Case Studies Summer Semester 2026 - Applications

1.1.1. (LS1) Barley 

There are two kinds of barley, spring barley and winter barley. Usually spring barley is used for beer brewing. Since the spring barley prices rise, it is interesting to replace it by winter barley. To characterize the influence of this replacement on beer quality, beer was brewed on a lab scale and analyzed. The project goal is the statistical analysis of the experimental data.

1.1.2. (LS2) Agroforst

At the TUM research farm Roggenstein a agroforest system with ten experimental micro landscapes is established to study the effects of different agroforestry systems compared to conventional agricultural or forestal use. Focus of the project is setting up concepts for research data management as well as data analysis.

1.1.3. (LS3) Ultradian rhythms under extreme conditions

Analysis of activity rhythms during sleep in submariners

What are ultradian rhythms and why do they matter?

■ In chronobiology, ultradian rhythms are rhythms with a period of < 24 h. While most research focuses on circadian rhythms (period ≈ 24 h), ultradian rhythms are less well studied and understood.

■ Ultradian rhythms can be found, for example, in movement during sleep and switching between sleep stages. So far, they have hardly been studied under extreme conditions, such as low light and low activity levels combined with shift work, as seen in data from a submarine mission.

■ Analysing the submariners’ data, we want to find out how their sleep varies between the mission and the pre- and post-mission. post-mission periods. To this end, we want to study their sleep activity rhythms and determine whether they are linked to sleep quality or sleepiness.

Goals and challenges of the project

■ Work with real-life data → data cleaning

■ Applying this data to the existing framework as the locomotor inactivity during sleep (LIDS)

■ Find or adapt mathematical methods to detect rhythms (Wavelets, Singular spectrum analysis, Hidden Markov models, etc.)

■ Statistical testing of the results

1.1.4. (LS4) Unlocking the Secrets of DNA: From Sequences to Disease Dynamics (mPox)

DNA sequencing has become remarkably affordable, and DNA sequence data are now available on an unprecedented scale. The pressing question is: what can we actually learn from these data?

One fascinating application of pathogen DNA sequences is the estimation of key parameters in dynamic models, such as the well-known reproduction number. But we can go even further: it is possible to detect mechanisms and patterns of spread directly from DNA sequences.

The method relies on the coalescent theory: by examining pathogen samples from n ∈ N individuals, we obtain n distinct gene sequences. When comparing these sequences, mutations are almost inevitable. The greater the differences between two sequences, the less closely related they are. This information allows us to reconstruct possible ancestral trees—much like how phylogenetics reveals the evolutionary relationships among species (e.g., humans are more closely related to gorillas than to horses).

In phylodynamics, this same approach is used to build a ”family tree” of pathogens. What makes this particularly exciting is that such trees also encode information about the dynamics of disease spread—and we can harness this for deeper insights.

In this project, we will explore this method hands-on, applying it to mPox (monkeypox) data. mPox is a compelling case study: historically confined mainly to Africa, infections surged globally around 2022, appearing suddenly in Europe, North America, and beyond. The key question is: Can we trace this dramatic shift in the DNA data itself?

Project plan:

(a) Understand the basic theory of phylodynamics

(b) understand the statistical tools which are available

(c) Set up a dynamic ODE model for the mPox

(e) use the phylodynamics-tools to investigate Pox DNA samples with the aim to detect traces of the recent dramatic spread of mPox

Supervisor: Johannes Müller.

1.1.5. (LS5) Epidemics in real world situations

Epidemic management relies on mathematical models that capture both, disease spread and countermeasures. Due to the variety of possible scenarios, no universal strategy exists; instead, tailored solutions are developed. 
From previous studies, a kind of compartmental model structure in the form of an ODE system including statistically-based general rules for the implementation of countermeasures is available. The aim of this study is to develop a strategy to deduce decision rules for a concrete situation and to focus on few rules which are plausible and easy to handle. 

