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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>in: Journal of Physics: Conference Series</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.2514/6.2018-1366</article-id>
      <title-group>
        <article-title>Enabling Reuse of Knowledge from Coupled Systems in Aerospace Engineering</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ildar Baimuratov</string-name>
          <email>ildar.baimuratov@l3s.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Tim Wittenborg</string-name>
          <email>tim.wittenborg@l3s.uni-hannover.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ihar Antonau</string-name>
          <email>ihar.antonau@tu-braunschweig.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Susanna Baars</string-name>
          <email>s.baars@tu-braunschweig.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Cluster of Excellence SE2A - Sustainable and Energy-Eficient Aviation, Technical University of Braunschweig</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Institute for Acoustics and Dynamics, Technical University of Braunschweig</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute of structural analysis, Technical University of Braunschweig</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>L3S Research Center, Leibniz University Hannover</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>TIB - Leibniz Information Centre for Science and Technology</institution>
          ,
          <addr-line>Hannover</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2018</year>
      </pub-date>
      <volume>1510</volume>
      <issue>1</issue>
      <fpage>215</fpage>
      <lpage>222</lpage>
      <abstract>
        <p>With the advancement of computational power and physical solvers, the complexity of coupled systems in the aerospace domain will continue to grow. Currently, engineers often model such systems from scratch or reuse local files, despite the potential to formalize, store, and share expert knowledge for broader reuse. In this work, we focus on the open-source software KRATOS Multiphysics, which supports coupled simulations through its CoSimulationApplication. The input JSON files for KRATOS describe deeply nested and interconnected structures, making them dificult to interpret and reuse. To enhance the FAIRness (Findability, Accessibility, Interoperability, and Reusability) of this data, we leverage RDF and OWL standards of the Semantic Web. However, manually constructing semantic graphs and ontologies from such lfies is both labor-intensive and prone to human error. To address this, we propose an automated procedure for extracting reusable knowledge from coupled simulation data and storing it in a centralized, human- and machine-interpretable knowledge base. Our contribution includes an algorithm that automatically translates KRATOS CoSimulationApplication JSON input files into RDF graphs and derives OWL ontologies from them, capturing generalizable patterns of coupled systems. We validate this approach through a proof-of-concept implementation applied to two representative use cases. Our results demonstrate that the extracted knowledge can be visualized and queried, ofering capabilities that were previously achievable only through manual inspection and analysis of JSON files.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Coupled modeling</kwd>
        <kwd>Aerospace engineering</kwd>
        <kwd>Knowledge extraction</kwd>
        <kwd>FAIR</kwd>
        <kwd>OWL</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        To advance and explore new aerospace technologies, it is essential to model and solve increasingly
complex problems that span multiple disciplines. With ongoing improvements in computational power
and advanced physical solvers, the complexity of multidisciplinary models and their analysis is expected
to grow significantly. As a result, tools and support systems are needed to help future engineers better
understand, visualize, and manage the data generated by their models and simulations [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>
        Moreover, the FAIR principles emphasize the need for computational systems to Find, Access,
Interoperate, and Reuse data with minimal human intervention [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. In the context of coupled modeling,
formalized representations are essential to structure and share domain knowledge efectively. Several
data models have been developed for the aerospace engineering, including XML-based formats such
as CPACS [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], CMDOWS [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], and KADMOS [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], as well as OWL-based semantic approaches [
        <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
        ].
Despite these advancements, significant challenges remain, particularly limited knowledge sharing and
the lack of unified data standards, which hinder the full potential of knowledge-based engineering [ 8].
