The research group Computational Science and Mathematical Methods (CSMM) under the supervision of Prof. Dr. Martin Frank is an interdisciplinary research group working on different challenges in mathematical modeling. The group brings together researchers from Scientific Computing and Mathematics (SCM/SCC), the Institute for Applied and Numeric Mathematics (IANM) as well as external partners from industry and academia (see Tab Network below). We are unified by our interest in method-oriented mathematics, in mathematical modeling inspired by applications, and in the didactics of mathematical modeling.
Our research focuses on bringing modern mathematical techniques such as modeling, simulation, optimization, inverse problems, uncertainty quantification, and machine learning/artificial intelligence into the real-world. Both by teaching them to students in schools and universities and by advancing the research in relevant fields of application. Furthermore, we take an interest in kinetic theory, developing models, numerical methods and software implementations and combining them with the aforementioned techniques.
Here on our website, you can follow our research activities, find information on our courses and courses offered, as well as find currently advertised positions and theses.
Contact: katharina.bata∂kit.edu
Research Interests: Didactics of Machine Learning, Simple Approaches to Complex Mathematics, Mathematical Modeling, Higher Education Didactics
Projects: Group Leader, CAMMP, Simulierte Welten
As team leader, I support the doctoral students and student assistants of the CAMMP team in the organization and implementation of CAMMP activities and the associated educational research. I prepared for this position with my doctorate in mathematics education on the teaching and learning of machine learning methods for engineering students. I am passionate about educational research into the accessibility of complex mathematical content and the impact of different teaching and learning formats.
Contact: jakim.eckert∂kit.edu
Research interests: didactics, data cleaning, machine learning, mathematical modeling
Projects: CAMMP, Simulierte Welten
Possible thesis topics: CAMMP Offerings
Preparing realistic and authentic problems for students and thus contributing to a mature use of modern technologies is essential for me. In the CAMMP project, I develop and test teaching and learning materials in the context of mathematical modeling. My research interest is especially on data cleaning and how to design its mathematical aspects through modeling offerings and workshops. For this purpose, teaching and learning arrangements are developed to teach students about mathematical modeling itself on the one hand and about mathematics in the context of data cleaning on the other hand.
Contact: s hofmann ∂does-not-exist.kit edu
Research interests: Natural Language Processing, Statistical Tests, Markov Chain, Mathematical Modeling
Projects: CAMMP, Simulierte Welten
Possible thesis topics: CAMMP proposals
To apply mathematics and make it comprehensible, that is what I see as a desirable goal for mathematics education. Therefore, after my state examination as a teacher at the KIT in the subjects mathematics and physics, I decided to do a PhD in the project CAMMP. In the context of this project, I am creating workshops for students in which mathematical problems are treated in an authentic and realistic way. Specifically, teaching and learning material on the topic of natural language processing is to be created. For this purpose, a workshop on word prediction on a smartphone has already been developed, where the mathematical problem is modeled with Markov chains. Furthermore, learning material on speech recognition is to be developed.
Contact: alexander.jesser∂kit.edu
Research interests: Mathematical Modeling, Transport Equations, Inverse problems, High Performance Computing, Neural Networks
Projects: ZEBRA, QUANTOM
As an industry phd student, I work on joint research and development projects of the KIT and the company AiNT. My work focuses on projects in the context of Prompt Gamma Activation Analysis (PGAA), a measurement technique that enables non-destructive material analysis. Applications include environmental analysis and characterization of radioactive waste. My task is the development of algorithms to solve specific mathematical problems for these applications and to implement high-performance software for it. The methods I use include mathematical modelling, transport equations and inverse problems.
Contact: stephan.kindler∂kit.edu
Research interests: Mathematical modeling, machine learning, neural networks, didactics, student labs.
Projects: CAMMP, Simulated Worlds
Possible thesis topics: CAMMP proposals
My focus is on the didactics of mathematics and the development of teaching and learning materials in order to make the application areas of mathematics tangible for students. Specifically, I am working on machine learning with the help of neural networks and links to mathematics didactics in schools. The goal is to develop workshops for different school levels with different focuses in order to pick up the respective basic mathematical concepts and questions of the learners.
