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.

In particular, 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 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*

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.

### Selected publications

Author | Title | Year | Journal/Proceedings | Reftype | Link |
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Minakowska, M., Richter, T. & Sager, S. | A finite element / neural network framework for modeling suspensions of non-spherical particles - Concepts and medical applications [BibTeX] |
2021 | Vietnam Journal of Mathematics | article | url |

BibTeX:
@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} } |
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Schweidtmann, A., Esche, E., Fischer, A., Kloft, M., Repke, J., Sager, S. & Mitsos, A. | Machine Learning in Chemical Engineering: A Perspective [BibTeX] |
2021 | Submitted to Chemie Ingenieur Technik | article | |

BibTeX:
@article{Schweidtmann2021, author = {Schweidtmann, A.M. and Esche, E. and Fischer, A. and Kloft, M. and Repke, J. and Sager, S. and Mitsos, A.}, title = {Machine Learning in Chemical Engineering: A Perspective}, journal = {Submitted to Chemie Ingenieur Technik}, year = {2021}, note = {submitted} } |
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Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D. & Ramadhan, A. | Universal differential equations for scientific machine learning [BibTeX] |
2020 | misc | ||

BibTeX:
@misc{Rackauckas2020, author = {C. Rackauckas and Y. Ma and J. Martensen and C. Warner and K. Zubov and R. Supekar and D. Skinner and A. Ramadhan}, title = {Universal differential equations for scientific machine learning}, year = {2020}, note = {arXiv preprint arXiv:2001.04385} } |
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Sager, S. & Zeile, C. | On Mixed-Integer Optimal Control with Constrained Total Variation of the Integer Control [BibTeX] |
2020 | Computational Optimization and Applications | article | DOI url |

BibTeX:
@article{Sager2020b, 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}, year = {2020}, url = {http://www.optimization-online.org/DB_HTML/2019/10/7432.html}, doi = {http://dx.doi.org/10.1007/s10589-020-00244-5} } |
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Zeile, C., Robuschi, N. & Sager, S. | Mixed-Integer Optimal Control under Minimum Dwell Time Constraints [BibTeX] |
2020 | Mathematical Programming | article | DOI url |

BibTeX:
@article{Zeile2020, author = {Zeile, C. and Robuschi, N. and Sager, S.}, title = {Mixed-Integer Optimal Control under Minimum Dwell Time Constraints}, journal = {Mathematical Programming}, year = {2020}, pages = {1--42}, url = {https://link.springer.com/article/10.1007/s10107-020-01533-x}, doi = {https://doi.org/10.1007/s10107-020-01533-x} } |
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Sager, S., Bernhardt, F., Kehrle, F., Merkert, M., Potschka, A., Meder, B., Katus, H. & Scholz, E. | Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification [BibTeX] |
2019 | Preprint (Optimization Online) | article | url |

BibTeX:
@article{Sager2020, author = {Sager, S. and Bernhardt, F. and Kehrle, F. and Merkert, M. and Potschka, A. and Meder, B. and Katus, H. and Scholz, E.}, title = {Expert-Enhanced Machine Learning for Cardiac Arrhythmia Classification}, journal = {Preprint (Optimization Online)}, year = {2019}, note = {submitted}, url = {http://www.optimization-online.org/DB_HTML/2019/10/7421.html} } |
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Jost, F., Sager, S. & Le, T. | A Feedback Optimal Control Algorithm with Optimal Measurement Time Points [BibTeX] |
2017 | Processes | article | url |

BibTeX:
@article{Jost2017, author = {Jost, F. and Sager, S. and Le, T.T.T.}, title = {A Feedback Optimal Control Algorithm with Optimal Measurement Time Points}, journal = {Processes}, year = {2017}, volume = {5}, number = {10}, pages = {1--19}, url = {http://www.mdpi.com/2227-9717/5/1/10} } |
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Sager, S. | Sampling Decisions in Optimum Experimental Design in the Light of Pontryagin's Maximum Principle [BibTeX] |
2013 | SIAM Journal on Control and Optimization | article | url |

BibTeX:
@article{Sager2013, author = {Sager, S.}, 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}, year = {2013}, volume = {51}, number = {4}, pages = {3181--3207}, url = {https://mathopt.de/publications/Sager2013.pdf} } |
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Sager, S., Bock, H. & Diehl, M. | The Integer Approximation Error in Mixed-Integer Optimal Control [BibTeX] |
2012 | Mathematical Programming A | article | url |

BibTeX:
@article{Sager2012a, author = {Sager, S. and Bock, H.G. and Diehl, M.}, title = {{T}he {I}nteger {A}pproximation {E}rror in {M}ixed-{I}nteger {O}ptimal {C}ontrol}, journal = {{M}athematical {P}rogramming {A}}, year = {2012}, volume = {133}, number = {1--2}, pages = {1--23}, url = {https://mathopt.de/publications/Sager2012a.pdf} } |

Further references of the MathOpt group can be found on this page.