      </p>
      <p>We focus on the open-source software KRATOS Multiphysics [9, 10], which provides a flexible
framework for developing multidisciplinary solvers. Coupled simulations within KRATOS are handled
by the CoSimulationApplication [11], which relies on JSON files as input. These JSON configurations are
typically created manually by engineers, embedding expert knowledge that could otherwise be
formalized, stored, and reused to define new problems more eficiently. The JSON files often contain deeply
nested, interconnected structures that are dificult for new users to interpret, yet include a significant
amount of reusable components and recurring patterns. Thus, applying RDF and OWL standards can
help align the data with FAIR principles and enhance its machine readability and interoperability.</p>
      <p>To enhance accessibility and reuse, we propose a centralized knowledge base that is both
humanand machine-interpretable for storing data from coupled simulations. However, manually designing
and populating such a knowledge base is time-consuming and prone to human error. To address this,
we develop an automated approach for extracting reusable knowledge from previously implemented
coupled systems. Specifically, we present an algorithm that converts input JSON files from the KRATOS
CoSimulationApplication into RDF format and derives OWL axioms to describe unique classes of
coupled systems. We validate this algorithm through a proof of concept, applying it to two distinct use
cases, and demonstrate how the proposed approach improves the accessibility and reusability of data in
coupled modeling.</p>
      <p>The paper is organized as follows: section 2 reviews related work; section 3 provides background on
the KRATOS CoSimulationApplication; section 4 describes the proposed method; section 5 presents its
application to two use cases; section 6 discusses the results; and finally, section 7 concludes the paper.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>Aerospace engineering makes use of various data models, languages, and ontologies, with XML being
the most widely adopted. Vargas-Hernandez et al. [12] employed bond graphs to develop a CAD tool for
designing complex electromechanical systems using a standardized taxonomy of elements. Agrawal et
al. [13] developed a platform-independent visualization framework for solving multidisciplinary design
optimization (MDO) problems. Jackson and Hildreth [14] proposed a flight dynamics model exchange
standard. Nagel et al. [15] introduced the Common Parametric Aircraft Configuration Scheme (CPACS),
a unified XML-based data model for interfacing between various MDO systems. Munjulury [ 16]
presented RAPID, a relational-based tool for aircraft geometry design. Van Gent [17] introduced the
Common MDO Workflow Schema (CMDOWS), a graph-based, application-agnostic formalization of
multidisciplinary design analysis and optimization (MDAO) workflows.</p>
      <p>Another widely adopted approach is the use of Unified Modeling Language (UML). Lu [ 18] applied
an object-oriented framework to model data for aircraft conceptual design. Oh et al. [19] proposed a
mapping methodology to facilitate the exchange of product structure data between CAD and product
data management systems. Böhnke [20] compared CPACS [15], STEP1, and UML in terms of their
suitability for data integration in preliminary aircraft design, concluding that a combination of UML or
SysML with XML ofers the most benefits.</p>
      <p>Researchers have also developed specialized software tools to model knowledge in aerospace
engineering. Sung &amp; Park [21] introduced a component-based product data management system implemented
in Java. Haney [22] developed a data engineering system using Microsoft Access to support aerospace
design and forecasting tasks. Herbst [23] presented ADDAM, an object-oriented aircraft design
environment implemented in MATLAB. The Python implementation of CMDOWS, known as
Knowledgeand Graph-based Agile Design for Multidisciplinary Optimization System (KADMOS), was introduced
by Van Gent [17]. Similarly, Risueño et al. [24] developed the MDAO Workflow Design Accelerator
(MDAx) in Python, extending the XDSM format with additional design rules.</p>
      <p>In this work, we focus on knowledge representation methods with embedded semantics. Using
RDF, Bang et al [25] developed Daphne, an intelligent assistant designed to support the architecture of
Earth-observing satellite systems. Herrero [26] proposed a Digital Thread for airplane design, modeled
as a knowledge graph to enable seamless data integration across the design process.</p>
      <p>
        Studies utilizing OWL predominantly rely on manual modeling using the Protégé tool. Curran et
al. [27] proposed the Knowledge Optimized Manufacture and Design (KNOMAD) ontology. Kuofie [ 28]
introduced the Rationale-based Design Explanation (RaDEX) framework. Verhagen &amp; Curran [29]
developed an ontology for the aerospace composite manufacturing domain. Zhao et al. [30] constructed
a knowledge base for spacecraft overall design. More recently, Franzén et al. [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] presented an ontology
that captures required functions, design alternatives, and requirements, and applied Description Logic
reasoning to generate suitable concepts to fulfill specific functions.
      </p>
      <p>
        Some studies go a step further by incorporating rule-based reasoning using SWRL. Hoogreef et
al. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] developed an MDO advisory system with decision rules modeled in SWRL. Roelofs &amp; Vos [31]
proposed a method for formally describing technologies based on the Basic Formal Ontology, using
graph transformation rules to represent logic. Markusheska et al. [32] created an ontology for the
automated scheduling of aircraft cabin assembly processes, where SWRL rules are applied to classify
and infer data.
