Complex System Modelling with Live Data and Learning - KoSyMo

GAMM annual meeting, Stuttgart, March 2026

Christian Cierpka, Jan Heiland, Sebastian Sachs

TU Ilmenau, Mathematics/Thermodynamics

Teaching Project KoSyMo

Idea of KoSyMo

Natural interdisciplinary learning at student level:

  1. Students of maths and engineering work simultaneously on the same experiment
  1. The engineers do measurements – the mathematicians fiddle with the data
  1. As model and data should match, both parties are coerced into each others issues

A common language and understanding is developed

Engineers:

  • windtunnel experiment with
    • cheap but inaccurate optical observation
    • accurate but typically unfeasible direct measurements

Intermediate:

  • data server

Math students:

  • use training data to identify a model
  • use the model and live data for live prediction of the direct measurements

Technical Challenges

  • we need real experiments
    • everything else is less immediate
  • wind tunnel experiments are expensive
    • we deploy modern but rather low-tech optical cameras
  • data needs to be available online at real time
    • fortunately, the low-tech camera produces slim data streams
  • direct interaction to enforce collaboration
    • we set up data streaming infrastructure across the campus

Fast and Cheap Windtunnel Data

event-based cameras in wind tunnels

  • easy setup
  • no (extra) safety requirements
  • students can operate them
  • fast measurements
  • slim data stream

… so much different from traditional observation techniques

Online Availability of Data

A streaming infrastructure across the campus is set up

  • preferred setup: only open source and standard tools
  • ssh tunnels and open python libraries
  • still evaluating if functionality that comes with the camera should be included(*)
  • all in line with requirements by the local computing centers

(*) a full SDK is shipped with the camera – it is convienient but less standard and with the risk of a lock in

Model Synthesis and Evaluation

Math students shall

  • use offline data to train their models
  • and online streams to test it
  • state-of-the art methods are tested on real data
  • direct feedback on the performance
  • direct interaction with the windtunnel operators

Teaching Goals and Integration in Curricula

Intended teaching contents

  • Maths: Data handling, modelling, prediction and control
  • Engineering: Modern measurement techniques, data processing and modelling

Integration in the study program

  • Maths: integral part of the course “mathematical modelling”
  • Engineers: mandatory study projects in “measurement techniques”

Additional competencies

  • design of experiments, quality assessment of data
  • programming on servers, server infrastructure maintainance
  • time management

Summary and Conclusion

Interdisciplinary Teaching Project KoSyMo with

  • Christian Cierpka (Thermodynamics)
  • Jan Heiland (Mathematics)
  • Sebastian Sachs (Thermodynamics)
  • Meryem Al Zaben and Aaima Arshad (Master student assistants)

Funded through Stifterverband with funds from Freistaat Thüringen

Summary and Conclusion

  • Interdisciplinary project work on a relevant but tractable experiment
  • easy setup and operation
  • enabled by modern hardware and dedicated infrastructure
  • students become aware of each others topics and methods
  • direct feedback for immediate teaching experience
  • secondary skills like project management or maintainance of infrastructure are trained implicitly too

That’s it

Thanks for listening. Questions? Now? Anytime later through jan.heiland@tu-ilmenau.de










References

Altmann, Robert, and Jan Heiland. 2015. “Wie Steuert Man Einen Kran?” Schnappschüße moderner Mathematik aus Oberwolfach.
Benner, Peter, Pawan Goyal, Jan Heiland, and Igor Pontes Duff. 2022. “Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows.” Electron. Trans. Numer. Anal. 56: 28–51. https://doi.org/10.1553/etna_vol56s28.
Cierpka, Christian, Henning Otto, Constanze Poll, Jonas Hüther, Sebastian Jeschke, and Patrick Mäder. 2021. “SmartPIV: Flow Velocity Estimates by Smartphones for Education and Field Studies.” Experiments in Fluids 62. https://doi.org/10.1007/s00348-021-03262-z.
Cierpka, Christian, Tom Weier, and Gunter Gerbeth. 2008. “Evolution of Vortex Structures in an Electromagnetically Excited Separated Flow.” Experiments in Fluids 45: 943–53. https://doi.org/10.1007/s00348-008-0512-6.
———. 2010. “Synchronized Force and Particle Image Velocimetry Measurements on a NACA 0015 in Poststall Under Control of Time Periodic Electromagnetic Forcing.” Physics of Fluids 22. https://doi.org/10.1063/1.3466662.
Fehr, Jörg, Jan Heiland, Christian Himpe, and Jens Saak. 2016. “Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction Software.” AIMS Mathematics 1 (3): 261–81. https://doi.org/10.3934/Math.2016.3.261.
Heiland, Jan, and Yongho Kim. 2025. “Polytopic Autoencoders with Smooth Clustering for Reduced-Order Modeling of Flows.” Journal of Computational Physics 521 (January): 113526. https://doi.org/10.1016/j.jcp.2024.113526.
Kähler, Christian J., Tommaso Astarita, Pavlos P. Vlachos, Jun Sakakibara, Rainer Hain, Stefano Discetti, Roderick La Foy, and Christian Cierpka. 2016. “Main results of the 4th International PIV Challenge.” Experiments in Fluids 57. https://doi.org/10.1007/s00348-016-2173-1.
Ratz, M, S Sachs, J König, and C Cierpka. 2023. “A Deep Neural Network Architecture for Reliable 3D Position and Size Determination for Lagrangian Particle Tracking Using a Single Camera.” Measurement Science and Technology 34: 105203. https://doi.org/10.1088/1361-6501/ace070.
Rusch, Alexander, and Thomas Rösgen. 2023. “TrackAER: Real-Time Event-Based Quantitative Flow Visualization.” Experiments in Fluids 64. https://doi.org/10.1007/s00348-023-03673-0.
Sachs, Sebastian, Manuel Ratz, Patrick Mäder, Jörg König, and Christian Cierpka. 2023. “Particle Detection and Size Recognition Based on Defocused Particle Images: A Comparison of a Deterministic Algorithm and a Deep Neural Network.” Experiments in Fluids 64. https://doi.org/10.1007/s00348-023-03574-2.
Sharifi Ghazijahani, Mohammad, and Christian Cierpka. 2024. “Echo State Networks for Modeling Turbulent Convection.” Scientific Reports 14. https://doi.org/10.1038/s41598-024-79756-7.
Willert, Christian E. 2023. “Event-Based Imaging Velocimetry Using Pulsed Illumination.” Experiments in Fluids 64. https://doi.org/10.1007/s00348-023-03641-8.
Willert, Christian E., and Joachim Klinner. 2022. “Event-Based Imaging Velocimetry: An Assessment of Event-Based Cameras for the Measurement of Fluid Flows.” Experiments in Fluids 63. https://doi.org/10.1007/s00348-022-03441-6.