Optimization with machine learning models embedded

Data-driven surrogate models can learn nonlinear input-output relations and replace expensive simulations or experiments in optimization. We develop formulations and software to optimize over trained machine learning models, including deterministic global optimization.

Challenge

Machine learning models such as neural networks and Gaussian processes are increasingly used as surrogates for complex thermodynamics, unit operations, or experimental data. To use them in process design and operation, they have to be embedded into optimization problems. These problems are nonconvex, so local solvers may return suboptimal designs, and naive formulations quickly become intractable.

Our approach

This line of work originates from Artur M. Schweidtmann's PhD research at RWTH Aachen University ("Global optimization of processes through machine learning", advised by Prof. Alexander Mitsos). There, reduced-space formulations for deterministic global optimization with artificial neural networks and Gaussian processes embedded were developed and implemented in the MeLOn toolbox for the global solver MAiNGO.

At TU Delft, we continue this work:

  • Mixed-integer formulations for ReLU networks. reluMIP uses progressive bound tightening to create strong MIP encodings of trained ReLU networks, so that they can be embedded in mixed-integer programs.
  • Kolmogorov-Arnold networks (KANs) as surrogate models for deterministic global process optimization (software).
  • Optimization over graph neural networks for computer-aided molecular design.
  • Constrained and physics-informed surrogates that satisfy balance equations (ENFORCE, physics-informed machine learning).

Key publications

  • Karia, T., Lastrucci, G., & Schweidtmann, A. M. (2025). Kolmogorov Arnold Networks (KANs) as surrogate models for global process optimization. Systems and Control Transactions (Proceedings of ESCAPE 35). doi:10.69997/sct.195815 · Details
  • McDonald, T., Tsay, C., Schweidtmann, A. M., & Yorke-Smith, N. (2024). Mixed-integer optimisation of graph neural networks for computer-aided molecular design. Computers & Chemical Engineering, 185, 108660. doi:10.1016/j.compchemeng.2024.108660 · Details
  • Schweidtmann, A. M., Weber, J. M., Wende, C., Netze, L., & Mitsos, A. (2022). Obey validity limits of data-driven models through topological data analysis and one-class classification. Optimization and Engineering, 23(2), 855–876. doi:10.1007/s11081-021-09608-0 · Details
  • Schweidtmann, A. M., Bongartz, D., Grothe, D., Kerkenhoff, T., Lin, X., Najman, J., & Mitsos, A. (2021). Deterministic global optimization with Gaussian processes embedded. Mathematical Programming Computation, 13(3), 553–581. doi:10.1007/s12532-021-00204-y · Details
  • Schweidtmann, A. M., & Mitsos, A. (2019). Deterministic global optimization with artificial neural networks embedded. Journal of Optimization Theory and Applications, 180(3), 925–948. doi:10.1007/s10957-018-1396-0 · Details
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