Machine Learning and Optimal Experimental Design for Thermodynamic Property Modeling


Start: 2022-02-01
End: 2025-02-28
Principal Investigators: Roland Herzog, Markus Richter
Staff: Viktor Martinek, Ophelia Frotscher
Funded by: DFG within the Priority Program funding scheme
Part of: Machine Learning in Chemical Engineering (SPP 2331)

Project Description

For many tasks in chemical and energy engineering, the accurate knowledge of thermodynamic properties (e.g., pressure and temperature with density and speed of sound) and the phase behavior of the involved fluids plays a key role. In science, such properties are required for the basic understanding of chemical-physical behavior and for the development of predictive models. For industry, thermodynamic properties are the basis for the design of safe and sustainable processes and machinery. However, the quality of property calculations using equations of state (EOS) depends largely on the availability and accuracy of experimental data. Measurements of such data are often carried out within the frame of a dense grid of measurement points, which delivers a comprehensive data set. Nevertheless, with the aim to develop an accurate EOS, this approach is time-consuming, while it is unclear whether all data are ultimately substantial to the model development. As a result, the required time and financial expenditure makes the generation of reliable models rather limited. Considering this, it is highly desirable to significantly reduce the model development time by limiting the amount of experimental data to the required extent and to involve functional forms, which enable short computing times for the application in process simulation. Therefore, the major goal of the research project is to tackle the aforementioned issues by realizing a specific interplay between (1) interpretable machine learning (ML) to find the ideal functional form of the EOS, (2) optimal experimental design to find the most appropriate measurement points and (3) the actual experiment. A potential workflow can be imagined as follows; starting from initial thermodynamic property measurements, ML-based EOS modeling is used to create a first functional form. This form is used to predict the next most informative measurements, which can then be used as input for further EOS modeling. When to terminate this workflow is inherent part of the project’s research schedule. One important output of the project is an in-situ software tool for thermodynamic measurement planning and model development, which considers the measurement effort, model accuracy and interpretability.

