models be jointly integrated to efectively inform
process improvement and optimization, while addressing the dynamic and multi-dimensional
nature of real-world processes?
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Pillar 3: Ensuring Explainability in Predictive Models</title>
        <p>As predictive models become increasingly sophisticated, particularly those leveraging advanced deep
learning architectures like GNNs, ensuring their transparency and interpretability becomes essential
for trust and informed decision-making in BPM. Moreover, representing the multidimensional nature of
business processes, like PKGs, further compounds the challenge of model explainability, as it introduces
intricate dependencies between process activities, resources, and data elements. Therefore, this pillar
extends Pillar 1 by specifically addressing the heightened challenge of model explainability and ensuring
that predictive models remain not only powerful but also transparent and trustworthy for end-users.</p>
        <p>
          Recent research in process mining highlights the growing importance of explainable AI (XAI) to
support user trust and efective decision-making [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]. General XAI techniques, including feature
attribution, local explanations, and model-agnostic methods, have been extensively surveyed [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ],
providing a solid foundation for integrating interpretability into deep learning workflows.
        </p>
        <p>Given that this research project leverages GNNs to model and predict PKGs, explainability techniques
tailored to GNNs are particularly relevant. Recent research provides a comprehensive taxonomy of
XAI methods for GNNs, highlighting the challenges of explaining graph-based predictions [16]. By
incorporating these insights, this research will develop XAI techniques that make PKG-based forecasting
models more interpretable and actionable for process stakeholders. This aligns with the broader goal
of empowering stakeholders with predictive tools that are not only accurate and comprehensive but
also transparent and trustworthy. The corresponding pillar, therefore, addresses the following guiding
research question:
• RQ3: How can explainable AI techniques improve the interpretability and trustworthiness of
predictive business process models based on graph neural networks?</p>
      </sec>
      <sec id="sec-2-4">
        <title>2.4. Pillar 4: Validating Findings Through Real-Life Case Studies</title>
        <p>A crucial step in operationalizing data-driven research findings is to evaluate them in real-world business
settings. This research will apply the developed forecasting models (Pillar 1), simulation techniques
(Pillar 2), and explainability frameworks (Pillar 3) to real-life case studies across diverse industries. By
testing these approaches in practical environments, we will assess their efectiveness, refine the models
based on empirical insights, and demonstrate their value for decision-making in BPM, guided by the
following final research question
• RQ4: How can real-life case studies validate and refine predictive process forecasting models for
practical business applications?</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Progress to Date</title>
      <sec id="sec-3-1">
        <title>3.1. Literature Review</title>
        <p>This section describes the current progress, focusing on Pillar 1: Enhancing Process Representations
and Predictive Models.</p>
        <p>To achieve the four key pillars, it was necessary to conduct a comprehensive literature review. This
review serves as a foundation for understanding the current role of time series in the field of process
mining, including how and when they are applied. Hence, the aim of this paper is to clarify the extent
to which time series analysis has been integrated into process mining methodologies and to uncover
potential areas for further exploration and improvement.</p>
        <p>As part of this literature review paper, I had the opportunity to present an initial version of the
insights from my analysis at the International Conference on Process Mining of the Belgian Operational
Research Society (ORBEL) in Maastricht in February. This event not only ofered exposure to the latest
developments in the field but also provided valuable feedback from experts, which I have incorporated
into the further development of my research. Building on this input, I am preparing a journal paper.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Initial Steps in Enhancing Process Representations and Predictive Models</title>
        <sec id="sec-3-2-1">
          <title>3.2.1. Exploring Actor-Level Performance Dynamics</title>
          <p>This research extends the predictive modeling focus introduced in Section 1 by investigating both the
resource and performance perspectives as critical dimensions in process forecasting. Motivated by
recent work, which proposes a decomposition method to disaggregate performance measures according
to actor behavior [17], this research seeks to address the limitations of traditional process mining
approaches that often collapse diverse actor behaviors into single aggregate measures [18]. Traditional
methods overlook distinctions between uninterrupted work by the same actor, resumed work after an
interruption, and handovers between diferent actors.</p>
          <p>Although the authors introduced a resource-aware perspective, their work remains high-level and
does not explicitly model the temporal causality of actor behaviors, an essential aspect for understanding
process dynamics. To address this, our research incorporates a temporal dimension into performance
analysis, transforming performance metrics into time series that capture temporal variations in actor
behavior. The analysis also seeks to uncover causal relationships among these time series using Granger
causality [19], aiming to reveal how diferent actor behaviors influence process outcomes.</p>
          <p>Ultimately, this work aims to develop a comprehensive framework for understanding process
performance at the actor level, serving as a descriptive foundation for incorporating the resource perspective
into predictive models and exploring interactions among diferent process dimensions. The goal is to
develop this research into a workshop paper for submission to BPM 2025.</p>
        </sec>
        <sec id="sec-3-2-2">
          <title>3.2.2. Incorporating Resource Perspectives into Predictive Models</title>
          <p>Drawing on insights from the actor-level analysis, the research now incorporates resource perspectives
into time-series-based predictive models (e.g., ARIMAX). These models will be benchmarked against
traditional models that do not account for resource interactions, providing evidence of the added value
of multi-dimensional forecasting.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion</title>
      <p>This research seeks to advance business process forecasting by combining multi-dimensional process
representations, advanced predictive models, simulation, and explainability. The initial progress within
Pillar 1 sets a strong foundation for subsequent work on the other pillars, paving the way toward a
comprehensive framework for data-driven BPM.</p>
    </sec>
    <sec id="sec-5">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author used GPT-4 to check grammar, spelling, and improve
the writing structure. Additionally, ChatGPT was consulted to better understand related concepts,
particularly those found in Graph Neural Network (GNN) literature. No AI-generated content was
directly copied into the publication. The author reviewed and edited all AI-assisted input as needed and
takes full responsibility for the content of this publication.