      </p>
      <p>The most relevant related work includes methods that incorporate automated knowledge extraction
workflows. Dadzie et al. [ 33] introduced a methodology for extracting knowledge from textual and
multimedia documents in the aeronautics domain, using both manual and automated techniques, and
representing the information with RDF and OWL DL. Khilwani &amp; Harding [34] developed a framework
for managing corporate memory by extracting information from documents, converting it into RDF
resources, and identifying relationships using Latent Semantic Analysis. Ezhilarasu &amp; Jennions [35]
proposed the Framework for Aerospace Vehicle Reasoning (FAVER), which combines an Adaptive
Neuro-Fuzzy Inference System (ANFIS) with causal reasoning. Berquand [36] applied natural language
processing (NLP) techniques to extract an ontology of domain-specific models and rules from documents,
storing the results in TypeDB2. De Leon [37] proposed an approach to enhance association rule mining
for Entry, Descent, and Landing datasets by leveraging a user-defined knowledge graph implemented
using SysML and Neo4j. However, automated knowledge extraction specifically from coupled systems
remains an open and underexplored area.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Background</title>
      <p>This section provides background on the coupled modeling software that forms the focus of our work.
Coupled problems are often addressed using black-box solvers. However, solving multidisciplinary
and mixed-fidelity problems through co-simulation requires software that supports eficient coupling
strategies, manages the complexity of data exchange between heterogeneous solvers and models, and
ensures proper synchronization across multiple processes. KRATOS Multiphysics [9, 10] is a free,
open-source framework for the development of multidisciplinary simulation software. It is particularly
well-suited to our study, as it has been designed to support complex, coupled simulation scenarios and
emphasizes generality, reusability, and extensibility, ofering a wide range of tools for implementing finite
element applications. It also provides a unified interface for interaction between internal applications
and externally controlled solvers, thereby reducing implementation overhead and simplifying data
synchronization, especially when compared to traditional distributed data exchange approaches where
individual solvers are connected directly to one another.</p>
      <p>Co-simulation capabilities in KRATOS are provided by the CoSimulationApplication [11], which
manages data exchange and process coordination in coupled simulation environments. This application
relies on a JSON file with a specific structure as its input. The core component of the file is the
solver_settings section, which defines the configuration of the coupled system. Its main elements
include:
• type: Specifies the coupling method, such as weak or strong coupling using Gauss-Seidel or</p>
      <p>Jacobi strategies.
• num_coupling_iterations: Sets the maximum number of coupling iterations allowed.
• data_transfer_operators: Defines how data is transferred between solvers or codes, either
through direct copying or using KRATOS mapping.
• convergence_accelerators: Used to accelerate convergence in strongly coupled simulations.</p>
      <p>Available only for strongly coupled solvers.
• convergence_criteria: Specifies the criteria for determining when the coupled problem is
considered solved. Also only applicable for strongly coupled solvers.
• coupling_sequence: Describes the sequence in which disciplines are solved and data is
synchronized, establishing the order for initializing and executing the coupling process.
• input_data_list: Defines the input data flow. For example, “Discipline 1” receives “data 1” from
“Discipline 2”, stores it as “data 1”, and applies “operation 1”.
• output_data_list: Specifies the output data flow in a manner similar to the input configuration.
• solvers: Lists all solvers or external codes involved in the co-simulation, describing shared
meshes, coupled variables or data fields, and communication methods for data exchange.
• solver_wrapper_settings: Contains solver-specific parameters, including settings for I/O
communication and mesh/data synchronization.</p>
      <p>Listing 1 presents a fragment of a typical KRATOS CoSimulation JSON configuration. As shown, the
structure is deeply nested and consists of numerous interconnected components. In JSON format, this
complexity can be challenging for new users to comprehend. Moreover, the configuration includes a
significant amount of reusable structural patterns and recurring entities. Therefore, we propose that a
graph-based representation of this data could ofer a more intuitive and accessible way to understand
and interact with the configuration.
{
"data_transfer_operators": {</p>
      <p>"operation 1": {...}
},
"coupling_sequence": [
{
"name": "Displine 1",
"input_data_list": [</p>
      <p>{
},
{
}</p>
      <p>}
], ...</p>
      <p>"name": "Displine 2", ...