At the same time I work as a mathematics and chemistry teacher at the Goethe-Gymnasium in Karlsruhe.
Contact: emil.loevbak∂kit.edu
Research interests: uncertainty quantification, multilevel Monte Carlo, hybrid methods, kinetic equations, adjoint methods, fusion energy
Projects:
I am a postdoctoral researcher with a current focus on uncertainty quantification for kinetic equations. I am interested in improving the performance of stochastic simulation methods as well as how to use them in the settings of optimization and inverse problems. The main application area of interest in my work is that of neutral particle simulations in fusion. I have priorly worked on the development of asymptotic-preserving multilevel Monte Carlo methods, the introduction of reversible pseudorandom number generators for adjoint Monte Carlo simulation and contributed to various pieces of software within the above mentioned topics. You can find more information here.
Contact: tim.ortkamp∂kit.edu
Research interests: Mathematical modeling & optimization, machine learning, radiotherapy treatment planning
Projects: Inverse Radiotherapy Treatment Planning using Machine Learning Outcome Prediction Models, HIDSS4Health
Possible thesis topics: Multi-label (N)TCP profile optimization on sparse imbalanced data for radiotherapy treatment planning (Master thesis)
My research activity as a PhD student takes place within the Helmholtz Information & Data Science School for Health (HIDSS4Health), through which I am affiliated with the research groups Computational Sciences and Mathematical Methods at KIT and Radiotherapy Optimization at DKFZ. I focus on the mathematical optimization of radiotherapy planning, primarily by integrating ML-based models for TCP (tumor control probability) and NTCP (normal tissue complication probability) as biological endpoints, thereby enabling a more personalized treatment. A major component of this is the development of gradient-based, efficient optimization approaches with respect to radiomic and dosimetric variables, as well as the computational implementation in the open-source frameworks pyanno4rt and matRad.
Contact: chinmay.patwardhan∂kit.edu
Research interests: Dynamical low-rank approximation, model order reduction, kinetic simulations, uncertainty quantification, HPC
Projects: CRC-1173 B9, DLRA for simulation of radiation
I am a PhD student at the Collaborative Research Center 1173 in the project B9 and a part of the Computational Mathematics and Modelling for Applied Sciences (CoMMAS) group within the Scientific Computing and Mathematics Department. My research interests lie in the development and application of model-order reduction techniques to reduce computational costs for simulating kinetic equations. Additionally, I also work on quantifying uncertainties arising in these systems and developing a code base for HPC simulations. A more detailed information about my project can be found here.
Contact: yijia.tang∂kit.edu
Research Interests: Mathematical modeling, machine learning, kinetic theory
Projects: Structure-preserving deep neural networks to accelerate the solution of the Boltzmann equation
I am a postdoctoral reseacher in the CoMMAS team since Oct. 2023. My research focuses on the deep learning approach for kinetic equations. In particular, I am interested in the Boltzmann equation. I aim at building a suggorate model for the Boltzmann collision operator, which can preserve the basic entropy dissipation property. At the same time, it benefits from the efficiency of neural networks
Contact: alexandra.walter∂kit.edu
Research Interests: Machine Learning, Medical Image Segmentation, Dynamical Low-Rank Approximation, Model Order Reduction
Projects: Automated CTV delineation (HIDSS4Health)
As a PhD student of the interdisciplinary graduate school HIDSS4Health, I am conducting research at the interface between Data Science and Health since 2020. My focus is on improving automatic segmentation algorithms needed in tumor therapy to calculate each individual radiation plan. Since 2023 I have also been scientifically active in the field of model order reduction. For these projects, I am associated with both the CSMM group at KIT and the Computational Patient Models group at the German Cancer Research Center. I completed my master's degree in computer science at the University of Tübingen.
