BatCAT deliverable 3.1: Report on uncertainty quantification methodology

101137725/BatCAT/WP3/D3.1 D3.1: Report on uncertainty quantification methodology Grant agreement number: 101137725 Project acronym: BatCAT Project title: Battery Cell Assembly Twin Project website: http://batcat.info/ Project start date: 01.01.2024 Project duration: 42 months Call topic: HORIZON-CL5-2023-D2-01-03 Deliverable type1: Report (R) Related work package: WP3 Due date: 30.06.2025 Actual submission date: 29.06.2025 Responsible beneficiary: RPTU Dissemination level2: Public (PU) Abstract: This deliverable outlines the uncertainty quantification methodology developed in WP3 for key simulation techniques in battery cell manufacturing. The approach systematically categorizes uncertainty sources - method, model, and simulation - and is applied to both molecular dynamics and EOS modeling. Case studies highlight how algorithmic and solver choices affect prediction reliability. The methodology is designed to integrate seamlessly into BatCAT’s digital workflow, which connects physical simulations with business decision processes. By combining technical modeling with structured decision-making tools, the framework enables traceable and uncertainty-aware simulations for improved process control in digital twin applications. Author list Beneficiary Name Contact e-mail RPTU Simon Stephan simon.[email protected] 1 Deliverable type: R = Report, P = Prototype, D = Demonstrator, O = Other. 2 Dissemination level: PU = Public, SEN = Sensitive. Public Version v1 Page 2 of 24 RPTU Xueqi Zhang xueqi.z[email protected] LIST Jakub Lengiewicz [email protected] LIST Salim Belouettar salim.b[email protected] NMBU Martin Thomas Horsch martin.tho[email protected] Document history Version Date Reason/comment Revised by 0.1 20.06.2025 Initial draft Simon Stephan 0.2 28.06.2025 Pre-submission final draft Simon Stephan, Xueqi Zhang, Jakub Lengiewicz, Salim Belouettar, Gianluca Boccardo, Stephan Werth, Johanna Glutting, Martin Thomas Horsch 1.0 29.06.2025 Submitted Martin Thomas Horsch Disclaimer Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Climate, Infrastructure and Environment Executive Agency (CINEA). Neither the EU nor the CINEA can be held responsible for them. Abbreviations and acronyms AAD average absolute deviation BPMN business process model and notation CFD computational fluid dynamics DMN decision model and notation EMD equilibrium molecular dynamics EOS equation of state IIDSS interpretable industrial decision support system KER key exploitable result MCO multicriteria optimization MD molecular dynamics MoDoD model-distance-based outlier detection NEMD non-equilibrium molecular dynamics TMWG technical management working group UFD uncertainty flow diagram UQ uncertainty quantification BatCAT has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement no. 101137725. Public Version v1 Page 3 of 24 Contents 1. Executive summary ...................................................................................................................................... 4 2. Progress report (main activities) .................................................................................................................. 4 2.1. Overview of uncertainty quantification methodology ......................................................................... 4 2.2. Model uncertainty of EOS models........................................................................................................ 8 2.3. Method uncertainty of id EOS contribution ....................................................................................... 11 2.4. Systematic simulation uncertainties and statistical simulation uncertainties in molecular dynamics simulations ................................................................................................................................................. 13 2.5. Systematic simulation uncertainties in EOS modeling ....................................................................... 15 2.6. Method and model uncertainties in BPMN and DMN ....................................................................... 19 3. Conclusions ................................................................................................................................................. 21 4. References .................................................................................................................................................. 