],
"solvers": {
"Displine 1": {
"data": {</p>
      <p>"data 1": {...}, ...</p>
      <p>}, ...</p>
      <p>}, ...
}
}
"data": "data 1",
"from_solver": "Displine 2",
"from_solver_data": "data 1",
"data_transfer_operator": "operation 1"</p>
      <p>Listing 1: A fragment of the KRATOS CoSimulation configuration in JSON</p>
    </sec>
    <sec id="sec-4">
      <title>4. Method</title>
      <p>Currently, aerospace engineers typically model coupled systems either from scratch or by reusing
locally available files. Our goal is to streamline this process by developing a centralized knowledge
base with structured representations, thereby making knowledge from prior coupled simulations more
FAIR. This knowledge base includes semantic representations of coupled simulation data in RDF,
enhancing interoperability, as well as general knowledge encoded as OWL axioms, which supports
human understanding in the formulation and validation of new coupled systems.</p>
      <p>Since manual ontology development and knowledge base population are time-consuming and dificult
to maintain, our approach is data-driven. While existing tools such as JSON2RDF3 can convert JSON
into RDF, preliminary experiments revealed that these tools fail to accurately capture the underlying
data model of the KRATOS CoSimulationApplication and do not support the extraction of generalized
knowledge from the data. To address this limitation, we develop an automated workflow that extracts
both information and reusable knowledge from KRATOS input JSON files and consistently imports it
into the knowledge base. For shortness, we refer to this algorithm as CoSim2OWL. This process consists
of two main steps: 1) Populating the knowledge base with coupled simulation data extracted from a
JSON file and translating it into RDF, and 2) Deriving OWL class axioms that semantically describe the
RDF data.</p>
      <p>Figure 1 illustrates our proposed approach. On the left, the diagram depicts the current
multidisciplinary analysis (MDA) workflow, where aerospace engineers typically model coupled systems from
scratch. On the right is the enhanced workflow we propose, which incorporates a knowledge base to
support reuse and automation. In our approach, JSON files containing data from previous experiments
are processed by a Python module implementing the CoSim2OWL algorithm. This module extracts
relevant information and stores it in an OWL-based knowledge base. In subsequent experiments,
knowledge at various levels of granularity can be retrieved from the knowledge base via SPARQL queries
to support the formulation of new coupled systems. Looking ahead, we plan to further streamline
knowledge retrieval by developing an API for the knowledge base and integrating it with existing
graphical user interfaces for KRATOS, such as FlowGraph4. In the diagram, components highlighted
in green represent elements implemented in this work, while dotted elements indicate planned future
developments.</p>
      <sec id="sec-4-1">
        <title>4.1. Translating coupled system data into RDF</title>
        <p>This subsection describes the first stage of the CoSim2OWL workflow — translating coupled system
data into RDF format. The knowledge base, denoted as , is initialized with a single predefined
class, coupled_system (we use teletype font to denote knowledge base objects). This class serves
as the superclass for all coupled systems extracted from the CoSimApp JSON files. For each coupled
system, the algorithm begins by instantiating the coupled_system class with a named individual
, which corresponds to a specific coupled system described in the input JSON. The algorithm then
recursively parses the JSON structure, generating RDF triples and populating  accordingly. At each
iteration, the algorithm constructs an RDF triple using the RDF resource created in the previous step as
the subject , a key from the current JSON object as the predicate name , and the corresponding value
as the object . The resulting triple (, , ) is then added to the knowledge base. This recursive
traversal continues until the entire JSON structure has been processed and fully represented in RDF.</p>
        <p>The object value  in a JSON key-value pair can be one of three types: 1) a JSON object, 2) an
array, or 3) a literal. Depending on the type, the CoSim2OWL algorithm generates the corresponding
RDF triple using diferent procedures. For clarity and precision, this part of the algorithm is described
formally in Algorithm 1. If  is a JSON object, it is converted into an owl:NamedIndividual  using
Algorithm 2. This sub-algorithm also assigns the newly created individual to a specific OWL class
, determined based on the predicate name  that links  to the subject . The algorithm then</p>
        <sec id="sec-4-1-1">
          <title>3https://github.com/AtomGraph/JSON2RDF 4https://github.com/KratosMultiphysics/Flowgraph</title>
