Machine Learning
We are interested in optimization methods to train machine learning models. But we are also interested in ways to combine mathematical modeling of expert knowledge, machine learning, and optimization under uncertainty in real time. Several ongoing projects in clinical decision making, energy, and mobility investigate innovative ways to combine them with the ultimate goal of adaptive, efficient, reliable, and understandable algorithms for decision making. I am head of an informal steering committee for Artificial Intelligence at the OVGU, see more details here, and member of the scientific committee of DFG SPP 2331: Machine Learning in Chemical Engineering. Knowledge Meets Data: Interpretability, Extrapolation, Reliability, Trust. Within SPP 2331 we run a project on Machine Learning for the Design and Control of Power2X Processes with Application to Methanol Synthesis.
My group is working on Mathematical Foundations of Machine Learning with a particular focus on the optimization for ML models, optimization with embedded ML models, and ML for intrinsic optimality principles. Much of of our research is stimulated by applications. We published surveys on challenges in the intersection between Machine Learning and Chemical Engineering and use cases for Machine Learning and Digital Twins in Oncology.
As one example, our research project on an optimization-driven analysis of (semi-) autonomous urban traffic can be seen here. A survey paper for the interested public with the title Mathematical Optimization and Machine Learning for Efficient Urban Traffic is available as a preprint.
A complementary approach was used in the paper Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification, a preprint is available here. The main focus of our research here is interpretability, which we obtain from a classification in a lower-dimensional space of optimization-generated features.
An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. In a joint paper with Martyna Minakowska and Thomas Richter we derived and validated a new machine learning driven framework to determine the drag, lift, rotational and pitching torque coefficients for different non-spherical particles in a fluid flow.
Members of the group have been actively participated in the Scientific Machine Learning project in julia.
Undergraduate theses in the group address aspects of algorithmic optimization and are thus hence always linked to machine learning. Examples of theses addressing machine learning directly of the last five years are the following:
- Felix Bernhardt, 2018: Comparison of machine learning, domain-specific and hybrid models for discrimination of cardiac arrhythmias
- Christoph Plate, 2019: Approximation der Überlappungswahrscheinlichkeit zweier Rechtecke mittels neuronaler Netze, Bachelor
- Adrian-Manuel Reimann, 2019: Feature Selection mittels Support Vector Machines zur medizinischen Diagnostik von Schlafapnoe, Bachelor
- Paul Scharnhorst, 2019: Optimal Control Methods for Deep Learning
- Jan Schneider, 2019: Geometric Methods in Dynamic Averaging for Decentralized Deep Learning in Automated Driving (with Volkswagen, Wolfsburg)
- Bastian Radloff, 2020: Transformer-Models for Multilabel Topic Classification of Global Development News (with Devex, Barcelona)
- Adrian Reimann, 2021: Machine Learning Ansätze für Zeitreihen bei akuter lymphatischer Leukämie
- Kilian Bock, 2021: Active Learning for maximizing model utility in material science on a small fractographic data set
- Jan Krause, 2021: Investigation of Options to handle 3D MRI data via convolutional neural networks - applications in knee osteoarthritis classification
- Julien Brandes, 2023: Gurobi Machine Learning, Bachelor
- Martha Vollmar, 2023: Untersuchung der Lebensdauer von Einbauteilen in einem Rohrreaktor durch Maschinelles Lernen
- Timon Klein, 2023: Machine Learning Classification of Brain States Based on MEG Recordings
Many ongoing PhD projects address machine learning, usually for complex dynamic systems. For example, we are interested in using mixed-integer optimal control for an efficient training of deep neural networks and in optimal control using hybrid models, symbolic regression, optimal experimental design for neural networks, inverse optimal control and inverse reinforcement learning.