As models become more complex—especially when incorporating aspects like psychology and economics as refinements of the usual compartmental structured model —manual strategy design may reach its limits and and exploration of new techniques to tackle this problem may be appropriate. 

1.1.6. Supply-chain Optimization with Embargo Constraints (DO-Supply-Chains) - Discrete Optimization

This case study project, together with SAP, challenges you to optimize the global supply chain of a high-tech company producing smartphones and accessories. The objective is to manage the flow of goods (from raw component to final customer delivery) across a network of factories, warehouses, and distribution centers. Each smartphone is assembled from modular components that can vary for example by quality level, vendor, or functionality, resulting in a large number of product variants. Modeling every variant separately is typically computationally too expensive. To reflect the complexities of modern international trade, we consider embargo constraints: You must ensure that the Bill of Materials (BOM) for each finished product complies with the trade policies of the destination country. For example, smartphones for the U.S. market are prohibited from including SoCs (System on a Chip) from Chinese companies, while devices produced for the European Union may only use batteries from certified Japanese or South Korean suppliers. Especially in today's geopolitical climate, embargo restrictions are critical, and companies must ensure their supply chains remain both compliant and resilient.

1.1.7. Energy Flexibility in Production Scheduling (DO-Energy) - Discrete Optimization

In modern electricity markets dominated by variable renewable energy sources, energy flexibility is becoming a key component. Industrial production facilities with high energy demands can provide valuable flexibility services to the grid. By adjusting their energy consumption in response to market signals, these consumers can help to balance supply and demand, reduce costs, and support grid stability. This project, in cooperation with Siemens, aims to develop models and methods to identify potential adjustments to production plans that can be offered as flexibility services, while meeting all production requirements. Your task is to develop a system that generates such flexibility offers, while taking important constraints into account. This includes meeting all job deadlines, considering machine capacities, and taking base loads of machines into account in order to avoid excessive switching on and off.

1.1.8. Vehicle Allocation Optimization (DO-Car-Rental) - Discrete Optimization

SIXT is one of Europe’s leading car rental companies, operating hundreds of branches. Each branch must efficiently allocate its vehicle inventory to fulfill customer reservations while maximizing both customer satisfaction and profitability. This is a complex operational challenge that combines data management, constraint satisfaction, and decision-making under uncertainty. Each morning, a branch faces the following scenario: 

• A set of confirmed reservations from customers, each specifying their requested vehicle group and rental dates
• Limited vehicle capacity across different car groups – some groups may be overbooked
• Defined upgrade paths: certain vehicle groups are eligible substitutes for others (e.g., a customer can upgrade from economy to premium)

In cooperation with SiXT, the central question being investigated is: which customer receives which car?

1.1.9. Graph-based Optimal Transport for Keypoint Matching (NLO-Graph-OT) - Nonlinear Optimization

This project together with the Chair of Computer Aided Medical Procedures aims to enhance Optimal Transport (OT) solvers by incorporating Graph Neural Networks (GNNs) to address the lack of geometric consistency in feature matching. The main motivation of the study is that a lot of real objects are symmetric and thus impose ambiguity. Traditional OT approaches focus on similarity measures and often neglect important neighboring information in geometric settings, proper in computer vision or graphics problems, resulting in the production of huge noise in pose estimation tasks. To tackle this problem, we hypothetize that when the object is symmetric, there are many correct matches of points around its symmetric axis and we can leverage this fact via Optimal Transport and Graph Learning.

1.1.10. Synthesis of Model Predictive Control and Reinforcement Learning for Vehicle Control (NLO-Vehicle) - Nonlinear Optimization

Autonomous vehicles require intelligent control strategies to navigate complex and dynamic environments safely and efficiently. Model Predictive Control (MPC) leverages a predictive model to anticipate future system behavior and determines control actions accordingly through mathematical optimization. However, the performance of classical MPC relies heavily on accurate system models, which can be challenging to obtain and maintain in real-world scenarios. Reinforcement Learning (RL), on the other hand, excels at learning performant policies through trial and error, making it highly effective in situations in which model parameters are unknown. By integrating RL with MPC, the limitations of each individual approach can be mitigated, creating a more adaptable control system. In this project, together with Siemens, RL should be employed to learn and refine the unknown model parameters of the autonomous vehicle, as well as the parameters of the cost function used by MPC. The goal of the project is to understand the advantages and disadvantages of each control approach and to explore how they can be combined to achieve the best control performance. 