22 Public Version v1 Page 4 of 24 1. Executive summary This deliverable presents a comprehensive methodology for the identification and quantification of uncertainties in modeling and simulation of battery manufacturing processes. The concept is generic and can be applied to practically any simulation technique. The objective is to improve the reliability, reproducibility, and transparency of modeling and simulation of battery manufacturing processes It was tested and validated using two specific simulation techniques, namely molecular simulation using classical force fields and equations of state (EOS). The report covers a description of the developed uncertainty quantification methodology – first giving an overview; then, giving details and demonstrating the application to exemplary modeling techniques. These two examples differ significantly demonstrating the robustness of the uncertainty quantification methodology. In the second part of the BatCAT project, we will apply the novel uncertainty quantification methodology to battery manufacturing use cases. The increasing complexity of digital manufacturing processes, combined with the integration of models, simulations, and experimental data, necessitates a rigorous approach to uncertainty quantification (UQ) and reliability assessment. Uncertainty Quantification (UQ) is a cornerstone of the BatCAT project’s strategy to develop reliable, transparent, and actionable digital twins for battery cell manufacturing. D3.1 addresses this challenge by developing a formal methodology for the representation, propagation, and management of uncertainty across the manufacturing data space and supporting provenance tracking. The objectives of the deliverable D3.1 is to: • Develop a formal model and methodology for representing uncertainty and reliability. • Establish mechanisms for uncertainty propagation. • Support evidence aggregation from heterogeneous sources. • Enable documentation of uncertainties in models, simulations, and experimental data. 2. Progress report (main activities) 2.1. Overview of uncertainty quantification methodology In BatCAT, a formal methodology for uncertainty quantification has been developed as a key exploitable result (KER). This methodology is a core component of Work Package 3 (Interoperability Infrastructure), specifically Task 3.4. The focus was on the uncertainty quantification of modeling and simulation techniques used for batter production modeling. Yet, also experimental data uncertainty was incorporated in the developed uncertainty quantification methodology. We have developed a comprehensive methodology for the identification and quantification of uncertainties across different modeling and simulation techniques. The methodology is built as a Public Version v1 Page 5 of 24 hierarchical concept, i.e. has three main elements. Thus, the uncertainties of battery manufacturing digital twins can be broadly classified into three overarching categories (see also Fig. 1): • Method Uncertainty: Each modeling and simulation method (could also be experimental method), inherently carries its own uncertainty. These uncertainties are a result of the basic assumptions and simplifications of the method. Depending on their assumptions and complexity, models approximate physical phenomena to different degrees of accuracy, resulting in uncertainties of the digital twin with regard to reality, e.g. the simplifications of classical molecular dynamics simulations where Newtonian mechanics are used. Another example could be simplifications of a macroscopic computational fluid dynamics (CFD) simulation, e.g. regarding the turbulence model and which balance equations are considered in the method. • Model Uncertainty: For a given method, a specific model has to be employed for the execution of a simulation, e.g. a specific model for a given substance and its thermophysical properties. A specific model consists usually of a mathematical backbone and its parameters. The model parameters were usually trained to some experimental data at some point. A given model will reflect reality only to a certain degree and, during the parameter adjustment, choices were made which aspects are very accurate captured by the model and which other aspects only moderately accurately – knowing that compromises have to be made for practically all models. For example, a specific force field has to be used in a classical molecular dynamics simulation that comprises specific model parameters that were adjusted to viscosity and gas solubility data. Thus, using the same method, different models can lead to varying outcomes. • Simulation Uncertainty: During the execution of a simulation (or experiment), additional uncertainties arise. This includes statistical uncertainty – stemming from randomness or chaotic system behavior – as well as systematic uncertainty, which can be introduced through algorithmic implementation, numerical settings, or software-specific behavior. Uncertainty Quantification Method Uncertainty Model Uncertainty Simulation Uncertainty Simulation Statistical Uncertainty Simulation Systematical Uncertainty Figure 1: Overview of uncertainty quantification methodology for modelling and simulation of battery manufacturing processes. Public Version v1 Page 6 of 24 These categories form the conceptual basis for our uncertainty quantification