Machine Learning and Optimal Experimental Design for Thermodynamic Property Modeling


Mar 2025Feb 2028
PIs
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 play a key role. Such properties are required for the fundamental understanding of chemical-physical behavior and for the development of predictive models. Thermodynamic properties are also the basis for the design of safe, sustainable and energy efficient processes and machinery. However, the quality of property predictions depends largely on the availability and accuracy of experimental or simulated data, as well as on the modeling techniques used. Thermodynamic property measurements are typically the most accurate data source and are often carried out on a dense grid of measurement points, which delivers a seemingly comprehensive data set. With the goal to develop an accurate thermodynamic property model, this approach is time-consuming, while it is unclear whether all data contribute substantially to the model development. As a result, although fundamental knowledge can be generated, the required time and financial expenditure make the generation of reliable models rather limited. It is thus highly desirable to significantly reduce the model development time by limiting the amount of acquired data, whether experimental or simulated, to the required extent. Additionally, models developed should exhibit concise functional forms to allow for efficient evaluation and facilitate their use in process simulations. Therefore, the major goal of the proposed project is to tackle the aforementioned issues using a synergistic combination of (1) interpretable machine learning in the form of symbolic regression, to find better functional forms to model thermodynamic properties, (2) optimal experimental design, to find the most appropriate data points, and (3) the actual data acquisition. During the first phase of the priority program, a workflow was applied, where, starting from initial thermodynamic property data, machine learning-based equation-of-state modeling is used to create a first functional form. This form is used to identify the next most informative measurements, which can then be used as input for further equation-of-state modeling. In the second project phase this workflow is applied to investigate mixtures. To this end, liquid-liquid equilibria are investigated, and application-specific models are created for use in process designs. In addition, symbolic regression will be used to develop physics-based fundamental equations of state for pure substances and particularly mixtures.

