DFG-Graduiertenkolleg: π³ Parameter Identification – Analysis, Algorithms, Applications

The new Research Training Group „Parameter Identification – Analysis, Algorithms, Applications”, funded by the German Science Foundation (DFG), is hosted by the Center for Industrial Mathematics since October 2016. Mathematicians from algebra/topology, from applied analysis and from statistics are also involved. Furthermore, five associated scientists from the faculties Physics/Electrical Engineering, Biology/Chemistry and Production Engineering plus the European Molecular Biology Lab in Heidelberg are integrated.

The task of retrieving biological, physical, or technical parameters from measured data is as universal as the quest to determine system parameters for optimisation/controlling complex processes.

Accordingly, parameter identification is at the core of multiple applications in all fields of natural sciences, engineering, life sciences, and industrial applications. The demand for tackling ever more complex models in terms of non-linearity, sensitivity, coupling of systems or for including specific expert information as side constraints, provides numerous challenges in mathematical modelling and for designing, analysing, and implementing appropriate algorithms.

The RTG is focused on deterministic parameter identification tasks on the interface between applied mathematics and scientific computing that are formulated as functional minimisation problems. The different scientific approaches considered share modelling characteristics as well as mathematical challenges and they naturally meet when it comes to designing efficient algorithms.

The RTG-team with the PhD students in the center focuses on the development of new mathematical methods for parameter identification tasks and its application to real industrial applications. The research program is split into three research areas: inverse problems, direct optimization and mathematical data analysis;  each equipped with one industrial benchmark application. We take great care to equip the PhD students of the RTG with the necessary mathematical competence and to enhance scientific independence. The mathematical qualification concept includes compact courses and reading courses on advanced research topics. Supervision is based on separately defined tasks for main supervisor, co-advisors, and PhD advisory committee. Research and training in study groups consisting of four to six PhD students is a further characteristic feature of π³.

Publications

1. S. Dittmer, T. Kluth, P. Maaß, D. Otero Baguer.
   Regularization by architecture: A deep prior approach for inverse problems.
   Journal of Mathematical Imaging and Vision, :456-470, Springer Verlag, 2020.

   DOI: 10.1007/s10851-019-00923-x
   online at: http://link.springer.com/article/10.1007/s10851-019-00923-x

2. J. Clemens, T. Kluth, T. Reineking.
   β - SLAM: Simultaneous Localization an Grid Mapping with Beta Distributions.
   Information Fusion, 52:62-75, Elsevier, 2019.

   DOI: 10.1016/j.inffus.2018.11.005

3. A. Konschin, A. Lechleiter.
   Reconstruction of a Local Perturbation in Inhomogeneous Periodic Layers from Partial Near Field Measurements.
   Inverse Problems, 35(11), 114006, IOPscience, 2019.

   DOI: 10.1088/1361-6420/ab1c66

4. J. Jacobsen, J. Behrmann, R. Zemel, M. Bethge.
   Excessive Invariance Causes Adversarial Vulnerability.
   International Conference on Learning Representations (ICLR), 2019.
   

   online at: https://openreview.net/forum?id=BkfbpsAcF7

5. J. Jacobsen, J. Behrmann, N. Carlini, F. Tramer, N. Papernot.
   Exploiting Excessive Invariance caused by Norm-Bounded Adversarial Robustness.
   SafeML Workshop, ICLR, 2019.
   

   online at: https://arxiv.org/abs/1903.10484

6. S. Dittmer, E. King, P. Maaß.
   Singular values for ReLU layers.
   IEEE Transactions on Neural Networks and Learning Systems, Article , 2019.

   online at: https://ieeexplore.ieee.org/document/8891761

7. T. Kluth, B. Jin, G. Li.
   On the Degree of Ill-Posedness of Multi-Dimensional Magnetic Particle Imaging.
   Inverse Problems, Article ID 095006 34(9), 2018.

