# Projects

The Industrial Mathematics group is involved in numerous national and international research projects with its research on applied mathematics from the core areas of Deep Learning and Inverse Problems.

### KIWi - Hybrid Parameter Identification with Invertible Networks

BMBF-Project**PI**: Tobias Kluth

In the near future, many wind turbines (WTs) will reach the end of their design life, typically 20 years. In the joint project KIWi, data- and model-based methods for model correction and for parameter identification in inexact models are used to enable a more accurate determination of the estimation of the load in wind turbines and thus to extend their possible lifetime.

### TorchPhysics - A deep learning library for differential equations

Differential equations have to be solved in a wide variety of applications, usually by means of numerical simulations. Classical methods such as the Finite Element Method have shown to be succesful in various problems. However, some differential equations are very difficult to solve with classical methods, for example due to nonlinearities or their multi-scale character. Therefore, the aim of this project is to create a software package that combines various deep learning approaches for usage in various applications and further research. The project is developed in cooperation with the Robert Bosch GmbH.

### π³ - Parameter Identification – Analysis, Algorithms, Applications

DFG-Project**Duration**: 01.10.2016 - 30.09.2025**PI**: Peter Maaß

In the Research Training Group π3 Parameter Identification - Analysis, Algorithms, Implementations, PhD students at the interface of Applied Mathematics and Scientific Computing focus on parameter identification issues, which are essentially modeled by minimizing appropriate objective functionals.

### Inverse problems - Theories, methods and implementations

DFG-Projekt**Duration**: 01.01.2021 - 31.12.2023**PI**: Peter Maaß

Research on inverse problems has been an important, active field in applied mathematics for decades with a strong influence on many disciplines. In this German-Chinese mobility program, knowledge and ideas are exchanged, thus laying the foundation for long-term collaboration.

### Design-KIT - Artificial intelligence in mechanical component development

BMBF-Projekt**Duration:** 01.10.2020 - 31.03.2022**PI**: Peter Maaß

In the Design-KIT project, methods of artificial intelligence and machine learning are scientifically investigated for the design of components for launch vehicles and their usefulness for the corresponding industrial application is evaluated.

### KIDOHE - AI-supported documentation for midwives

BAB-Projekt**Duration:** 01.05.2020 - 28.02.2022**PI**: Iwona Piotrowska-Kurczewski

KIDOHE aims to improve the stress and recourse situation of midwives by means of an innovative, intelligent, decision-support system. This system will represent both scientifically based expertise and experiential knowledge of midwives in networks (e.g. semantic networks, Bayesian networks or neural networks).

### D-MPI - Dynamic Inverse Problems in Magnetic Particle Imaging

DFG-Projekt**Duration**: 01.05.2020 - 30.04.2023**PI**: Tobias Kluth

Magnetic Particle Imaging (MPI) is an imaging technique with promising medical applications based on the behavior of superparamagnetic iron oxide nanoparticles. In D-MPI, the dynamic aspects of concentration dynamics, magnetic field dynamics, and particle magnetization dynamics are studied to facilitate modeling and reconstruction of the data.

### DELETO - Machine learning in correlative MR and high-throughput NanoCT.

BMBF-Projekt**Duratio**: 01.04.2020 - 31.03.2023**PI**: Tobias Kluth

In DELETO, Deep Learning methods for solving inverse problems will be decisively developed to make more accurate and efficient the reconstruction methods based on Structural Priors and Motion Correction in the field of correlative MR and high-throughput NanoCT, which are computationally expensive due to the large amount of data. The goal is to integrate these methods into next-generation devices.

### HYDAMO - Hybrid data-driven and model-based simulation of complex flow problems in the automotive industry

BMBF-Projekt**Duration:** 01.04.2020 - 31.03.2023**PI**: Peter Maaß

On complex materials such as sand, mud or snow, vehicle stability is not always a given: Collisions or vehicle rollover may be unavoidable. The goal of HYDMAO is to integrate data-driven and model-based approaches into an overall solution based on a continuum mechanics problem from the vehicle industry that has been insufficiently understood to date. This is intended to decisively improve the computer-aided mapping of the associated process.

### MALDISTAR - Study on quality assessment, standardization and reproducibility of MALDI imaging mass spectrometry data

KTS-Projekt**Duration**: 01.07.2019 - 30.06.2022**PI**: Peter Maaß

MALDI imaging represents an established method for the spatial study of biomolecules. However, despite many advantages, it is becoming increasingly clear that the data are subject to high variability. For this reason, quality assessment tools and new calibration and cross-normalization methods are being developed in MALDISTAR.

### ROMSOC - Reduced Order Modelling, Simulation and Optimization of Coupled Systems

EU-Project**Duration**: 01.11.2017 - 31.08.2022**PI**: Peter Maaß

The scientific goal of the PhD program is to develop the mathematical foundations and methods in the increasingly virtual development of industrial products and processes, focusing on coupling methods, model reduction techniques, and optimization methods.

### ML-X-RAY - Machine learning and X-ray technology for measuring inhomogeneous cable and pipe products

BAB-Project**Duration**: 01.03.2021 - 31.10.2022**PI:** Peter Maaß

In production engineering, the purity of a product and the associated quality control play a central role. To ensure maximum material and cost savings, the reliable measurement of the manufactured products as well as the detection of deviations with regard to the given product specification is indispensable. The aim of ML-X-RAY is the further development of a measuring system for the inspection of inhomogeneous cable and pipe products with the help of innovative approaches from the field of Machine Learning or Deep Learning in the form of Convolutional Neural Networks. The project is being carried out in cooperation with the industrial partner SIKORA AG.