Associated Publications

  • Machine learning for thermodynamic property modeling Proceedings
    Roland Herzog and Viktor Martinek
    Oberwolfach Reports 23(2) · 2026
    doi:10.4171/owr/2026/26
    BibLaTeX 
    @ARTICLE{HerzogMartinek:2026:1,
  AUTHOR = {Herzog, Roland and Martinek, Viktor},
  EDITOR = {Ghattas, Omar and Heinkenschloss, Matthias and Reich, Sebastian and Schillings, Claudia},
  PUBLISHER = {European Mathematical Society Publishing House},
  BOOKTITLE = {Workshop: Mathematical Foundation of Digital Twins},
  DATE = {2026-10},
  DOI = {10.4171/owr/2026/26},
  JOURNALTITLE = {Oberwolfach Reports},
  NUMBER = {2},
  TITLE = {Machine learning for thermodynamic property modeling},
  VOLUME = {23},
}
  • Symbolic regression for shared expressions – introducing partial parameter sharing Proceedings
    Viktor Martinek and Roland Herzog
    Parallel Problem Solving from Nature – PPSN XIX, p.251-266 · 2026
    arXiv:2601.04051 doi:10.1007/978-3-032-36229-2_16
    BibLaTeX 
    @INPROCEEDINGS{MartinekHerzog:2026:2,
  AUTHOR = {Martinek, Viktor and Herzog, Roland},
  PUBLISHER = {Springer Nature Switzerland},
  BOOKTITLE = {Parallel Problem Solving from Nature -- PPSN XIX},
  DATE = {2026-08},
  DOI = {10.1007/978-3-032-36229-2_16},
  EPRINT = {2601.04051},
  EPRINTTYPE = {arXiv},
  PAGES = {251--266},
  TITLE = {Symbolic regression for shared expressions -- introducing partial parameter sharing},
}
  • A shared expression to predict monomer consumption in itaconate–acrylate radical copolymerizations developed with symbolic regression Preprint
    Viktor Martinek, Marco Drache, Frederic Matussek, Moritz Baumert, Lennart Arendes, Jelena Fiosina, Ophelia Frotscher, Roland Herzog and Sabine Beuermann
    2026
    doi:10.26434/chemrxiv.15005769/v1
    BibLaTeX 
    @ONLINE{MartinekDracheMatussekBaumertArendesFiosinaFrotscherHerzogBeuermann:2026:1,
  AUTHOR = {Martinek, Viktor and Drache, Marco and Matussek, Frederic and Baumert, Moritz and Arendes, Lennart and Fiosina, Jelena and Frotscher, Ophelia and Herzog, Roland and Beuermann, Sabine},
  PUBLISHER = {American Chemical Society (ACS)},
  DATE = {2026-07},
  DOI = {10.26434/chemrxiv.15005769/v1},
  TITLE = {A shared expression to predict monomer consumption in itaconate--acrylate radical copolymerizations developed with symbolic regression},
}
  • Shape constraints in symbolic regression using penalized least squares Chapter
    Viktor Martinek, Julia Reuter, Ophelia Frotscher, Sanaz Mostaghim, Markus Richter and Roland Herzog
    Machine Learning and Principles and Practice of Knowledge Discovery in Databases, p.224-239 · 2026
    arXiv:2405.20800 doi:10.1007/978-3-032-25305-7_16
    BibLaTeX 
    @INBOOK{MartinekReuterFrotscherMostaghimRichterHerzog:2026:1,
  AUTHOR = {Martinek, Viktor and Reuter, Julia and Frotscher, Ophelia and Mostaghim, Sanaz and Richter, Markus and Herzog, Roland},
  EDITOR = {Cerrato, Mattia and Kalinauskaitė, Danguolė and Lukoševičius, Mantas and Pechenizkiy, Mykola and Šutienė, Kristina},
  PUBLISHER = {Springer Nature Switzerland},
  BOOKTITLE = {Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
  DATE = {2026-05},
  DOI = {10.1007/978-3-032-25305-7_16},
  EPRINT = {2405.20800},
  EPRINTTYPE = {arXiv},
  PAGES = {224--239},
  TITLE = {Shape constraints in symbolic regression using penalized least squares},
}
  • Reference correlation of the viscosity of neon Article
    Sofia Sotiriadou, Konstantinos D. Antoniadis, Marc J. Assael, Viktor Martinek, Monika Thol and Marcia L. Huber
    International Journal of Thermophysics 47(5) · 2026
    doi:10.1007/s10765-026-03745-3
    BibLaTeX 
    @ARTICLE{SotiriadouAntoniadisAssaelMartinekTholHuber:2026:1,
  AUTHOR = {Sotiriadou, Sofia and Antoniadis, Konstantinos D. and Assael, Marc J. and Martinek, Viktor and Thol, Monika and Huber, Marcia L.},
  PUBLISHER = {Springer Science and Business Media LLC},
  DATE = {2026-04},
  DOI = {10.1007/s10765-026-03745-3},
  JOURNALTITLE = {International Journal of Thermophysics},
  NUMBER = {5},
  TITLE = {Reference correlation of the viscosity of neon},
  VOLUME = {47},
}
  • Fast symbolic regression benchmarking Chapter
    Viktor Martinek
    Advances in Swarm Intelligence, p.307-317 · 2026
    arXiv:2508.14481 doi:10.1007/978-981-95-0985-0_25
    BibLaTeX 
    @INBOOK{Martinek:2025:3,
  AUTHOR = {Martinek, Viktor},
  PUBLISHER = {Springer Nature Singapore},
  BOOKTITLE = {Advances in Swarm Intelligence},
  DATE = {2026},
  DOI = {10.1007/978-981-95-0985-0_25},
  EPRINT = {2508.14481},
  EPRINTTYPE = {arXiv},
  PAGES = {307--317},
  TITLE = {Fast symbolic regression benchmarking},
}
  • Correlation for the viscosity of methane (CH4) from the triple point to 625 K and pressures to 1000 MPa Article
    Sofia G. Sotiriadou, Konstantinos D. Antoniadis, Marc J. Assael, Viktor Martinek and Marcia L. Huber
    International Journal of Thermophysics 47(1) · 2026
    doi:10.1007/s10765-025-03690-7
    BibLaTeX 
    @ARTICLE{SotiriadouAntoniadisAssaelMartinekHuber:2025:1,
  AUTHOR = {Sotiriadou, Sofia G. and Antoniadis, Konstantinos D. and Assael, Marc J. and Martinek, Viktor and Huber, Marcia L.},
  PUBLISHER = {Springer Science and Business Media LLC},
  DATE = {2026-01},
  DOI = {10.1007/s10765-025-03690-7},
  JOURNALTITLE = {International Journal of Thermophysics},
  NUMBER = {1},
  TITLE = {Correlation for the viscosity of methane (CH4) from the triple point to 625~K and pressures to 1000~MPa},
  VOLUME = {47},
}

Associated Software

  • Fast symbolic regression benchmarking
    Viktor Martinek
    2025
    doi:10.5281/zenodo.15469873 GitHub
    BibLaTeX 
    @SOFTWARE{Martinek:2025:1,
  AUTHOR = {Martinek, Viktor},
  URL = {https://github.com/viktmar/FastSRB/},
  DATE = {2025},
  DOI = {10.5281/zenodo.15469873},
  TITLE = {Fast symbolic regression benchmarking},
}
  • Thermodynamics-informed symbolic regression (TiSR). A tool for the thermodynamic equation of state development
    Viktor Martinek
    2023
    doi:10.5281/zenodo.8317546 GitHub
    BibLaTeX 
    @SOFTWARE{Martinek:2023:1,
  AUTHOR = {Martinek, Viktor},
  URL = {https://github.com/scoop-group/TiSR/},
  DATE = {2023},
  DOI = {10.5281/zenodo.8317546},
  TITLE = {Thermodynamics-informed symbolic regression (TiSR). A tool for the thermodynamic equation of state development},
}

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