Selected publications
2026
article
Optimal Experiments for Hybrid Modeling of Methanol Synthesis Kinetics
Computers & Chemical Engineering
@article{Kaps2026,
author = {Kaps, Lothar and Leipold, Johannes and Plate, Christoph and Martensen, Carl Julius and Kortuz, Wieland and Seidel-Morgenstern, Andreas and Kienle, Achim and Sager, Sebastian},
title = {Optimal Experiments for Hybrid Modeling of Methanol Synthesis Kinetics},
journal = {Computers \& Chemical Engineering},
publisher = {Elsevier BV},
year = {2026},
volume = {204},
pages = {109387},
doi = {10.1016/j.compchemeng.2025.109387}
}
2026
article
Superstructure Optimization with Embedded Neural Networks for Sustainable Aviation Fuel Production
Chemical Engineering Journal
@article{Klimek2026,
author = {Klimek, Alexander and Plate, Christoph and Sager, Sebastian and Sundmacher, Kai and Ganzer, Caroline},
title = {Superstructure Optimization with Embedded Neural Networks for Sustainable Aviation Fuel Production},
journal = {Chemical Engineering Journal},
publisher = {Elsevier BV},
year = {2026},
volume = {535},
pages = {175172},
url = {http://arxiv.org/abs/2509.09796},
doi = {10.1016/j.cej.2026.175172}
}
2026
article
On lifting strategies for optimal control problems
optimization online preprint 34160
@article{Lampel2026,
author = {Lampel, Robert and Sager, Sebastian},
title = {On lifting strategies for optimal control problems},
journal = {optimization online preprint 34160},
year = {2026},
url = {https://optimization-online.org/?p=34160}
}
2026
article
Optimal experimental design for universal differential equations
IEEE Transactions on Automatic Control
@article{Plate2025,
author = {Plate, Christoph and Martensen, Carl Julius and Sager, Sebastian},
title = {Optimal experimental design for universal differential equations},
journal = {IEEE Transactions on Automatic Control},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
year = {2026},
volume = {71},
number = {3},
pages = {1521--1536},
url = {http://arxiv.org/abs/2408.07143},
doi = {10.1109/tac.2025.3609533}
}
2026
article
An analysis of optimization problems involving ReLU neural networks
Optimization and Engineering
@article{Plate2026,
author = {Plate, Christoph and Hahn, Mirko and Klimek, Alexander and Ganzer, Caroline and Sundmacher, Kai and Sager, Sebastian},
title = {An analysis of optimization problems involving ReLU neural networks},
journal = {Optimization and Engineering},
publisher = {Springer Science and Business Media LLC},
year = {2026},
volume = {27},
number = {3},
pages = {2573--2605},
url = {https://arxiv.org/abs/2502.03016},
doi = {10.1007/s11081-026-10075-8}
}
2026
article
Temporal kinetics of brain state effects on visual perception
Scientific Reports
@article{Schmid2026,
author = {Schmid, Paul and Klein, Timon and Minakowski, Piotr and Sager, Sebastian and Reichert, Christoph and Knight, Robert T. and D\"urschmid, Stefan},
title = {Temporal kinetics of brain state effects on visual perception},
journal = {Scientific Reports},
publisher = {Springer Science and Business Media LLC},
year = {2026},
volume = {16},
number = {1},
pages = {14689},
doi = {10.1038/s41598-026-50974-5}
}
2026
misc
Adjoint-Compatible Surrogates of the Expected Information Gain for Optimal Experimental Design
ArXiV preprint 2603.26431
@misc{deMontella2026,
author = {de Montella, Luc and Sager, Sebastian},
title = {Adjoint-Compatible Surrogates of the Expected Information Gain for Optimal Experimental Design},
journal = {ArXiV preprint 2603.26431},
year = {2026},
note = {Submitted revisions to SIAM Journal on Uncertainty Quantification},
url = {https://arxiv.org/abs/2603.26431}
}
2025
article
Generalized Inverse Optimal Control and its Application in Biology
Annual Reviews in Control
@article{Banga2025,
author = {Banga, Julio R. and Sager, Sebastian},
title = {Generalized Inverse Optimal Control and its Application in Biology},
journal = {Annual Reviews in Control},
publisher = {Elsevier BV},
year = {2025},
volume = {60},
pages = {101029},
doi = {10.1016/j.arcontrol.2025.101029}
}
2025
article
Flexible Patched Brain Transformer model for EEG decoding
Scientific Reports
@article{Klein2025,
author = {Klein, Timon and Minakowski, Piotr and Sager, Sebastian},
title = {Flexible Patched Brain Transformer model for EEG decoding},
journal = {Scientific Reports},
publisher = {Springer Science and Business Media LLC},
year = {2025},
volume = {15},
number = {1},
pages = {10935},
url = {https://www.nature.com/articles/s41598-025-86294-3},
doi = {10.1038/s41598-025-86294-3}
}
2025
article
Mitigating Subject Dependency in EEG Decoding with Subject-Specific Low-Rank Adapters