   DOI: 10.1088/1361-6420/aad015

8. D. Otero Baguer, I. Piotrowska, P. Maaß.
   Inverse Problems in designing new structural materials.
   7th International Conference on High Performance Scientific Computing, 19.03-23.03.2018, Hanoi, Vietnam.
   

   DOI: 10.1007/978-3-030-55240-4_8

9. J. Leuschner, M. Schmidt, P. Fernsel, D. Lachmund, T. Boskamp, P. Maaß.
   Supervised Non-negative Matrix Factorization Methods for MALDI Imaging Applications.
   Bioinformatics, bty909 , 2018.

   DOI: 10.1093/bioinformatics/bty909

10. C. Meerpohl, K. Flaßkamp, C. Büskens.
    Optimization Strategies for Real-Time Control of an Autonomous Melting Probe.
    2018 American Control Conference (ACC), 2018, Milwaukee, WI, USA.
    

    DOI: 10.23919/ACC.2018.8430877

11. K. Schäfer, M. Runge, K. Flaßkamp, C. Büskens.
    Parameter Identification for Dynamical Systems Using Optimal Control Techniques.
    European Control Conference (ECC) 2018, 12.06.-15.06.2018, Limassol, Cyprus.
    

    DOI: 10.23919/ECC.2018.8550045

12. W. Heins, C. Büskens.
    Two-Level Forecast-Based Energy and Load Management for Grid-Connected Local Systems Using General Load and Storage Models.
    18th International Conference on Environment and Electrical Engineering (EEEIC), 12.06-15.06.2018, , Italy.
    
13. P. Fernsel, P. Maaß.
    A Survey on Surrogate Approaches to Non-negative Matrix Factorization.
    Vietnam Journal of Mathematics, 46(4):987-1021, Springer Verlag, 2018.

    DOI: 10.1007/s10013-018-0315-x

14. J. Behrmann, S. Dittmer, P. Fernsel, P. Maaß.
    Analysis of Invariance and Robustness via Invertibility of ReLU-Networks.
    Zur Veröffentlichung eingereicht.

    online at: https://arxiv.org/abs/1806.09730

15. J. Behrmann, C. Etmann, T. Boskamp, R. Casadonte, J. Kriegsmann, P. Maaß.
    Deep Learning for Tumor Classification in Imaging Mass Spectrometry.
    Bioinformatics, 34(7):1215-1223, Oxford University Press, 2018.

    DOI: 10.1093/bioinformatics/btx724

16. T. Kluth.
    Mathematical models for magnetic particle imaging.
    Inverse Problems, Article ID 083001 34(8), 2018.

    DOI: 10.1088/1361-6420/aac535

17. J. Clemens, C. Meerpohl, V. Schwarting, M. Rick, K. Schill, C. Büskens.
    Autonomous In-Ice Exploration of the Saturnian Moon Enceladus.
    69th International Astronautical Congress (IAC), 01.10.-05.10.2018, Bremen, Germany.
    
18. C. Bathke, T. Kluth, C. Brandt, P. Maaß.
    Improved image reconstruction in magnetic particle imaging using structural a priori information.
    International Journal on Magnetic Particle Imaging, Article ID 1703015, 3(1), 10 pages, 2017.

    DOI: 10.18416/ijmpi.2017.1703015

19. T. Kluth, P. Maaß.
    Model uncertainty in magnetic particle imaging: Nonlinear problem formulation and model-based sparse reconstruction.
    International Journal on Magnetic Particle Imaging, Article ID 1707004 3(2), 10 pages, 2017.

    DOI: 10.18416/ijmpi.2017.1707004

20. T. Gerken, A. Lechleiter.
    Reconstruction of a Time-dependent Potential from Wave Measurements.
    Inverse Problems, Article ID 094001 33(9), IOPscience, 2017.

    Ausgezeichnet als Highlight Paper

    DOI: 10.1088/1361-6420/aa7e07
    online at: http://iopscience.iop.org/article/10.1088/1361-6420/aa7e07