Contact: mingliang.zhong∂kit.edu
Research interests: Lattice Boltzmann method, Uncertainty Quantification
Projects: OpenLB, integration of uncertainty quantification in the Lattice Boltzmann method for fluid flows
Lattice Boltzmann method has been widely used in theoretical studies and engineering applications as a computational method for fluids with significant advantages. However, the physical models of the practical problem in the real world contain many uncertainties. Using uncertainty quantification methods to quantify uncertainty based on LBM as a deterministic model is an important aspect of my PhD research.
| Name | Aktueller Kontakt | Abschlussjahr | Webseite |
|---|---|---|---|
| Pia Stammer | p.k.stammer∂tudelft.nl | 2023 | |
| Gayatri Čaklović | 2023 | ||
| Steffen Schotthöfer | schotthofers∂ornl.gov | 2023 | https://scsteffen.github.io/ |
| Maqsood Mubarak Rajput | |||
| Sarah Schönbrodt | sarah.schönbrodt∂plus.ac.at | 2022 | https://schoenbrodt.info/en/ |
| Maren Hatteuhr | 2022 | ||
| Jannick Wolters | mail∂jannick-wolters.de | ||
| Kirsten Wohak | 2021 | ||
| Jonas Kusch | jonas.kusch∂nmbu.no | 2020 | |
| Thomas Camminady | 2020 | ||
The precise spatial delineation of cancerous tissue (CTV) and healthy tissue in radiation therapy is necessary to prevent side effects and the reoccurrence of the tumor. This task is difficult for humans as well as for machine learning algorithms. Expert guidelines are formulated to establish a best in class delineation standard in clinical practice. The goal of this research project is to combine this human knowledge with convolutional neuronal networks used for medical image segmentation. As part of the HIDSS4Health the research area is located at the interface between data science and life science. It takes place at the KIT in cooperation with the DKFZ.
Associated: Alexandra Walter
CAMMP stands for Computational and Mathematical Modeling Program. It is an extracurricular offer of the Karlsuher Institut für Technologie (KIT) for pupils of different ages. We want to make the public aware of the social importance of mathematics and simulation sciences. For this purpose, pupils actively engage in problem solving with the help of mathematical modeling and computer use in various event formats together with teachers. In doing so, they explore real problems from everyday life, industry or research.
Associated: Stephanie Hofmann, Stephan Kindler, Jakim Eckert
Helmholtz UQ tackles uncertainty in data, analyses, and predictions from diverse domains that are represented by our use cases. We explore commonalities in estimating and dealing with uncertainty in these areas and learn from potential differences.
The Helmholtz UQ website can be viewed here.
Associated: Maqsood Rajput, Jonas Kusch
Half of all cancer patients receive radiotherapy as part of their treatment schedule. To control the trade-off between tumor control probability (TCP) and normal tissue complication probability (NTCP), radiotherapy dosage is calculated and optimized prior to treatment based on individual patient data, e.g. computed tomographic cross sectional images. Existing attempts that directly use TCP and NTCP in planning, while technically feasible, rely on simple low-parametric, often univariate models and have been consistently questioned with regards to accuracy and usability in treatment planning. Therefore, this project aims at superseding these approaches by incorporating state-of-the-art machine learning models for TCP and NTCP into the radiotherapy treatment plan optimization process.
Associated: Tim Ortkamp
Outstanding teacher training in the MINT subjects forms the basis for meeting Germany's urgent need to promote young talent in the MINT field. The starting point for the joint MINT²KA project, which is unique in Baden-Württemberg in terms of linking teacher training and the MINT sector, are the student laboratories and teaching-learning laboratories already established at the Karlsruhe Institute of Technology (KIT) and the Karlsruhe University of Education (PH), which are being expanded and further developed in the subjects of mathematics, chemistry and physics within the framework of the MINT² KA project, and extended to other school levels in each case
Associated: Maren Hattebuhr, Kirsten Wohak, Sarah Schönbrodt
The QUANTOM® project is related to the research field “non-destructive declaration/analysis of (legacy) waste” of the program for research on the decommissioning of nuclear installations funded by the German Federal Ministry of Education and Research. Framatome GmbH, the Aachen Institute for Nuclear Training GmbH and the Fraunhofer Institute for Scientific Technological Trend Analysis are cooperating to develop an innovative drum inspection system for non-destructive analysis, to enable the material description and plausibility checking of radioactive waste conditioned in 200-litre steel drums. The aim of the project is to develop, construct and test the inspection system.