NeurIPS 2025 BrainBodyFM Workshop
@article{Klein2025b,
author = {Klein, Timon and Minakowski, Piotr and Sager, Sebastian},
title = {Mitigating Subject Dependency in EEG Decoding with Subject-Specific Low-Rank Adapters},
journal = {NeurIPS 2025 BrainBodyFM Workshop},
year = {2025},
url = {https://neurips.cc/virtual/2025/122104}
}
2025
misc
On liftings that improve convergence properties of Newton’s Method for Boundary Value Optimization Problems
optimization online preprint 29392
@misc{Lampel2025,
author = {Lampel, Robert and Sager, Sebastian},
title = {On liftings that improve convergence properties of Newton’s Method for Boundary Value Optimization Problems},
journal = {optimization online preprint 29392},
year = {2025},
note = {Submitted to Optimisation Methods and Software},
url = {https://optimization-online.org/?p=29392}
}
2025
article
A geometric framework for momentum-based optimizers for low-rank training
NeurIPS 2025
@article{Schotthoefer2025,
author = {Schotth{\"o}fer, Steffen and Klein, Timon and Kusch, Jonas},
title = {A geometric framework for momentum-based optimizers for low-rank training},
journal = {NeurIPS 2025},
year = {2025},
url = {https://arxiv.org/abs/2506.17475}
}
2024
misc
Data-Driven Discovery of Feedback Mechanisms in Acute Myeloid Leukaemia: Alternatives to classical models using Deep Nonlinear Mixed Effect modeling and Symbolic Regression
bioRxiv preprint
@misc{Martensen2024,
author = {Martensen, Carl Julius and Korsbo, Niklas and Ivaturi, Vijay and Sager, Sebastian},
title = {Data-Driven Discovery of Feedback Mechanisms in Acute Myeloid Leukaemia: Alternatives to classical models using Deep Nonlinear Mixed Effect modeling and Symbolic Regression},
journal = {bioRxiv preprint},
publisher = {openRxiv},
year = {2024},
doi = {10.1101/2024.06.17.599366}
}
2024
misc
dynamicOED.jl
GitHub repository
@misc{Martensen2024b,
author = {Martensen, C.J. and Plate, C. and Sager, S.},
title = {dynamicOED.jl},
journal = {GitHub repository},
publisher = {GitHub},
year = {2024},
url = {https://github.com/mathopt/DynamicOED.jl}
}
2024
article
DynamicOED.jl: A Julia package for solving optimum experimental design problems
Journal of Open Source Software
@article{Martensen2024c,
author = {Martensen, Carl Julius and Plate, Christoph and Sager, Sebastian},
title = {DynamicOED.jl: A Julia package for solving optimum experimental design problems},
journal = {Journal of Open Source Software},
publisher = {The Open Journal},
year = {2024},
volume = {9},
number = {98},
pages = {6605},
doi = {10.21105/joss.06605}
}
2023
incollection
Towards machine learning of power-2-methanol processes
33rd European Symposium on Computer Aided Process Engineering
@incollection{Martensen2023,
author = {Martensen, Carl Julius and Plate, Christoph and Ke{\ss}ler, Tobias and Kunde, Christian and Kaps, Lothar and Kienle, Achim and Seidel-Morgenstern, Andreas and Sager, Sebastian},
title = {Towards machine learning of power-2-methanol processes},
booktitle = {33rd European Symposium on Computer Aided Process Engineering},
publisher = {Elsevier},
year = {2023},
series = {Computer Aided Chemical Engineering},
pages = {561--568},
doi = {10.1016/b978-0-443-15274-0.50089-5}
}
2023
article
Digital Twins in Oncology
Journal of Cancer Research and Clinical Oncology
@article{Sager2023,
author = {Sager, Sebastian},
title = {Digital Twins in Oncology},
journal = {Journal of Cancer Research and Clinical Oncology},
publisher = {Springer Science and Business Media LLC},
year = {2023},
volume = {149},
number = {9},
pages = {5475--5477},
url = {https://link.springer.com/article/10.1007/s00432-023-04633-1},
doi = {10.1007/s00432-023-04633-1}
}
2021
incollection
Mathematical Optimization and Machine Learning for Efficient Urban Traffic
German Success Stories in Industrial Mathematics
@incollection{Bethge2022,
author = {Bethge, Johanna and Findeisen, Rolf and Duc Le, Do and Merkert, Maximilian and Sager, Sebastian and Savchenko, Anton and Rewald, Hannes},
title = {Mathematical Optimization and Machine Learning for Efficient Urban Traffic},
booktitle = {German Success Stories in Industrial Mathematics},
publisher = {Springer International Publishing},
year = {2021},
editor = {K\"{u}fer, Karl-Heinz and Maass, Peter and Milde, Anja and Schulz, Volker},
series = {Mathematics in Industry},
pages = {113--120},
url = {https://mathopt.de/publications/Bethge2020.pdf},
doi = {10.1007/978-3-030-81455-7_19}
}
2021
article
A finite element / neural network framework for modeling suspensions of non-spherical particles - Concepts and medical applications
