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

@article{Sager2023, author = {Sager, Sebastian}, title = {Digital Twins in Oncology}, journal = {Journal of Cancer Research and Clinical Oncology}, publisher = {Springer}, year = {2023}, pages = {1--3} }

@incollection{Bethge2022, author = {Bethge, J. and Findeisen, R. and Le, D.D. and Merkert, M. and H., Rewald and Sager, S. and Savchenko, A. and Sorgatz, S.}, title = {Mathematical Optimization and Machine Learning for Efficient Urban Traffic}, booktitle = {KoMSO Success Stories on Mathematics in Industry}, publisher = {Springer}, year = {2022}, editor = {K\"{u}fer, Karl-Heinz and Maass, Peter and Milde, Anja and Schulz, Volker}, pages = {113--120}, url = {https://mathopt.de/publications/Bethge2020.pdf} }

@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} }

@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}, year = {2021}, volume = {16}, number = {12}, pages = {e0261571}, url = {http://www.optimization-online.org/DB_HTML/2019/10/7421.html} }

@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}, year = {2021}, volume = {78}, number = {2}, pages = {575--623}, url = {http://www.optimization-online.org/DB_HTML/2019/10/7432.html}, doi = {10.1007/s10589-020-00244-5} }

@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 = {Chemie Ingenieur Technik}, year = {2021}, doi = {10.1002/cite.202100083} }

@article{Zeile2021b, author = {Zeile, C. and Robuschi, N. and Sager, S.}, title = {Mixed-Integer Optimal Control under Minimum Dwell Time Constraints}, journal = {Mathematical Programming}, 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} }

@misc{Rackauckas2020, author = {Rackauckas, C. and Ma, Y. and Martensen, J. and Warner, C. and Zubov, K. and Supekar, R. and Skinner, D. and Ramadhan, A.}, title = {Universal differential equations for scientific machine learning}, year = {2020}, note = {arXiv preprint arXiv:2001.04385} }

@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} }

@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} }

@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} }