Associated Publications

  • Viktor Martinek, Ian Bell, Roland Herzog, Markus Richter and Xiaoxian Yang
    Entropy scaling of viscosity IV---application to 124 industrially important fluids
    Journal of Chemical & Engineering Data, 2025
    doi:10.1021/acs.jced.4c00451
    bibtex 
    @ARTICLE{MartinekBellHerzogRichterYang:2025:1,
  AUTHOR = {Martinek, Viktor and Bell, Ian and Herzog, Roland and Richter, Markus and Yang, Xiaoxian},
  PUBLISHER = {American Chemical Society (ACS)},
  DATE = {2025-01},
  DOI = {10.1021/acs.jced.4c00451},
  JOURNALTITLE = {Journal of Chemical \& Engineering Data},
  TITLE = {Entropy scaling of viscosity IV---application to 124 industrially important fluids},
}
  • Viktor Martinek, Julia Reuter, Ophelia Frotscher, Sanaz Mostaghim, Markus Richter and Roland Herzog
    Shape constraints in symbolic regression using penalized least squares, 2024
    arXiv:2405.20800
    bibtex 
    @ONLINE{MartinekReuterFrotscherMostaghimRichterHerzog:2024:1,
  AUTHOR = {Martinek, Viktor and Reuter, Julia and Frotscher, Ophelia and Mostaghim, Sanaz and Richter, Markus and Herzog, Roland},
  DATE = {2024-05},
  EPRINT = {2405.20800},
  EPRINTTYPE = {arXiv},
  TITLE = {Shape constraints in symbolic regression using penalized least squares},
}
  • Julia Reuter, Viktor Martinek, Roland Herzog and Sanaz Mostaghim
    Unit-aware genetic programming for the development of empirical equations
    Parallel Problem Solving from Nature – PPSN XVIII, p.168-183, 2024
    arXiv:2405.18896 doi:10.1007/978-3-031-70055-2_11
    bibtex 
    @INPROCEEDINGS{ReuterMartinekHerzogMostaghim:2024:2,
  AUTHOR = {Reuter, Julia and Martinek, Viktor and Herzog, Roland and Mostaghim, Sanaz},
  PUBLISHER = {Springer Nature Switzerland},
  BOOKTITLE = {Parallel Problem Solving from Nature – PPSN XVIII},
  DATE = {2024},
  DOI = {10.1007/978-3-031-70055-2_11},
  EPRINT = {2405.18896},
  EPRINTTYPE = {arXiv},
  PAGES = {168--183},
  TITLE = {Unit-aware genetic programming for the development of empirical equations},
}
  • Viktor Martinek, Ophelia Frotscher, Markus Richter and Roland Herzog
    Introducing thermodynamics-informed symbolic regression -- a tool for thermodynamic equations of state development, 2023
    arXiv:2309.02805
    bibtex 
    @ONLINE{MartinekFrotscherRichterHerzog:2023:1,
  AUTHOR = {Martinek, Viktor and Frotscher, Ophelia and Richter, Markus and Herzog, Roland},
  DATE = {2023-09},
  EPRINT = {2309.02805},
  EPRINTTYPE = {arXiv},
  TITLE = {Introducing thermodynamics-informed symbolic regression -- a tool for thermodynamic equations of state development},
}
  • Ophelia Frotscher, Viktor Martinek, Robin Fingerhut, Xiaoxian Yang, Jadran Vrabec, Roland Herzog and Markus Richter
    Proof of concept for fast equation of state development using an integrated experimental-computational approach
    International Journal of Thermophysics 44(7), 2023
    doi:10.1007/s10765-023-03197-z
    bibtex 
    @ARTICLE{FrotscherMartinekFingerhutYangVrabecHerzogRichter:2023:1,
  AUTHOR = {Frotscher, Ophelia and Martinek, Viktor and Fingerhut, Robin and Yang, Xiaoxian and Vrabec, Jadran and Herzog, Roland and Richter, Markus},
  PUBLISHER = {Springer Science and Business Media LLC},
  DATE = {2023-05},
  DOI = {10.1007/s10765-023-03197-z},
  JOURNALTITLE = {International Journal of Thermophysics},
  NUMBER = {7},
  TITLE = {Proof of concept for fast equation of state development using an integrated experimental-computational approach},
  VOLUME = {44},
}
  • Viktor Martinek
    Thermodynamics-informed symbolic regression (TiSR). A tool for the thermodynamic equation of state development, 2023
    doi:10.5281/zenodo.8317547 https://github.com/scoop-group/TiSR
    bibtex 
    @MISC{Martinek:2023:1,
  AUTHOR = {Martinek, Viktor},
  URL = {https://github.com/scoop-group/TiSR},
  DATE = {2023},
  DOI = {10.5281/zenodo.8317547},
  TITLE = {Thermodynamics-informed symbolic regression (TiSR). A tool for the thermodynamic equation of state development},
}
  • Ophelia Frotscher, Roland Herzog and Markus Richter
    Planning of measurement series for thermodynamic properties based on optimal experimental design
    International Journal of Thermophysics 42(7), 2021
    arXiv:2012.12098 doi:10.1007/s10765-021-02827-8
    bibtex 
    @ARTICLE{FrotscherHerzogRichter:2021:1,
  AUTHOR = {Frotscher, Ophelia and Herzog, Roland and Richter, Markus},
  PUBLISHER = {Springer Science and Business Media LLC},
  DATE = {2021-05},
  DOI = {10.1007/s10765-021-02827-8},
  EPRINT = {2012.12098},
  EPRINTTYPE = {arXiv},
  JOURNALTITLE = {International Journal of Thermophysics},
  NUMBER = {7},
  TITLE = {Planning of measurement series for thermodynamic properties based on optimal experimental design},
  VOLUME = {42},
}

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