Vietnam Journal of Mathematics
@article{Minakowska2021,
author = {Minakowska, M. and Richter, T. and Sager, S.},
title = {A finite element / neural network framework for modeling suspensions of non-spherical particles - Concepts and medical applications},
journal = {Vietnam Journal of Mathematics},
year = {2021},
volume = {49},
pages = {207--235},
url = {https://arxiv.org/abs/2009.10818}
}
2021
article
Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification
PLOS ONE
@article{Sager2021,
author = {Sager, Sebastian and Bernhardt, Felix and Kehrle, Florian and Merkert, Maximilian and Potschka, Andreas and Meder, Benjamin and Katus, Hugo and Scholz, Eberhard},
title = {Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification},
journal = {PLOS ONE},
publisher = {Public Library of Science (PLoS)},
year = {2021},
editor = {Schwenker, Friedhelm},
volume = {16},
number = {12},
pages = {e0261571},
url = {https://optimization-online.org/?p=16046},
doi = {10.1371/journal.pone.0261571}
}
2021
article
On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control
Computational Optimization and Applications
@article{Sager2021b,
author = {Sager, Sebastian and Zeile, Clemens},
title = {On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control},
journal = {Computational Optimization and Applications},
publisher = {Springer Science and Business Media LLC},
year = {2021},
volume = {78},
number = {2},
pages = {575--623},
url = {https://optimization-online.org/?p=16059},
doi = {10.1007/s10589-020-00244-5}
}
2021
article
Machine Learning in Chemical Engineering: A Perspective
Chemie Ingenieur Technik
@article{Schweidtmann2021,
author = {Schweidtmann, Artur M. and Esche, Erik and Fischer, Asja and Kloft, Marius and Repke, Jens-Uwe and Sager, Sebastian and Mitsos, Alexander},
title = {Machine Learning in Chemical Engineering: A Perspective},
journal = {Chemie Ingenieur Technik},
publisher = {Wiley},
year = {2021},
volume = {93},
number = {12},
pages = {2029--2039},
doi = {10.1002/cite.202100083}
}
2021
article
Mixed-Integer Optimal Control under Minimum Dwell Time Constraints
Mathematical Programming
@article{Zeile2021b,
author = {Zeile, Clemens and Robuschi, Nicol\`o and Sager, Sebastian},
title = {Mixed-Integer Optimal Control under Minimum Dwell Time Constraints},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media LLC},
year = {2021},
volume = {188},
number = {2},
pages = {653--694},
url = {https://link.springer.com/article/10.1007/s10107-020-01533-x},
doi = {10.1007/s10107-020-01533-x}
}
2020
misc
Universal differential equations for scientific machine learning
@misc{Rackauckas2020,
author = {Rackauckas, Christopher and Ma, Yingbo and Martensen, Julius and Warner, Collin and Zubov, Kirill and Supekar, Rohit and Skinner, Dominic and Ramadhan, Ali and Edelman, Alan},
title = {Universal differential equations for scientific machine learning},
publisher = {Springer Science and Business Media LLC},
year = {2020},
note = {arXiv preprint arXiv:2001.04385},
doi = {10.21203/rs.3.rs-55125/v1}
}
2017
article
A Feedback Optimal Control Algorithm with Optimal Measurement Time Points
Processes
@article{Jost2017,
author = {Jost, Felix and Sager, Sebastian and Le, Thuy},
title = {A Feedback Optimal Control Algorithm with Optimal Measurement Time Points},
journal = {Processes},
publisher = {MDPI AG},
year = {2017},
volume = {5},
number = {1},
pages = {10},
url = {http://www.mdpi.com/2227-9717/5/1/10},
doi = {10.3390/pr5010010}
}
2013
article
Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin's Maximum Principle
SIAM Journal on Control and Optimization
@article{Sager2013,
author = {Sager, Sebastian},
title = {{S}ampling {D}ecisions in {O}ptimum {E}xperimental {D}esign in the {L}ight of {P}ontryagin's {M}aximum {P}rinciple},
journal = {SIAM Journal on Control and Optimization},
publisher = {Society for Industrial \& Applied Mathematics (SIAM)},
year = {2013},
volume = {51},
number = {4},
pages = {3181--3207},
url = {https://mathopt.de/publications/Sager2013.pdf},
doi = {10.1137/110835098}
}
2012
article
The Integer Approximation Error in Mixed-Integer Optimal Control
Mathematical Programming
@article{Sager2012a,
author = {Sager, Sebastian and Bock, Hans Georg and Diehl, Moritz},
title = {{T}he {I}nteger {A}pproximation {E}rror in {M}ixed-{I}nteger {O}ptimal {C}ontrol},
journal = {Mathematical Programming},
publisher = {Springer Science and Business Media LLC},
year = {2012},
volume = {133},
number = {1-2},
pages = {1--23},
url = {https://mathopt.de/publications/Sager2012a.pdf},
doi = {10.1007/s10107-010-0405-3}
}