### SFB 1232 From colored states to evolutionary structural materials

DFG-Projekt**Duration**: 01.07.2016 - 30.06.2020**PI**: Peter Maaß

Whether it is the energy revolution or mobility: the demands on metallic materials of the future are growing, and their development is now playing a key role. It is fundamental to adapt the properties of the materials accordingly to the specific requirements. The selection of the most suitable alloy compositions and the adjustment of the corresponding crystals open up complex and diverse search spaces.

### MPI² - Model-based parameter identification in Magnetic Particle Imaging

BMBF-Project**Duration**: 01.12.2016 - 31.05.2020**PIs:** Peter Maaß, Tobias Kluth

In MPI², model-based methods and their efficient algorithmic implementation are explored. Magnetic particle imaging (MPI), a tomographic method based on tracking iron oxide nanoparticles in the human body, serves here as an application example.

### MaDiPath - Mass spectrometric profiling/grading for routine oncology digital pathology applications.

BMBF-Projekt**Duration**: 01.10.2015 - 30.09.2018

MaDiPath investigates the research and establishment of mass spectrometric methods, in this case MALDI Imaging, for digital pathology. The aim of the project is to develop methods that enable an objective, reproducible and automated basis for pathological tumor diagnostics and the personalized course and therapy planning based on this.

### MALDI Imaging Lab – An interdisciplinary core facility for the acquisition and analysis of imaging mass spectrometry data

DFG-Projekt**Duration**: 01.07.2011 - 31.12.2018**PI**: Peter Maaß

The MALDI Imaging Lab, MIL, is a core facility and research facility specialising in the acquisition of imaging mass spectrometric data. Both uni-internal and external interested parties can have their samples measured at the instrument centre. The services offered include sample preparation, measurement, possible post-treatments such as staining and microscopy, as well as computer-assisted evaluation of the data.

### HYPERMATH - Hyperspectral Imaging: Mathematical Methods for Innovations in Medicine and Industry

BMBF-Projekt**Duation**: 01.07.2013 - 30.10.2016**PI**: Peter Maaß

In HYPERMATH, data-adapted and application-specific approach functions for efficient data evaluation and approximations are determined. In addition, inherent localisation problems of the underlying measurement methods are mathematically captured and analysed. The procedures based on this take multi-scale structures into account in order to be able to efficiently process data sets with one trillion and more values.

### Entwicklung eines Digital-Staining-Verfahrens als pathologisch-histologisches Diagnosewerkzeug auf Basis der MALDI-Imaging-Technologie

BMWI-project**Duration**: 01.07.2014 - 30.06.2016**PI**: Peter Maaß

The project focuses on the development of novel mathematical methods for the evaluation of MALDI imaging spectra and the creation of Standard Operating Procedures (SOP) for sample preparation and data acquisition. These developments are exemplified by tumours from the pancreas and the lung as well as metastases from the liver and are thus directly related to important questions in oncology.

### SceneNet - Mobile Crowd Sourcing Video Scene Reconstruction

EU-Projekt**Duration**: 01.02.2013 - 30.01.2016**PI**: Peter Maaß

For some years now, concerts, sporting events or family celebrations can hardly do without filming the scenes with smartphones. These videos show only a small angle of the scenario and are often of low quality. The SceneNet project aimed to transfer audio-visual recordings of a public event into a video sequence of the highest quality. In this video, an event can then be viewed interactively from a wide variety of angles.

### MALDI AMK - 3D MALDI imaging for analysis of proteomic markers and clinical drug distribution

BMBF-Projekt**Duration**: 01.04.2011 - 30.07.2014**PI:** Peter Maaß

In this project, clinical oncological questions are explored directly in organs and tissues which require the context of the highly complex, heterogeneous 3D tissue composite in close cooperation with medical partners. A particular challenge here is 3D visualisation and direct interaction with this 3D data.

### UNLocX - Uncertainty principles versus localization properties, function systems for efficient coding schemes

EU-Projekt**Duration**: 01.09.2010 - 30.08.2013**PI**: Peter Maaß

A new generation of signal processing algorithms is to be tested, which - for example in medical image processing - will make it possible to tackle problems whose complexity was previously too high and, in addition, enable even more efficient compression and data transmission.

### SPP 1324 - Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces, and Applications to Nonlinear Inverse Parabolic Problems

DFG-Projekt**Duration**: 01.04.2009 - 01.12.2013**PI**: Peter Maaß

The realization that the embryogenesis of organisms is controlled by genes represents a milestone in modern biological research. This gave rise to the interest in understanding the processes involved quantitatively and, if possible, modeling them. This challenge is taken up by the cooperation project of the Center for Industrial Mathematics (ZeTeM) with the University of Marburg within the DFG priority program SPP 1324. Specifically, it is about the solution of an ill-posed, nonlinear operator equation Ax=y, which maps differentiably between Banach spaces.

### Spatially three-dimensionally resolved metabolic analysis for medicine

WFB-Projekt**Duration**: 01.07.2010 - 30.06.2012**PI**: Peter Maaß

In this project, technical process chains will be worked out to develop a 3D imaging method. This will enable the protein spectrum of an entire organ or disease-related lesion to be captured and analysed in its full complexity. This includes the distribution and metabolisation of active substances in the pathologically altered tissues (e.g. tumours) and the directly related therapy response.