taxonomies, opportunities and challenges toward responsible ai, Information Fusion 58 (2020)
82–115.
[16] H. Yuan, H. Yu, S. Gui, S. Ji, Explainability in graph neural networks: A taxonomic survey (2020).</p>
      <p>doi:10.48550/arXiv.2012.15445.
[17] E. L. Klijn, I. Tentina, D. Fahland, F. Mannhardt, Decomposing process performance based on actor
behavior, in: 2024 6th International Conference on Process Mining (ICPM), 2024, pp. 129–136.
doi:10.1109/ICPM63005.2024.10680657.
[18] A. Tour, A. Polyvyanyy, A. Kalenkova, Agent system mining: Vision, benefits, and challenges,</p>
      <p>IEEE Access 9 (2021) 99480–99494. doi:10.1109/ACCESS.2021.3095464.
[19] C. Granger, Investigating causal relations by econometric models and cross-spectral methods,
Econometrica 37 (1969) 424–438.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>R.</given-names>
            <surname>Poll</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Polyvyanyy</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Rosemann</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Röglinger</surname>
          </string-name>
          , L. Rupprecht,
          <article-title>Process forecasting: Towards proactive business process management</article-title>
          ,
          <source>in: Business Process Management</source>
          , Springer,
          <year>2018</year>
          , pp.
          <fpage>496</fpage>
          -
          <lpage>512</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>J. D.</given-names>
            <surname>Smedt</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. D.</given-names>
            <surname>Weerdt</surname>
          </string-name>
          ,
          <article-title>Predictive process model monitoring using recurrent neural networks, arXiv preprint (</article-title>
          <year>2020</year>
          ). URL: https://arxiv.org/abs/
          <year>2011</year>
          .02819.
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>S.</given-names>
            <surname>Kroeger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Rafles</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Jordan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Soellner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. F.</given-names>
            <surname>Zaeh</surname>
          </string-name>
          ,
          <article-title>Data model to enable multidimensional process mining for data farming based value stream planning in production networks</article-title>
          ,
          <source>Production Engineering</source>
          (
          <year>2024</year>
          ). URL: https://api.semanticscholar.org/CorpusID:273500321.
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <surname>W. M. P. van der Aalst</surname>
          </string-name>
          ,
          <article-title>Object-centric process mining: Dealing with divergence and convergence in event data</article-title>
          ,
          <source>in: Software Engineering and Formal Methods</source>
          , Springer,
          <year>2019</year>
          , pp.
          <fpage>3</fpage>
          -
          <lpage>25</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>D.</given-names>
            <surname>Fahland</surname>
          </string-name>
          ,
          <article-title>Process mining over multiple behavioral dimensions with event knowledge graphs</article-title>
          ,
          <source>in: Process Mining Handbook</source>
          , Springer,
          <year>2022</year>
          , pp.
          <fpage>274</fpage>
          -
          <lpage>319</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Xiao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Zheng</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Shi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Du</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Hong</surname>
          </string-name>
          ,
          <article-title>Knowledge graph-based manufacturing process planning: A state-of-the-art review</article-title>
          ,
          <source>Journal of Manufacturing Systems</source>
          <volume>70</volume>
          (
          <year>2023</year>
          )
          <fpage>417</fpage>
          -
          <lpage>435</lpage>
          . URL: https://www. sciencedirect.com/science/article/pii/S0278612523001577. doi:https://doi.org/10.1016/j. jmsy.
          <year>2023</year>
          .