methodology. Behind each category, variables (at least one for each category) exist which actually quantify the uncertainty. The sum of these uncertainties quantifies the deviation of the battery manufacturing digital twin to the real-world manufacturing process. We have applied and tested this methodology to multiple modeling and simulation steps and aspects of battery manufacturing. Several outcomes have already been published, including eight peerreviewed articles [Fer24, Ren24a, Ren24b, Sch24a, Sch24c, Sta24, Sta25, Ste24] and two articles [Hor24a, Hor24b] conducted in collaboration with BatCAT contributors. We have applied the uncertainty quantification methodology in the context of equations of state that were used for modeling thermophysical properties of fluids relevant for battery manufacturing. Moreover, we have applied the uncertainty quantification methodology to molecular dynamics simulations for battery cell manufacturing processes. Our work has focused on assessing and reducing method uncertainty, model uncertainty, and simulation uncertainty. Additionally, the methodology was developed incorporating various aspects and contributions from different BatCAT consortium partners, namely: • Formal Model Development: A formal model for uncertainty and reliability was developed. This development was coordinated with the semantics defined in Task 4.4, which focuses on metadata standardization and ontologies. This ensures that uncertainty is consistently represented across the knowledge base. • Uncertainty Propagation: The methodology was applied to uncertainty propagation across different stages of the process, notably over Business Process Model and Notation (BPMN). This is crucial for understanding how uncertainties accumulate and impact downstream steps in the battery manufacturing process. The real-time functionality will also implement uncertainty propagation/explainability based on surrogate models. • Evidence Aggregation: Formal methods were developed for aggregating and combining evidence. This is essential for synthesizing information from diverse sources (e.g., experimental data, multiphysics simulations, data-driven models) while accounting for their inherent uncertainties. • Integration with Provenance Tracking: The uncertainty quantification methodology was integrated into the provenance tracking system across the BatCAT data space. This linkage ensures that the origin and transformations of data are documented, allowing users to trace back the source of uncertainty and verify the lineage of results. • Input for Industrial Decision Support: The Interpretable Industrial Decision Support System (IIDSS) provides explainable measures for uncertainty quantification and its propagation. This means that the system does not just offer recommendations but also clarify the level of confidence or uncertainty associated with those recommendations, empowering informed human decision-making. • MCO Integration: The MCO (Multicriteria Optimization) methodology from ITWM, a core component of the IIDSS, is designed to provide reliable and self-documenting (explainable) metrics for uncertainty quantification and propagation during model parameterization. Public Version v1 Page 7 of 24 These efforts directly support the development of digital twin applications in battery manufacturing, where predictive models must be accurate, reproducible, and transparent to enable reliable process design, optimization, and control. Our uncertainty quantification methodology spans the entire simulation workflow: from data-driven parameter fitting to the propagation of uncertainty in multiscale modeling. By establishing protocols for model calibration, experimental data selection, and the systematic characterization of statistical and systematic uncertainties, we provide a robust framework for integrating different levels of uncertainties of modeling and simulation in battery manufacturing. This provides a robust and widely applicable framework. In the following sections, results from individual aspects of the uncertainty quantification methodology are reported illustrating the robustness and general applicability of the approach. In total, three examples were studied exemplifying the general applicability of the uncertainty quantification framework. The first application example of our uncertainty quantification methodology focuses on the prediction of thermophysical properties using EOS, which are essential for modeling complex fluid behavior under conditions encountered in battery manufacturing processes. In this context, EOS frameworks such as PC-SAFT and SAFT-VR Mie were employed to compute key properties including phase equilibria, density, enthalpy, and the heat capacity of solvents. These EOS models are based on the Helmholtz energy formalism, which is decomposed into two components: the intramolecular (id) contribution, representing energy stored within intramolecular