Required programming skills: Python. 

1.1.11.  Data-Driven Optimization for Turbulence Modeling (NLO-Turbulence) - Nonlinear Optimization

A key challenge in computational fluid dynamics is the trade-off between simulation accuracy and computational efficiency. Common approaches in industrial fluid flow simulations, such as Reynolds-averaged Navier–Stokes (RANS) models, are computationally efficient and robust. However, standard RANS models often struggle to accurately represent complex flow phenomena, such as flow separation and reattachment. More accurate simulation approaches exist, but they are typically too expensive for routine industrial use.

Recent data-driven approaches aim to improve turbulence models by incorporating information from high-fidelity simulations or experimental data while preserving computational efficiency. In this project, such approaches are investigated in cooperation with the industrial partner HAWE Hydraulik SE, which will provide high-fidelity reference data for selected benchmark flow configurations exhibiting free shear and reattachment behavior.

The project focuses on the development of a modern optimization framework for calibrating turbulence model parameters using this reference data. From a mathematical perspective, key challenges arise from the limited availability of gradient information and the restricted number of feasible model evaluations, despite the relative efficiency of RANS simulations. The project combines mathematical modeling, nonlinear optimization, and applied fluid dynamics in an industrially relevant setting.

1.1.12. S1: Implementation of gate-based quantum algorithms

During recent years, significant progress has been made in improving quantum hardware. Moreover, several quantum algorithms have been developed that have the potential to outperform classical algorithms. One well-known example is Shor's algorithm for factoring integers or . To be able to implement these algorithms, programming tools such as Qiskit and Pennylane for gate-based quantum computers have been developed. Using tools such as Qiskit and Pennylane a programmer has to create quite complex circuits, i.e., quite often one has to apply gates to single qubits. However, this makes the implementation of complex quantum algorithms quite complicated. A few years ago, Fraunhofer FOKUS has started the development of Qrisp (www.qrisp.eu), which is a Python-based programming tool considering high-level programming paradigms to facilitate the implementation of quantum algorithms. Since one can expect that the complexity of quantum algorithms will increase in the future, the usage of high-level programming tools will be indispensable to produce high-quality program code. This programming tool provides a systematic approach to quantum algorithm development such that quantum algorithms can be implemented, maintained, and improved in a convenient way. By this, the programming workload and proneness to errors can be kept at a low level. A series of programming abstractions are considered that are inspired by classical paradigms and focusing on the particular needs of a quantum developer. In contrast to many other programming tools for quantum algorithms, Qrisp allows the user to handle quantum variables and functions, which makes the implementation of complex algorithms more compact. An important feature of Qrisp is its ability to compile programs to the circuit level, making them executable on most existing quantum hardware. The introduced abstractions enable the Qrisp compiler to leverage algorithm structure for increased compilation efficiency. This can be achieved, although Qrisp performs barely any low-level optimization, such as other state-of-the-art packages. In this project the foundations of quantum computing and Qrisp are introduced.  

Required programming skills: Python

Sub-tasks:

• Study literature on gate based quantum computing.
• Implement some algorithms in Qrisp.
• Test the performance of your implementation by means of simulators and perform some resource estimation.

Literature:

• R. Seidel, S. Bock, R. Zander, R., M. Petric, N. Steinmann, N. Tcholtchev and M. Hauswirth. (2024). Qrisp: A framework for compilable high-level programming of gate-based quantum computers. arXiv preprint arXiv:2406.14792.
• www.qrisp.eu
• M. Nielsen and L. Chuang. (2010). Quantum computation and quantum information. Cambridge university press.

