Hybrid modeling

Hybrid models combine mechanistic knowledge with machine learning. We develop hybrid modeling methods that need less data than purely data-driven models, extrapolate more reliably, and respect physical laws.

Challenge

Purely data-driven models need large amounts of data, suffer from the curse of dimensionality, and often fail outside the range of their training data. Purely mechanistic models, on the other hand, are expensive to build and often miss phenomena that are not well understood. In chemical engineering, much of the available knowledge (balances, thermodynamics, kinetics) is too valuable to throw away, yet integrating such knowledge into deep learning architectures is still limited.

Our approach

Hybrid models combine mechanistic model components with data-driven ones, for example by learning unknown kinetics or property models with neural networks inside a set of balance equations. Such hybrid models need less data and allow extrapolation beyond the convex hull of the training data. Our work on hybrid modeling includes:

  • Hybrid modeling methodologies. A review of hybrid modeling methodologies and their use in chemical and biochemical engineering (Schweidtmann et al., 2023).
  • Hard-constrained neural networks. ENFORCE embeds nonlinear equality and inequality constraints into neural networks, so that predictions satisfy balances and other known relations.
  • Physics-informed machine learning. Physics-informed neural networks for dynamic reactor models and thermodynamically consistent surrogates.
  • Optimization with hybrid models. Deterministic global optimization of processes with neural networks embedded in mechanistic models (see optimization with surrogate models).
  • Context-aware learning for process design and retrofitting. In the MSCA project CoAUTHOR, Ulderico Di Caprio combines physical-chemistry information, expert knowledge, and data-driven methods with reinforcement learning to design new processes and retrofit existing ones.

The open-source platform HybridML supports building and training hybrid models that combine neural networks, arithmetic expressions, and differential equations.

Partners & funding

  • Marie Skłodowska-Curie Actions (MSCA) Postdoctoral Fellowship, project CoAUTHOR (Ulderico Di Caprio).

Key publications

  • Schweidtmann, A. M., Zhang, D., & von Stosch, M. (2024). A review and perspective on hybrid modeling methodologies. Digital Chemical Engineering, 10, 100136. doi:10.1016/j.dche.2023.100136 · Details
  • Lastrucci, G., & Schweidtmann, A. M. (2025). ENFORCE: Nonlinear constrained learning with adaptive-depth neural projection. arXiv preprint. arXiv:2502.06774 · Details
  • Lastrucci, G., Karia, T., Gromotka, Z., & Schweidtmann, A. M. (2025). Picard-KKT-hPINN: Enforcing nonlinear enthalpy balances for physically consistent neural networks. Systems and Control Transactions (Proceedings of ESCAPE 35). doi:10.69997/sct.108423 · Details
  • Merkelbach, K., Schweidtmann, A. M., Müller, Y., Schwoebel, P., Mhamdi, A., Mitsos, A., Schuppert, A., Mrziglod, T., & Schneckener, S. (2022). HybridML: Open source platform for hybrid modeling. Computers & Chemical Engineering, 160, 107736. doi:10.1016/j.compchemeng.2022.107736 · Details
  • Schweidtmann, A. M., Esche, E., Fischer, A., Kloft, M., Repke, J.-U., Sager, S., & Mitsos, A. (2021). Machine learning in chemical engineering: A perspective. Chemie Ingenieur Technik, 93(12), 2029–2039. doi:10.1002/cite.202100083 · Details
  • Schäfer, P., Caspari, A., Schweidtmann, A. M., Vaupel, Y., Mhamdi, A., & Mitsos, A. (2020). The potential of hybrid mechanistic/data-driven approaches for reduced dynamic modeling: Application to distillation columns. Chemie Ingenieur Technik, 92(12), 1910–1920. doi:10.1002/cite.202000048 · Details
  • Rall, D., Schweidtmann, A. M., Kruse, M., Evdochenko, E., Mitsos, A., & Wessling, M. (2020). Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning. Journal of Membrane Science, 608, 118208. doi:10.1016/j.memsci.2020.118208 · Details
  • Schweidtmann, A. M., Huster, W. R., Lüthje, J. T., & Mitsos, A. (2019). Deterministic global process optimization: Accurate (single-species) properties via artificial neural networks. Computers & Chemical Engineering, 121, 67–74. doi:10.1016/j.compchemeng.2018.10.007 · Details
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