HybridML: Open source platform for hybrid modeling

Kilian Merkelbach, Artur M. Schweidtmann, Younes Müller, Patrick Schwoebel, Adel Mhamdi*, Alexander Mitsos, Andreas Schuppert, Thomas Mrziglod, Sebastian Schneckener

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

14 Citations (Scopus)


Hybrid modelling, i.e., the combination of data-driven modelling with mechanistic model components, reduces the data demand and enables extrapolation of data-driven models. However, building, training and evaluation of hybrid models is cumbersome with current frameworks. We developed HybridML, an open-source modeling platform, in which hybrid models can be trained, i.e., combinations of artificial neural networks, arithmetic expressions, and differential equations. We employ TensorFlow for artificial neural network training and Casadi to integrate ordinary differential equations and provide gradients of differential model equations enabling continuous time representations. HybridML provides also a JSON interface for the model development. We apply HybridML to an industrial case study, in which the trained model is used to predict drug concentrations over time, based on physiological information about the patients. To demonstrate its versatility, we also present a nonlinear application, where HybridML is used to model the spread of the COVID-19 pandemic in German federal states based on the state's socio-economic attributes.

Original languageEnglish
Article number107736
JournalComputers and Chemical Engineering
Publication statusPublished - 2022
Externally publishedYes


  • Hybrid modeling
  • Machine learning
  • Modeling tools
  • Pharmacokinetics
  • Python
  • Tensorflow


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