Associated: Alexander Jesser
The aim of project B9 is to apply, adapt and implement the dynamical low-rank method for the simulation of radiation heat waves. Radiation heat waves arise when radiation from a hot source moves into a cold material. Physical phenomenons in which radiation heat waves are observed include plasma and astrophysics applications. Different challenges arise in the simulation of these waves. First, the phase space is high dimensional, as in addition to space and time it includes the directions in which radiation particles can travel as well energy. Second, interactions of particles with the material are described by highly oscillatory cross-sections, which require a finely resolved numerical discretization. We tackle these challenges by applying the dynamical low-rank method to this problem, which evolves the dynamics of a given system on a low-rank manifold. This strategy significantly reduces numerical costs and memory requirements while at the same time it allows for a satisfactory solution approximation.
Associated: Chinmay Patwardhan, Pia Stammer
Radiotherapy is one of the cornerstones of modern cancer treatment, being applied in 50% of all patients. It is based on a computerized patient model and a quantitative, spatial simulation of the radiation dose delivered to the patient's body. This enables computer-based optimization of every individual radiation treatment before the onset of therapy. In clinical practice, however, treatment optimization only considers one unique “best guess” treatment scenario, neglecting a number of sources of uncertainty along the workflow. The aim of this project is to develop an efficient computational pipeline for uncertainty management in ion beam therapy based on Monte Carlo algorithms for dose calculation. For this purpose, state-of-the-art methods from the mathematical uncertainty quantification community will be used to reduce the arithmetic load of the involved sampling processes by orders of magnitude.
The research project is a cooperation of KIT with the German Cancer Research Center within HIDSS4Health.
Associated: Pia Stammer
Within the context of the lead market competition EnergieUmweltwirtschaft.NRW, the federal state NRW is funding innovative developments in the field of environmental technologies with the help of European Union funds. Together with AiNT GmbH, the SCC is implementing the ZEBRA project (German acronym, for “non-destructive elemental analysis of raw materials and contaminated sites”) within this framework. Within the ZEBRA research project, an innovative measurement system is being developed for environmental and hazardous substance analysis. This measurement system is based on the prompt and delayed gamma neutron activation analysis (P&DGNAA). The project includes the construction and test operation of the measurement system and the development of new analytical methods for determining the mass fractions of all elements of the periodic system.
Associated: Jannick Wolters, Alexander Jesser
The KiT-RT (Kinetic Transport Solver for Radiation Therapy) framework is a high-performance open source platform for radiation transport. Its main focus is on radiotherapy planning in cancer treatment. To enable problem-specific method selection, the framework provides different deterministic solver types. This not only facilitates treatment planning, but also provides tools to investigate various research questions in the field of radiative transfer. This goal is supported by an easily extendable code structure that allows for straightforward implementation of additional methods and techniques.
Associated: Jonas Kusch, Steffen Schotthöfer, Pia Stammer, Jannick Wolters, Tianbai Xiao
The uncertainty quantification framework UQCreator provides various uncertainty propagation tools for hyperbolic conservation laws. Its main idea is to use kinetic numerical fluxes and source terms, which evaluate a given deterministic problem at different sample points. This hybridization of intrusive and non-intrusive methods (which we call semi-intrusive) significantly reduces numerical costs, yields an efficient parallelization with OpenMP and MPI while allowing an easy extension to various problems into the framework. Problems currently implemented in the framework include particle transport, radiation hydrodynamics, shallow water equations and gas dynamics. Different intrusive acceleration techniques such as adaptivity, multi-elements or filters can be used. Furthermore, the framework comes with different strategies to preserve hyperbolicity such as the intrusive polynomial moment or the hyperbolicity-preserving stochastic-Galerkin method.