degrees of freedom, and the residual (res) contribution, which accounts for intermolecular interactions. These models are formulated as a function of temperature and density, i.e. While the residual part is typically calibrated using experimental data, the id contribution must be supplied separately to ensure accurate caloric property predictions, which is for example critical for accurately describing the drying of the slurry in the digital twin. This is also highly relevant in battery manufacturing, where thermophysical properties such as isobaric heat capacity pc are critical for designing energy-efficient drying and solvent removal steps. All three uncertainty categories (cf. Fig. 1) were studied for EOS models, namely the method uncertainties, the model uncertainties, and the simulation uncertainties. The results are reported below in detail. In the second example molecular dynamics simulations for the prediction of transport properties relevant for battery manufacturing were considered. In this example, the method uncertainties as well as the simulation uncertainties were studied. As EOS are deterministic, statistical uncertainties are not a concern mostly; However, systematic simulation uncertainties are relevant and were studied here as an example. Moreover, the method uncertainty of EOS models was evaluated. Also, the model uncertainty of different EOS models was evaluated. This gives insights in the relations of the three main uncertainty categories within a single Public Version v1 Page 8 of 24 simulation method. For molecular dynamics simulations, our focus has been on the systematic simulation (i.e. execution-based) uncertainty as well as statistical simulation uncertainty, particularly in quantifying statistical variability and identifying sources of systematic deviation across different simulation engines and calculation methods for the prediction of transport properties for battery manufacturing processes. In the third example, Business Process Model and Notation (BPMN) were studied and specifically how the different uncertainties accumulate and propagate therein. This gives comprehensive insights in the applicability of the developed uncertainty quantification methodology. 2.2. Model uncertainty of EOS models The model uncertainty of EOS models was evaluated using a rigorous and large-scale parametrization approach for EOS models relevant for battery manufacturing processes, e.g. lubricant fluids, ceaning solvent fluids, electrolyte fluids etc. Therefore, we developed an algorithm that conducted a largescale parameterization effort involving over 705,000 experimental data points for 2,426 distinct substances. This comprehensive dataset includes the saturated densities, vapor pressure, enthalpy of vaporization, density, heat capacity, and speed of sound, enabling robust optimization of model parameters. The selection and quality of experimental data are recognized as key factors influencing the accuracy of molecular-based EOS predictions. Therefore, we implemented a model-distancebased outlier detection (MoDOD) algorithm [Sch24b] that automates the identification of inconsistent or erroneous data points. This method quantifies deviations between model predictions and data subsets and facilitates robust regression without the need for manual data curation. The entire pipeline (cf. Fig. 2), from data retrieval to parameter optimization, requires only a CAS number and EOS selection as input. It proceeds autonomously, significantly reducing human-induced variability and ensuring reproducibility. Importantly, in contrast to many existing parameterization approaches, we explicitly incorporate the id contributions based on quantum mechanical data such that also information on the uncertainty introduced by coupling is incorporated in the uncertainty quantification method. The optimized parameters include chain length m , segment size  , and dispersion energy  for PCSAFT, with additional parameters for SAFT-VR Mie describing the repulsive exponent  R and, in the case of associating fluids, the association energy AB  and volume AB  . Moreover, the resulting parameter sets are made available through the MolMod database [Ste19], enhancing accessibility for use in further modeling workflows, including digital twin environments. Public Version v1 Page 9 of 24 Figure 2: Flowchart for the algorithm for assessing the model uncertainty of EOS models for battery manufacturing. The algorithm carries out automatic fitting of substance specific parameters of molecularbased EOS models to experimental data and compares the results. Public Version v1 Page 16 of 24 cubic equations (e.g., Peng-Robinson, PSRK, VTPR) and more advanced molecular-based formulations (e.g., GERG-2008, PeTS, PC-SAFT, PCP-SAFT, SAFT-VR Mie). To ensure a meaningful cross-comparison, we selected a representative set of fluids: cyclohexane, carbon dioxide, methanol, acetone, methane, and