          <p>Manual formulation of MDA
tasks from scratch</p>
          <p>Reusing previously solved MDA tasks
done
not yet
Actor</p>
          <p>CoSimApp
input
JSON</p>
          <p>KRATOS
Multiphysics
MDA solver</p>
          <p>CoSim2OWL</p>
          <p>Python
Graphic user
interface</p>
          <p>KRATOS
FlowGraph
Actor</p>
          <p>MDA problems
knowledge base</p>
          <p>OWL
Python
API
recursively calls Algorithm 1, treating  as the new subject, to process any nested structure and add
further RDF triples to the knowledge base. If  is a literal, the algorithm either finds or creates an
owl:DataProperty  using the predicate name , and adds the triple (, , ) to . If 
is an array, the algorithm iterates over each element  in the array. For each item, it checks whether 
is a JSON object or a literal and applies the corresponding procedure as described above. Finally, the
algorithm returns the current subject , which can be reused in subsequent iterations or higher-level
operations.</p>
          <p>Algorithm 1 Triples generation from KRATOS CoSimulation configuration
Require: Knowledge base , subject , predicate name , object value 
if  is a JSON object then</p>
          <p>Apply Algorithm 2 to , , , , owl:Thing
else if  is an array then
for  ∈  do
if  is a JSON object then</p>
          <p>Get/create an owl:Class  by</p>
          <p>Apply Algorithm 2 to , , , , 
else</p>
          <p>Get/create an owl:DataProperty  by</p>
          <p>Add (, , ) to 
end if
end for
else</p>
          <p>Get/create an owl:DataProperty  by</p>
          <p>Add (, , ) to 
end if
return</p>
          <p>Algorithm 2 describes the translation of a JSON object value  into an owl:Named-Individual
. It is invoked from Algorithm 1 and receives the following inputs: the current knowledge base ,
an existing subject individual , the object value , the predicate name  connecting  to , and a
superclass  that serves as a parent for any class created for the individual . Within the algorithm, a
class  is either retrieved or created as a subclass of , based on the predicate name . The object
value  is then instantiated as an individual  of class . Using the same predicate name , an
owl:ObjectProperty  is retrieved or created to represent the relationship between  and . The
triple (, , ) is then added to the knowledge base . Afterward, the algorithm iterates over each
key-value pair (, ) within the JSON object , and recursively calls Algorithm 1 with the updated
parameters: the knowledge base , the new subject , key , and value . This recursive traversal
continues to generate additional RDF triples for the nested structure of .</p>
          <p>Algorithm 2 Translating JSON object of KRATOS CoSimulation configuration into named individual
Require: knowledge base , subject , predicate name , object value , object superclass 
Get/create an owl:Class  by  as an
Get/create an owl:ObjectProperty  by  owl:SubClassOf 
Instantiate  with 
for (, ) ∈  do</p>
          <p>Apply Algorithm 1 to , , ,</p>
          <p>Add (, , ) to 
end for
4.2. Describing classes of coupled systems with OWL axioms
Once a specific coupled system  is represented in the knowledge base , we derive general
knowledge from it by generating OWL axioms that capture recurring structural patterns as class
restrictions. This process is described in Algorithm 3. The algorithm iterates over each individual
 ∈ . For each individual, we compute the set of predicates  for which  is the subject:
() = { : ∃(, )}.</p>
          <p>For each predicate  ∈  , we collect the set of individuals  such that (, ) holds, i.e., the set of
objects connected to  via . We then determine the set of classes  to which the individuals in 
belong:</p>
          <p>(()) = { : ∃(, ),  ∈ }.</p>
          <p>For each class  ∈ , we count the number  of individuals in  that belong to . Then, for
each class  that  is an instance of, we generate OWL class axioms as follows: if  = 1, we add an
existential restriction:
otherwise, we add a cardinality restriction:
 ⊑ ∃.,
 ⊑= ..</p>
          <p>To summarize, for each key-value pair (, ) in the JSON object extracted from the input file of the
KRATOS CoSimulationApplication, we create an individual  in the knowledge base  to represent
the coupled system under consideration. The key  and value  are then passed to Algorithm 1, which
recursively traverses the structure of  and adds corresponding RDF triples to . Finally, we apply
Algorithm 3 to  in order to enrich the knowledge base with OWL axioms that capture generalizable
patterns and semantic constraints. These axioms generalize the observed patterns in the RDF data
into reusable, machine-interpretable OWL semantics, thereby enriching the knowledge base with
domain-level conceptual knowledge. The described CoSim2OWL algorithm has been implemented in
Python using the Owlready2 library [38]. The implementation is publicly available on GitHub5.
