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

@article{Huschto2019,
    author = {Huschto, T. and Podolskij, M. and Sager, S.},
    title = {The asymptotic error of chaos expansion approximations for stochastic differential equations},
    journal = {Modern {S}tochastics: {T}heory and {A}pplications},
    year = {2019},
    volume = {6},
    number = {2},
    pages = {145--165},
    doi = {10.15559/19-VMSTA133}
}

@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}
}

@inproceedings{Matke2017,
    author = {Matke, C. and Bienstock, D. and Munoz, G. and Yang, S. and Kleinhans, D. and Sager, S.},
    title = {Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies},
    booktitle = {Studies in Computational Intelligence: Complex Networks and Their Applications V},
    year = {2017},
    number = {693},
    pages = {809--820},
    doi = {10.1007/978-3-319-50901-3}
}

@inproceedings{Matke2017a,
    author = {Matke, Carsten and Medjroubi, Wided and Kleinhans, David and Sager, Sebastian},
    title = {Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID},
    booktitle = {Advances in Energy System Optimization},
    publisher = {Springer International Publishing},
    year = {2017},
    editor = {Bertsch, Valentin and Fichtner, Wolf and Heuveline, Vincent and Leibfried, Thomas},
    pages = {177--188},
    address = {Cham}
}

@article{Huschto2014,
    author = {Huschto, T. and Sager, S.},
    title = {{P}ricing {C}onspicuous {C}onsumption {P}roducts in {R}ecession {P}eriods with {U}ncertain {S}trength},
    journal = {{E}uropean {J}ournal of {D}ecision {P}rocesses},
    year = {2014},
    volume = {2},
    number = {1--2},
    pages = {3--30},
    url = {http://www.optimization-online.org/DB_HTML/2012/09/3620.html}
}

@article{Huschto2014a,
    author = {Huschto, T. and Sager, S.},
    title = {{S}olving {S}tochastic {O}ptimal {C}ontrol {P}roblems by a {W}iener {C}haos {A}pproach},
    journal = {{V}ietnam {J}ournal of {M}athematics},
    year = {2014},
    volume = {42},
    number = {1},
    pages = {83--113},
    url = {https://mathopt.de/publications/Huschto2014a.pdf}
}

@phdthesis{Huschto2014b,
    author = {Huschto, T.},
    title = {{N}umerical {M}ethods for {R}andom {P}arameter {O}ptimal {C}ontrol and the {O}ptimal {C}ontrol of {S}tochastic {D}ifferential {E}quations},
    school = {University Heidelberg},
    year = {2014},
    url = {https://mathopt.de/publications/Huschto2014.pdf}
}

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