          <volume>08</volume>
          .006.
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>S.</given-names>
            <surname>Guan</surname>
          </string-name>
          , X. Cheng, L.
          <string-name>
            <surname>Bai</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          <string-name>
            <surname>Zhang</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          <string-name>
            <surname>Li</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          <string-name>
            <surname>Zeng</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          <string-name>
            <surname>Jin</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Guo</surname>
          </string-name>
          ,
          <article-title>What is event knowledge graph: A survey</article-title>
          ,
          <year>2022</year>
          . URL: https://arxiv.org/abs/2112.15280. arXiv:
          <volume>2112</volume>
          .
          <fpage>15280</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>B.</given-names>
            <surname>Yu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Yin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Zhu</surname>
          </string-name>
          ,
          <article-title>Spatio-temporal graph convolutional networks: A deep learning framework for trafic forecasting</article-title>
          ,
          <source>arXiv preprint arXiv:1709.04875</source>
          (
          <year>2017</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>D.</given-names>
            <surname>Cao</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Wang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Duan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Zhang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>X.</given-names>
            <surname>Zhu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Huang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Tong</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Xu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Bai</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Tong</surname>
          </string-name>
          ,
          <article-title>Spectral temporal graph neural network for multivariate time-series forecasting</article-title>
          ,
          <source>in: Advances in Neural Information Processing Systems</source>
          , volume
          <volume>33</volume>
          ,
          <year>2020</year>
          , pp.
          <fpage>17766</fpage>
          -
          <lpage>17778</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <surname>K. M. Rashid</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <string-name>
            <surname>Louis</surname>
          </string-name>
          ,
          <article-title>Integrating process mining with discrete-event simulation for dynamic productivity estimation in heavy civil construction operations</article-title>
          ,
          <source>Algorithms</source>
          <volume>15</volume>
          (
          <year>2022</year>
          ). URL: https: //www.mdpi.com/1999-4893/15/5/173. doi:
          <volume>10</volume>
          .3390/a15050173.
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Wang</surname>
          </string-name>
          ,
          <article-title>An integrative process mining approach to mine discrete event simulation model from event data</article-title>
          , Theses, Université de Bordeaux,
          <year>2018</year>
          . URL: https://theses.hal.science/tel-01952795.
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>M.</given-names>
            <surname>Camargo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Dumas</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O.</given-names>
            <surname>González-Rojas</surname>
          </string-name>
          ,
          <source>Automated discovery of business process simulation models from event logs</source>
          ,
          <source>Decision Support Systems</source>
          <volume>134</volume>
          (
          <year>2020</year>
          )
          <article-title>113284</article-title>
          . URL: https://www. sciencedirect.com/science/article/pii/S0167923620300397. doi:https://doi.org/10.1016/j. dss.
          <year>2020</year>
          .
          <volume>113284</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>M.</given-names>
            <surname>Pourbafrani</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Jiao</surname>
          </string-name>
          ,
          <string-name>
            <surname>W. M. P. van der Aalst</surname>
          </string-name>
          ,
          <article-title>Simpt: Process improvement using interactive simulation of time-aware process trees</article-title>
          ,
          <source>arXiv preprint arXiv:2108</source>
          .
          <year>02052</year>
          (
          <year>2021</year>
          ). URL: https: //arxiv.org/abs/2108.
          <year>02052</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>N.</given-names>
            <surname>Mehdiyev</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Fettke</surname>
          </string-name>
          ,
          <article-title>Explainable Artificial Intelligence for Process Mining: A General Overview and Application of a Novel Local Explanation Approach for Predictive Process Monitoring</article-title>
          , Springer International Publishing,
          <year>2021</year>
          , p.
          <fpage>1</fpage>
          -
          <lpage>28</lpage>
          . URL: http://dx.doi.org/10.1007/978-3-
          <fpage>030</fpage>
          -64949-
          <issue>4</issue>
          _1. doi:
          <volume>10</volume>
          . 1007/978-3-
          <fpage>030</fpage>
          -64949-
          <issue>4</issue>
          _
          <fpage>1</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <surname>A. B. Arrieta</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          <string-name>
            <surname>Díaz-Rodríguez</surname>
            ,
            <given-names>J. D.</given-names>
          </string-name>
          <string-name>
            <surname>Ser</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Bennetot</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Tabik</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          <string-name>
            <surname>Barbado</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Garcia</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Gil-Lopez</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          <string-name>
            <surname>Molina</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          <string-name>
            <surname>Benjamins</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          <string-name>
            <surname>Chatila</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          <string-name>
            <surname>Herrera</surname>
          </string-name>
          ,
          <article-title>Explainable artificial intelligence (xai): Concepts,</article-title>
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>