argon, that span a broad range of molecular complexities and interaction types. Several of these substances are somewhere involved in battery production processes, e.g. as cleaning agent and gas in the environment. This makes them ideal candidates for benchmarking the consistency, accuracy, and implementation fidelity of different EOS software tools, i.e. determining systematic simulation uncertainties. The insights derived from these comparisons establish a robust methodological foundation, which can be extended to other batteryrelevant systems involving complex polar solvents and electrolyte mixtures. Such transferability is essential for enabling reliable EOS integration into digital twin frameworks supporting battery manufacturing and process optimization. Before comparing the accuracy of predictions across different software platforms and the resulting systematical simulation uncertainty, it is important to recognize that each implementation of an EOS is subject to inherent limitations regarding the range of supported equations of state and the availability of thermodynamic properties for specific substances. These constraints influence not only the types of calculations that can be performed but also the fidelity of the results produced. A comparison of the available models and property calculation capabilities across the different software tools is illustrated in Fig. 8. Figure 8: Overview of EOS and task availability across the evaluated software tools for EOS modelling for determining their systematic simulation uncertainty. Available Not available Public Version v1 Page 17 of 24 Initial results from our benchmarking study revealed noticeable discrepancies between implementations and therefore significant systematic simulation uncertainties - especially for more complex models such as PC-SAFT. These inconsistencies are exemplified by deviations in the predicted speed of sound for carbon dioxide as illustrated in Fig. 9, where the results varied significantly depending on the software used, i.e. significant systematic simulation uncertainties. Similar deviations were observed for other key thermodynamic properties, such as vapor pressure and enthalpy of vaporization – see Fig. 10. In this case, the property values of methanol were directly calculated as a function of temperature using the SAFT-VR Mie EOS by different software implementations. The results, presented in the diagram below, clearly demonstrate the presence of significant systematic simulation uncertainties. These are isolated systematic simulation uncertainties. Figure 9: Relative deviation (corresponding to systematic simulation uncertainties) in the predicted thermodynamic property of carbon dioxide calculated using different software implementations. Identical parameters and state points were applied across all tools. Two different EOS models were evaluated: (left) the cubic Peng–Robinson EOS, and (right) the molecular-based PC-SAFT EOS. The baseline for comparison is the median value of all results. Public Version v1 Page 18 of 24 Figure 10: Systematic simulation uncertainties obtained for the vapor pressure (left) and enthalpy of vaporization (right) of methanol as calculated using the SAFT-VR Mie EOS. Results from different software implementations are distinguished by color. These findings underscore the importance of accounting for implementation-specific uncertainties, i.e. systematic simulation uncertainties, when applying EOS in multiscale simulation frameworks for battery manufacturing. Even small differences in property predictions at the thermodynamic level can propagate through coupled models - impacting, for example, thermal management strategies or solvent evaporation simulations in battery production workflows. This is particularly relevant for digital twins, where accuracy and consistency across all modeling layers are essential for meaningful prediction and control. In conclusion, while EOS provide substantial advantages in terms of computational efficiency and scalability compared to molecular simulations, their deterministic nature does not guarantee consistency across different implementations. Thus, significant systematic simulation uncertainties are present in both (and also in other) simulation techniques. As a result, benchmarking systematic simulation uncertainties are now available. Transparent documentation of algorithmic details are vital to reduce systematic simulation uncertainties for ensuring that these models can be reliably used in the development and deployment of digital twins for battery manufacturing. Both molecular simulation and EOS approaches are particularly important in the context of digital twin applications for battery manufacturing, where predictive models at the molecular level serve as the foundation for capturing macroscopic behavior and supporting real-time process control. While molecular simulations offer detailed