Associated: Jonas Kusch, Jannick Wolters
Julia is a dynamical language which balances flexibility and efficiency.
This project applies itself to providing a portable toobox for the study of kinetic theory and scientific machine learning.
It concerns theoretical and numerical studies of the kinetic theory of gases, photons, plasmas, neutrons, etc.The finite volume method
is employed to conduct 1-3 dimensional numerical simulations on CPUs and GPUs that solve, for example, the Boltzmann equation and the related neural kinetic equations.
Associated: Tianbai Xiao
| title | type | semester | place |
|---|---|---|---|
| Oberseminar (Computational Science and Mathematical Methods) | Seminar (S) | WS 23/24 | |
| Tutorial for 0155450 (Introduction to Kinetic Theory) | Übung (Ü) | WS 23/24 | |
| Introduction to Kinetic Theory | Vorlesung (V) | WS 23/24 |
| title | type | semester | place |
|---|---|---|---|
| Uncertainty Quantification | Vorlesung (V) | SS 2023 | |
| Tutorial for 0164400 (Uncertainty quantification) | Übung (Ü) | SS 2023 |
| title | type | semester | place |
|---|---|---|---|
| Tutorial for 0155450 (Introduction to Kinetic Theory) | Übung (Ü) | WS 22/23 | |
| Introduction to Kinetic Theory | Vorlesung (V) | WS 22/23 |
| title | type | semester | place |
|---|---|---|---|
| Übungen zu 0155400 (Optimierungstheorie) | Übung (Ü) | SS 2022 | |
| Optimierungstheorie | Vorlesung (V) | SS 2022 | |
| Oberseminar Computational Science and Mathematical Methods | Seminar (S) | SS 2022 | |
| Uncertainty Quantification | Vorlesung (V) | SS 2022 | |
| Tutorial for 0164400 (Uncertainty quantification) | Übung (Ü) | SS 2022 |
| title | type | semester | place |
|---|---|---|---|
| Tutorial for 0155450 (Introduction to Kinetic Theory) | Übung (Ü) | WS 21/22 | |
| Introduction to Kinetic Theory | Vorlesung (V) | WS 21/22 |
| title | type | semester | place |
|---|---|---|---|
| Oberseminar Computational Science and Mathematical Methods | Seminar (S) | SS 2021 | |
| Uncertainty Quantification | Vorlesung (V) | SS 2021 |
- If you are interested in a thesis in our group, please feel free to contact us directly. You can get an overview of our research interests and projects in the tab "Team" . Some old offers from CSMM group members are also available hTopics Master & Bachelor Studentsere. These are not all up to date, but might give an insight into possible topics. Please try to identify the group member(s) who you find most fitting to your interests and address your inquiry to them -
| Title | Supervisors |
|---|---|
| Influence of Adversarial Learning on Parotid Gland Segmentation and Assessment of Cut-off Parotid Gland Reconstruction | Alexandra Walter and Prof. Oliver Jäkel (DKFZ) |
| Effects of Low Dscrepancy Sampling for High Dimensional Neural Network Training wth Application to the Entropy Closure Problem | Steffen Schotthöfer and Prof. Martin Frank |
| Investigation of Neural Network Prediction Performance for Structured Problems | Steffen Schotthöfer and Prof. Martin Frank |
| Physics Informed Neural Networks for Dynamical Systems | Steffen Schotthöfer and Prof. Martin Frank |
| Data-Driven Surrogate Models for Corrosion Simulation | Frank, Ludwig Waibel (Daimler), Steffen Schotthöfer and Prof. Martin Frank |
| First Collision Source Methods for Radiation Therapy | Jonas Kusch, Pia Stammer and Prof. Martin Frank |
| Modelisation of Uncertainties for Treatment Planning | Pia Stammer, Niklas Wahl (DKFZ) and Prof. Martin Frank |
| Bayesian Long Short-Term Memory Networks for Proton Dose Prediction | Tim Ortkamp, Niklas Wahl (DKFZ) and Prof. Lena Maier-Hein (DKFZ) |
| Multikriterielle Optimierung und ihre Anwendung in der inversen Radiotherapieplanung | Tim Ortkamp, Prof. Martin Frank and P.D. Gudrun Thäther |
| Restringierte Optimierung von maschinellen Lernmodellen zur Vorhersage des Behandlungserfolgs in der Radiotherapie | Tim Ortkamp, Prof. Martin Frank and P.D. Gudrun Thäther |