5https://anonymous.4open.science/r/coupled_modelling-3909/
Algorithm 3 Generation of OWL axioms describing classes of coupled systems
Require: 
for  ∈  do
 = ()
 = ()
for  ∈  do
 = (())
for  ∈  do
 = (, (())
for  ∈  do
if  == 1 then</p>
          <p>⊑ ∃.
else</p>
          <p>⊑= .
end if
end for
end for
end for
end for</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Use Cases</title>
      <p>To validate the proposed workflow, we examine two case studies of coupled systems from the aerospace
engineering domain. Both cases involve fluid-structure interaction (FSI) problems but difer in the
type of models used: 1) analytical functions and 2) finite element-based physical models (FEM). The
developed prototype is applied to extract a knowledge base from each of these coupled systems.</p>
      <sec id="sec-5-1">
        <title>5.1. Analytical Functions</title>
        <p>The first use case involves a simplified aero-structural system consisting of a two-dimensional airfoil
mounted on a spring. This airfoil–spring system is modeled using an analytical approach originally
developed by Sobieszczanski-Sobieski in [39], see Figure 2.</p>
        <p>The analytical model consists of two coupled disciplines: 1) the fluid dynamics around the airfoil and
2) the structural behavior of the supporting spring system. These disciplines are coupled through two
shared variables: the elastic support pitch angle of the airfoil (Φ ) and the resulting lift force (). The
model operates according to the following process:
1. The lift force acting on the airfoil is computed using aerodynamic equations and is directly
transferred to the structural model by simple data copying.
2. The deformation of the spring system caused by the applied lift force  alters the elastic support
pitch angle Φ , which is then passed back to the aerodynamic model. This updated pitch angle is
used to recompute the lift force.</p>
        <p>3. The process repeats iteratively until a stationary point is reached.</p>
        <p>Due to the assumed nonlinear relationship between the lift coeficient and the pitch angle, the solution
cannot be obtained analytically in a single step. Instead, it requires iterative resolution using a strong
coupling strategy.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. FE-Based Physical Models</title>
        <p>The second use case is based on a finite element model of an aeroelastic ONERA M6 wing, see Figure 3.
The ONERA M6 wing is a well-established benchmark case for validating computational fluid dynamics
(CFD) methods in external aerodynamic flows. Its relatively simple geometry, combined with the
presence of complex transonic phenomena, such as local supersonic regions, shock waves, and turbulent
boundary layer separation, makes it particularly suitable for such evaluations. Due to its extensive
use in the literature as a reference case [40], the ONERA M6 wing has become a de facto standard for
assessing the accuracy and performance of CFD codes.</p>
        <p>(a) photo from [40]
(b) numerical CFD mesh</p>
        <p>The open-source SU2 solver [41] is used to solve the steady 3D Euler equations and compute the
aerodynamic forces of the CFD model. The structural mechanics (SM) model shares the same geometry
as the ONERA M6 wing and is discretized using solid tetrahedral finite elements. It is solved using the
KRATOS StructuralMechanicsApplication. The FE-based coupled model can be described as follows:
1. The coupled problem is solved using the KRATOS CoSimulationApplication, which employs a
strong Gauss–Seidel coupling strategy as specified in the type property of the input JSON file.
To accelerate convergence and reduce computational cost, convergence acceleration methods are
defined in the convergence_accelerators section.
2. The CFD and SM models are remotely orchestrated by the CoSimulationApplication and executed
sequentially according to the order specified in coupling_sequence.
3. The SU2 solver, defined in the solvers section, computes the aerodynamic solution and outputs
the lift force.
4. The lift force is transferred from the CFD model to the SM model using a mapping strategy
provided by the KRATOS MappingApplication, as specified in the data_transfer_operators
property, see Figure 4a.