insights into microscopic interactions, EOS provide a computationally efficient means of extending these insights to broader thermodynamic conditions and process-relevant time scales. Accurate and reproducible data from both modeling strategies are essential to ensure that the digital twin reliably reflects the physical system. In this context, structured metadata plays a critical role by providing the transparency, consistency, and traceability needed to quantify uncertainties and ensure the credibility of multiscale simulations. These two simulation techniques were used to illustrate the general applicability of the developed uncertainty quantification methodology. Public Version v1 Page 19 of 24 2.6. Method and model uncertainties in BPMN and DMN Battery manufacturing involves complex workflows that span physical, chemical, and operational domains. To achieve high efficiency and quality, it is essential to bridge the gap between technical processes and business logic. BatCAT introduces a unified modeling approach using BPMN (Business Process Model and Notation), DMN (Decision Model and Notation), and a novel construct Uncertainty Flow Diagrams (UFDs) to support uncertainty aware decision-making in battery production. BPMN provides a graphical representation of workflows with tasks, events, and decision gateways. BatCAT uses BPMN to represent tasks at multiple levels: • Macro-level: Entire production lines. • Meso-level: Machineor process-specific flows. • Micro-level: Operator interactions. DMN rules define the business decisions that guide task execution. Examples include: • Batteries classification based on test results. • Process parameter selection. • Re-routing of out-of-spec batches. BPMN and DMN do not natively model uncertainty. Key limitations include: • Inability to capture statistical or epistemic uncertainty. • Lack of traceable uncertainty propagation. • Difficulty in integrating simulation uncertainty. Figure 11: Figure 11: Overview of the envisaged solution showing the steps of design, specification, translation, and analysis [Cam24]. Public Version v1 Page 20 of 24 Fig. 11 illustrates the methodological context of the UFD approach. This approach is primarily intended for engineers building adaptive systems and is designed to be used at the design stage. The core purpose of this methodology, as depicted in Fig. 11, is to take existing design and implementation artefacts as input and produce a report detailing the impact of UPI on key system properties. This output report is crucial for enabling engineers to make informed decisions regarding necessary design and implementation adjustments to mitigate the effects of UPI on the system’s properties and goals. The process itself is iterative, allowing for the incremental refinement of the system’s design and implementation. The methodology presented in Fig. 11 comprises the following distinct steps: • S0. Design & implementation: – This initial stage precedes the rest of the process if the necessary set of design and implementation artefacts is not already available at the outset. – It represents the foundational work from which the subsequent analytical steps build upon. • S1a. UFD specification: – This step involves engineers actively constructing UFDs. – The construction of these diagrams is informed by existing system artefacts and the knowledge of stakeholders, such as members of the engineering team or domain experts. • S1b. Requirements formalisation: – Concurrently with UFD specification, this step focuses on the formalisation of system requirements. – These requirements can encompass various aspects, including constraints (e.g. qualityrelated), system goals, and other pertinent system properties. • S2. Translation: – Following the specification of UFDs, this stage involves the translation of the UFDs into formal specifications. – These formal specifications then serve as the input for the tools that will be utilised in the subsequent propagation analysis step. • S3. Propagation analysis: – This is the final analytical step, where propagation analysis is conducted using formal analysis tools. – The outcome of this analysis provides results that inform how various uncertainties interact and, consequently, how they affect the set of system properties that were formalised in step S1b. UFDs overlay BPMN to explicitly represent uncertainty: • Each BPMN task maps to a UFD action. • UFD actions include metadata for input, process, and output uncertainty. UFDs allow: • Traceable uncertainty propagation through workflows. Public Version v1 Page 21 of 24 • Task-level risk estimation. • Dynamic adaptation of decisions using DMN. This enables a closed-loop system: • Simulations/data provide quantified uncertainties. • UFDs translate these into workflow uncertainty contexts. • DMN rules adapt operations accordingly. The architecture is structured as follows: Simulation + Data Analytics → Uncertainty Quantification → UFDs → BPMN Tasks → DMN Decisions This flow ensures that operational decisions are informed by scientific insights and quantified risks. 