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hybridGamma: a thermodynamically consistent framework for hybrid modelling of activity coefficients


  • Ulderico Di Caprio Center for Industrial Process Technology, Department of Chemical Engineering, KU Leuven, Agoralaan Building B, 3590 Diepenbeek, Belgium
  • Jan Dègreve Process Engineering for Sustainable Systems, Department of Chemical Engineering, KU Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
  • Peter Hellinckx Faculty of Applied Engineering, University of Antwerp, Groenenborgerlaan 171, 2000 Antwerp, Belgium
  • Steffen Waldherr Chemical Reactor Engineering and Safety (CREaS), Department of Chemical Engineering, KU Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium / University of Vienna, Molecular Systems Biology (MOSYS), Department of Functional and Evolutionary Ecology, Faculty of Life Sciences, 1030 Vienna, Austria
  • M. Enis Leblebici



activity coefficients, hybrid model, physical consistency, vapor-liquid equilibria, Gibbs-Duhem equation


Predicting molecular interactions is a crucial step for chemical process modelling. It requires the full knowledge of the analyzed system, however, this is often impossible in complex real-world cases. Machine learning (ML) techniques overcome this bottleneck and enhance systems predictability using data. Hybrid modelling (HM) is an established technique combining first-principle information and ML techniques. This work introduces a mathematical framework to predict activity coefficients employing HM approach. The obtained models are physically consistent and can handle systems with unknown components or external sources of deviation. The framework is validated on experimental and in-silico cases employing different training approaches. In all the tested cases, the HM showed remarkable prediction capabilities with coefficients of determination R2 above 0.98 for the predicted variables. This work proposes and develops a novel way to approach the HM of molecular interactions by embedding physical laws within the model structure. We encountered three main benefits in applying thermodynamically consistent HMs for activity coefficients: the reduction of tenable parameters, the increased prediction capabilities, and the physical-consistent behavior of the model.


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