5. The KRATOS StructuralMechanicsApplication, also defined in solvers, computes the resulting
structural displacements in response to the transferred aerodynamic loads, see Figure 4b.
6. This process is repeated iteratively until convergence is reached, as defined by the criteria specified
in convergence_criteria.</p>
        <p>(a) lift force
(b) structural displacements</p>
      </sec>
      <sec id="sec-5-3">
        <title>5.3. Results</title>
        <p>To extract a knowledge base from the described coupled systems, we process the input JSON files
corresponding to each case and create an instance of the coupled_system class for each. The instance for
the first use case is labeled low_fid_models, while the second use case is represented by the instance
Onera_FSI. We then run our prototype to translate the JSON data into a graph-based representation
and to derive semantic knowledge from it. The resulting knowledge base contains 549 axioms, 41
classes, 41 individuals, 32 data properties, and 13 object properties. Figure 5 visualizes the part of the
knowledge base corresponding to the low_fid_models coupled system.</p>
        <p>As an example of the generated axioms, Figure 6a illustrates the properties of the solvers_1 class,
which represents both the low_fid_fluid and spring_structure solver instances. This class is a
subclass of solvers and is required to be connected to two instances of the data_1 class, one instance
of io_settings_1, and one instance of solver_wrapper_settings_1. Additionally, it possesses
a string value for the has_type property. Figure 6b shows the properties of the low_fid_fluid
individual.</p>
        <p>(b) Properties of a generated instance
(a) Properties of a generated class</p>
        <p>As an example of how the knowledge base can be utilized, Listing 2 demonstrates a SPARQL query that
retrieves all solvers used in previous experiments. This query returns solvers such as low_fid_fluid
and spring_structure from the first coupled system, as well as SM and CFD from the second coupled
system. This information previously could only be obtained by manually collecting and inspecting local
JSON files.</p>
        <p>SELECT DISTINCT ?solver
WHERE {
?solver rdf:type ?solvers .</p>
        <p>?solvers rdfs:subClassOf kb:solvers .
}
-------------------------------------------------------spring_structure
low_fid_fluid
SM
CFD
Listing 2: SPARQL query for retrieving solver instances across all coupled systems in the knowledge
base</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Discussion</title>
      <sec id="sec-6-1">
        <title>6.1. Improvements over existing conversion tools</title>
        <p>In this subsection, we demonstrate that existing tools for converting JSON data into RDF are not
suficient for our goals. Listing 3 shows RDF in TTL format generated by the JSON2RDF tool based
on the airfoil–spring system, while Listing 4 presents RDF generated by our approach using the same
content. The two outputs difer in both structure and semantic expressiveness. The RDF generated by
JSON2RDF contains blank nodes, which require deep path traversal when querying. In contrast, our
tool creates named individuals, giving each resource an identifiable IRI. The output from JSON2RDF
is also harder to maintain and reuse, as it is less modular. Finally, the RDF produced by our approach
explicitly employs OWL classes and properties, enabling more advanced semantic modeling.
...
:solver_settings [
:convergence_accelerators [
:data_name "pitch_angle";
:solver "low_fid_fluid" ;
:type "aitken"
] ;
:data_transfer_operators [ :
direct_transfer [
:mapper_settings [
:mapper_type "</p>
        <p>nearest_neighbor" ;
:echo_level "3"^^xsd:int
] ;
:type "kratos_mapping"
] ] ;
:echo_level "3"^^xsd:int ;
:num_coupling_iterations "20"^^xsd:</p>
        <p>int ;
:type "coupled_solvers.</p>
        <p>gauss_seidel_strong" ;
...</p>
        <p>Listing 3: RDF generated by JSON2RDF
...
:instance_3 rdf:type owl:NamedIndividual ,</p>
        <p>:solver_settings_1 ;
:has_convergence_accelerators :instance_6 ;
...
:has_data_transfer_operators :instance_4 ;
...
:has_echo_level 3 ;
:has_num_coupling_iterations 20 ;
:has_type "coupled_solvers.</p>
        <p>gauss_seidel_strong" .
...
:instance_6 rdf:type owl:NamedIndividual ,</p>
        <p>:convergence_accelerators_1 ;
:has_data_name "pitch_angle" ;
:has_solver "low_fid_fluid" ;
:has_type "aitken" .