| Machine Learning for radiotherapy outcome prediction based on imbalanced data | Tim Ortkamp, Prof. Martin Frank and P.D. Gudrun Thäther |
| Uncertainty-aware Multi-criteria Dose Optimization for Radiation Therapy | Pia Stammer, Prof. Markus Klute (Institute of Experimental Particle Physics - ETP) and Prof. Martin Frank |
| Piece-wise Objective Functions for Uncertainty-aware IMRT Dose Optimization | Pia Stammer, Prof. Achim Streit (SCC/Institute of Telematics) and Prof. Martin Frank |
In its core business, AiNT GmbH offers a wide range of services in the field of nuclear technology.
Especially in the development of innovative measurement systems (see project ZEBRA and QUANTOM), the CSMM working group is a long-standing cooperation partner of the company. In addition to the core business in the field of research and development, AiNT GmbH also offers education and training programs, services in the field of radiological and material characterization of residual and waste materials by means of nuclear radiation measurement technology, as well as the in-house ICOND fair.
Associated: Alexander Jesser, Jannick Wolters
As part of the Helmholtz Information and Data Science Academy (HIDA) the Helmholtz Information & Data Science School for Health (HIDSS4Health) promotes doctoral researchers working at the interface between data science and life science. The selected doctoral researchers will be offered a structured training program to develop key qualifications for science and industry.
The homepage of HIDSS4Health can be found here.
Associated: Pia Stammer, Alexandra Walter
The KIT Center "MathSEE" bundles interdisciplinary mathematical research at KIT since October 2018.The Collaborative Research Center 1173 "Wave Phenomena: Analysis and Numerics" and other existing collaborations form the basis for the emergence of MathSEE. Our members from the career level of PhD students onwards cooperate in exchange formats and interdisciplinary research projects in methodological areas. Our graduate school, MathSEED, offers a comprehensive program for doctoral and master's students to promote interdisciplinary training of young researchers. The MathSEE offers to strengthen interdisciplinary mathematical research at KIT and its visibility.
Associated: Maren Hattebuhr, Kirsten Wohak
The SFB 1173 »wave phenomena« is sponsored by the Deutschen Forschungsgemeinschaft (DFG).
Waves are everywhere, and understanding their behavior leads us to understand nature. The goal of CRC 1173 Wave Phenomena« is therefore to analytically understand, numerically simulate, and eventually manipulate wave propagation under realistic scenarios by intertwining analysis and numerics.
Associated: Jonas Kusch, Steffen Schotthöfer
We unconsciously encounter simulations in many everyday situations: The daily weather forecast, the non-destructive crash test for the registration of our car, lightweight and material-saving plastic parts on household appliances or investment strategies for funds and pension investors.
An interdisciplinary team has set itself the task of bringing the subject of simulation and mathematical modelling to schools. How do we recognize simulations? How are the results to be understood? And what do employees in computing centres work on? Simulated Worlds clarifies these questions in an age-appropriate way for pupils
Associated: Maren Hattebuhr, Kirsten Wohak, Sarah Schönbrodt, Stephanie Hofmann
In the young persons lab, you can't miscalculate, you don't need a calculator, no formulas and no equations. You just have to be curious, observe, puzzle and experiment. More than 80 experimental stations await visitors young and old. In addition to school classes, interested individuals are also very welcome.
Associated: Maren Hattebuhr, Kirsten Wohak, Sarah Schönbrodt, Stephanie Hofmann