3. Conclusions In this work, we have established a comprehensive methodology for uncertainty quantification. We have applied and tested this methodology in different simulation techniques, e.g. molecular dynamics simulations and EOS modeling, with a focus on specific applications in battery production and digital twin environments. Here, examples were chosen from the modeling of fluid properties in battery cell manufacturing processes. The uncertainty quantification methodology rigorously categorizes different and independent uncertainty sources, namely method uncertainties, model uncertainties, and simulation uncertainties. The latter were sub-divided into systematic simulation uncertainties and statistical simulation uncertainties. This framework enables a comprehensive coverage of different and diverse effects causing deviations from predictions of a battery cell manufacturing digital twin from a real process. We systematically tested this methodology using several examples. The results did not only confirm the applicability of the uncertainty quantification methodology, but also provide novel insights in the applicability and reliability of specific modeling and simulation techniques for battery manufacturing modeling. On the one hand, molecular dynamics simulations provide detailed, bottom-up insight into the behavior of fluids and materials in battery cell manufacturing, but are inherently subject to statistical noise and sensitivity to simulation protocols. We systematically examined how different algorithms, sampling methods, and software engines influence systematical simulation uncertainties of key transport properties. To improve transparency and traceability, we emphasized the importance of structured metadata to capture simulation details, numerical settings, and sources of error, enabling more consistent and comparable computational experiments. On the other hand, EOS models, such as PC-SAFT and SAFT-VR Mie, offer deterministic and efficient tools for predicting thermodynamic properties over wide ranges of temperature, pressure, and composition relevant for battery cell manufacturing. Through large-scale data-driven parameterization and benchmarking Public Version v1 Page 22 of 24 studies, we demonstrated how differences in EOS implementation and solver algorithms can lead to considerable discrepancies, even when using the same theoretical model and substance parameters. Thereby, both model and method uncertainties were individually quantified. These findings highlight the necessity of implementation-sensitive uncertainty evaluation, especially when these models are embedded in higher-level process simulations. BatCAT’s integrated use of BPMN, DMN, and UFDs enables seamless coordination of physical and business models in battery manufacturing. UFDs provide a formal mechanism to represent and propagate uncertainty, allowing for risk-aware process control and optimization. This integration closes the loop between simulations, real-world operations, and decision-making. We will employ the developed uncertainty quantification methodology in different multi-physics simulation techniques for specific battery cell manufacturing process simulations in the second part of the BatCAT project. Moreover, the results on the uncertainty quantification methodology will be disseminated appropriately. 4. References [Cam24] J. Cámara, S. Hahner, D. Perez-Palacin, A. Vallecillo, M. Acosta, N. Bencomo, R. Calinescu, S. Gerasimou: Uncertainty Flow Diagrams: Towards a Systematic Representation of Uncertainty Propagation and Interaction in Adaptive Systems, Proc. 19th Intl. Symp. on Software Engineering for Adaptive and Self-Managing Systems, 37-43 (2024) DOI. [Fer24] D. Fertig, H. Hasse, S. Stephan: Molecular Dynamics Study of Adsorption and Wetting of Mixtures of Simple Fluids on Planar Walls, J. Phys. Chem. C 128, 11340-11354 (2024) DOI. [Hor24a] M. T. Horsch, D. Romanov, E. Valseth, S. Belouettar, L. E. Córdova López, J. Glutting, M. A. Janssen, P. Klein, A. Linhart, M. A. Seaton, E. Dypvik Sødahl, N. Vizcaino, S. Werth, S. Stephan, I. T. Todorov, S. Chiacchiera, F. Al Machot: Battery manufacturing knowledge infrastructure requirements for multicriteria optimization based decision support in design of simulation, SeMatS 2024: The 1st International Workshop on Semantic Materials Science co-located with the 20th International Conference on Semantic Systems (SEMANTiCS), 1-8 (2024) DOI. [Hor24b] M. T. Horsch, S. Chiacchiera, I. T. Todorov, A. T. Correia, A. Dey, N. A. Konchakova, S. Scholze, S. Stephan, K. Tøndel, A. Sarkar, M. H. Karray, F. Al Machot, B. Schembera: Exploration of core concepts required for midand domain-level ontology development to facilitate explainable-AIreadiness of data and models, DAO-XAI 2024: 4th International Workshop on Data meets Applied Ontologies in Explainable AI, 1-10 (2024) DOI. [Hor25] M. Horsch, F. Al Machot, J. Vrabec: Scope of Physics-Based Simulation Artefacts, in: Proceedings of the International Workshop on Designing the Conceptual Landscape for a XAIR Validation Infrastructure, DCLXVI 2024, 61–80 (2025) DOI. [Ren24a] H. Renneis, S. Stephan: Characteristic Curves of Polar Fluids: (I) The Two-Center Lennard–Jones Plus Dipole Fluid, Int. J. Thermophys. 