...
:instance_4 rdf:type owl:NamedIndividual ,</p>
        <p>:data_transfer_operators_1 ;
:has_mapper_settings :instance_5 ;
:has_type "kratos_mapping" ;
rdfs:label "direct_transfer" .
...</p>
        <sec id="sec-6-1-1">
          <title>Listing 4: RDF generated by our approach</title>
          <p>6.2. Advancing FAIRness of coupled simulation data
In the current state of our approach, we do not perform a user evaluation, as we do not expect aerospace
engineers to interact directly with Semantic Web tools such as Protégé. We plan to conduct a user
study after integrating our approach with user-friendly interfaces like FlowGraph. In the meantime, we
provide an analysis of the FAIRness of the generated representation in comparison to the source JSON
data (see Table 1). This comparison shows that transforming coupled simulation configurations from
JSON into an ontology-based RDF representation makes a significant advancement in terms of FAIR
compliance. Whereas the original JSON files are functional only within their specific software ecosystem
and serve as siloed containers with implicit semantics, our approach transforms the configuration data
into a FAIR digital object. Each piece of information is assigned a unique identifier, embedded within
a formal, machine-interpretable schema, and linked through explicit, typed relationships. Moreover,
the proposed approach enhances data reusability and interoperability by reusing previously generated
classes and properties when modeling new coupled systems. For example, see Listing 5 and Listing 6,
which describe two instances, one from the low_fid_fluid model and the other from the Onera_FSI
model. Both instances belong to the same class, problem_data_1, as they share the exact same set of
properties and difer only in their echo level value. This ensures structural consistency and results in a
unified MDA knowledge base.
:instance_2 rdf:type owl:NamedIndividual ,</p>
          <p>:problem_data_1 ;
:has_parallel_type "OpenMP" ;
:has_echo_level 0 ;
:has_end_time 1.0 ;
:has_print_colors "true"^^xsd:boolean ;
:has_start_time 0.0 .
:instance_44 rdf:type owl:NamedIndividual ,</p>
          <p>:problem_data_1 ;
:has_parallel_type "OpenMP" ;
:has_echo_level 2 ;
:has_end_time 1.0 ;
:has_print_colors "true"^^xsd:boolean ;
:has_start_time 0.0 .</p>
          <p>Listing (5) An instance of problem data from the</p>
        </sec>
        <sec id="sec-6-1-2">
          <title>Listing (6) An instances of problem data from the</title>
          <p>low_fid_fluid model
Onera_FSI model</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusion</title>
      <p>In this research, we addressed the challenge of enabling the reuse of expert knowledge for modeling
coupled systems by representing it using RDF and OWL languages. We developed an automated
workflow to extract knowledge from KRATOS CoSimulationApplication input JSON files and store it in
a centralized knowledge base. As a result, our approach enhances the accessibility and interoperability of
MDA data and enables the extraction of unique, human- and machine-interpretable general patterns of
coupled systems. We validated our method through two use cases and demonstrated how the extracted
knowledge can be efectively visualized and queried, while previously accessing such knowledge
required manual collection and analysis of JSON files.</p>
      <p>Although our work represents only an initial step toward data FAIRification in the aerospace
engineering domain, addressing this challenge is essential to manage the imminent overflow of technical data
that can no longer be handled manually. In future work, we will validate the scalability of our approach
and further enhance the FAIRness of the data and knowledge stored in our knowledge base. Specifically,
we plan to further increase its FAIRness by synchronizing our resources with established knowledge
bases such as Wikidata and DBpedia. Additionally, we aim to extend the knowledge base with a Python
API to facilitate knowledge retrieval and integrate it with existing graphical user interfaces.</p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgments</title>
      <p>We would like to acknowledge the funding by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) under Germany´s Excellence Strategy – EXC 2163/1 - Sustainable and Energy
Eficient Aviation – Project-ID 390881007 and the German Ministry of Education and Research (BmBF)
for the project KISSKI AI Service Center (01IS22093C).</p>
    </sec>
    <sec id="sec-9">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author(s) used ChatGPT in order to: Grammar and spelling
check. After using these tool(s)/service(s), the author(s) reviewed and edited the content as needed and
take(s) full responsibility for the publication’s content.
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