45, 77 (2024) DOI. Public Version v1 Page 23 of 24 [Ren24b] H. Renneis, S. Stephan: Characteristic Curves of Polar Fluids: (II) The Two-Center Lennard–Jones Plus Quadrupole Fluid, Int. J. Thermophys. 45, 73 (2024) DOI. [Sch24a] S. Schmitt, H. Hasse, S. Stephan: Entropy Scaling for Diffusion Coefficients in Fluid Mixtures, Nat. Commun. 16, 2611 (2025) DOI. [Sch24b] A. Schnorr, D. Kaldi, J. Staubach, C. Garth, S. Stephan: Using Autonomous Outlier Detection Methods for Thermophysical Property Data, J. Chem. Eng. Data 69, 864–880 (2024) DOI. [Sch24c] S. Schmitt, H. Hasse, S. Stephan: Measurements and Equation of State Modeling of the Density of Five 1-Alcohols (C6-C10) at Pressures of up to 120 MPa, J. Chem. Eng. Data 69, 2967-2983 (2024) DOI. [Sta24] J. Staubach, H. Hasse, S. Stephan: Helmholtz Energy Models for Dipole Interactions: Review and Comprehensive Assessment, Fluid Ph. Equilib. 585, 114168 (2024) DOI. [Sta25] J. Staubach, S. Stephan: Characteristic Curves of the Stockmayer Fluid: Molecular Simulation and Equation of State Modelling, Fluid Ph. Equilib. 592, 114314 (2025) DOI. [Ste19] S. Stephan, M. Horsch, J. Vrabec, H. Hasse: MolMod - An Open Access Database of Force Fields for Molecular Simulations of Fluids, Mol. Sim. 45, 806–814 (2019) DOI. [Ste24] S. Stephan, V. Bråten, H. Hasse: Mass Transfer at Vapor-Liquid Interfaces of H₂O + CO₂ Mixtures Studied by Molecular Dynamics Simulation, J. Non-Equilib. Thermodyn. 49, 441–461 (2024) DOI. Appendix: Key concepts for uncertainty metadata standardization Our recommendation is to use the PTB's formalization of uncertainty, as standardized in its metadata standard D-SI, which is already taken over in the Metadata4Ing ontology. Sources: • D-SI (from PTB, Braunschweig) • Metadata4Ing (from NFDI4Ing) • MSO-EM (mid-level ontologies developed in BatCAT, see e.g. [Hor24a, Hor24b, Hor25]) • PIMS-II (previous work underlying to MSO-EM) Key concept: • uncertainty declaration – Definition: Articulation applied to a numerical variable to give an assessment of its uncertainty – Scope note: e.g., a coverage interval or an expanded uncertainty – Scope note: Uncertainty declaration is the domain of the relations has coverage probability (range: literal) and has statistical distribution (range: statistical distribution) Concepts associated with the key concept (all from D-SI, Metadata4Ing, PIMS-II): • assignment Public Version v1 Page 24 of 24 – Definition: Equality articulation by which a value is assigned to a variable with respect to a particular referent – Example: T = 200 K for substance o as it was measured in a particular cognitive step); T is the variable, 200 K is the value, and o is the referent. – Rule: assigns some value – Rule: assigns to some variable – Rule: has referent some thing (owl:Thing) • coverage interval – Definition: Articulation of a probabilistic-symmetric coverage interval for a real uncertainty – Rule: has coverage probability some literal (rdfs:Literal) – Rule: has interval maximum some literal – Rule: has interval minimum some literal – Rule: has standard uncertainty some literal • expanded uncertainty – Definition: Articulation of an expanded measurement, model, or simulation uncertainty – Rule: has coverage factor some literal • "Coverage factor: Numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded uncertainty" (JCGM 100:2008) – Rule: has coverage probability some literal – Rule: has uncertainty some literal • number – Definition: Lexeme that is numerical in nature – Rule: is literally some literal • numerical variable – Definition: Variable that expects a floating point or integer value – Scope note: A numerical variable can have an uncertainty declaration; a real (subclass of numerical variable) requires an uncertainty declaration. • property – Definition: Variable employed for the possible outcome of observations • quantity value – Rule: has magnitude some number – Rule: has unit some measurement unit • real – Definition: Numerical variable with a measurement unit and an uncertainty declaration – Rule: has uncertainty declaration some uncertainty declaration • statistical distribution – Definition: Probability distribution type (e.g., normal distribution) associated with the value of a variable through the variable's uncertainty declaration • value – Rule: is admissible for some variable • variable – Definition: Conventional that is employed for something to which values can be assigned