1.1.13. S2: Solving discrete quadratic optimization problems using simulated and quantum annealing

Many objective functions in discrete optimization have the form of quadratic polynomials. The variables are binary variable i.e. they attain either the value 0 or 1, while the coefficients are real. If the objective function is not combined with any constraint such type of optimization problem is denoted as QUBO (Quadratic Unconstrained Binary Optimization problem). A well-known class of solution methods for such problems are referred to as annealer-based optimization methods. The term "annealing" is derived from a cooling technique used in metallurgy. Heated metal is cooled in a controlled way such that its atoms have sufficient time to arrange themselves and form stable crystals. This results in a low-energy state of the metal that is considered to be stable. Optimization methods using annealing are heuristic search methods exploring in a controlled way an objective function for a sufficiently long time until they reach a stable and minimizing state. In this project, two different annealer-based methods are to be studied. One method is the simulated annealing method and the other one is the quantum annealing method. While the first one is based on principles from classical computing, the second one exploits principles from quantum mechanics such as tunneling effects. To learn the usage of both methods it is planned to use the software tools provided by D'Wave Quantum (Canadian company producing quantum computers for solving QUBOs). 

Required programming skills: Python

Sub-tasks:

• Understand the foundations of simulated and quantum annealing.
• Choose discrete optimization problems that can be formulated as QUBOs.
• Study the tools provided by D'Wave Quantum and use them to solve the optimization problems.
• Use either simulators or real quantum backends to produce numerical results.

Literature:

• Catherine C McGeoch. (2022). Adiabatic quantum computation and quantum annealing: Theory and practice. Springer Nature.
• E. Aarts and P. van Laarhoven.  (1989). Simulated annealing: An introduction. Statistica Neerlandica, 43(1), 31-52.

• F. Glover, G. Kochenberger and Y. Du. (2019). Quantum Bridge Analytics I: A tutorial on formulating and using QUBO models. 4or, 17(4), 335-371.

1.1.14. S3: Implementation of a blood flow simulator

Numerical simulation of blood flow has steadily gained importance in recent decades due to advances in computing power, efficient numerical algorithms, and imaging and reconstruction techniques. These advances are evoked by the fact that mathematical models enable a non-invasive treatment of cardiovascular diseases. In this project a dimensional reduced model is used for simulating blood flow within the main arteries of the systemic circulation. Thereby, simplified one-dimensional (1D) Navier-Stokes equations model flow within the main arteries, while the remainder of the vessel system and the heart are represented by ordinary differential equations or zero-dimensional (0D) models. All in all, we obtain a 1D-0D coupled model for flow in the main arteries. The main goal of this project is to include patient-specific data into the numerical simulations, in particular the duration of a heart beat or pulsation rate is considered. Measuring the pulsation rate or heart beat duration, an in-ear sensor provided by the company Cosinuss GmbH is used. Since the heart beat duration is a parameter of the 0D model for the heart, the measured data can directly be integrated into numerical model. As a consequence, the simulation data are now depending on patient-specific data.

Required programming skills: C++

Sub-tasks:

• Study the literature on dimensional reduced blood flow models in particular 1D-0D coupled blood flow models.
• Study the numerical methods of characteristics.
• Design a 0D model for the heart (left ventricle) and include this model into an exisiting implementation of the 1D-0D coupled blood flow model using the numerical methods of characteristics.
• Implement an interface reading data from the sensor and use these data to simulate blood flow in the systemic arteries. In this contex,t a collaboration with Cosinuss is intended.

Literature:

• T. Köppl and R. Helmig (2023). Dimension Reduced Modeling of Blood Flow in Large Arteries: An Introduction for Master Students and First Year Doctoral Students. Springer Nature, 2023.
• S. Acosta, C. Puelz, B. Riviere, D. Penny and C. Rusin (2015). Numerical Method of Characteristics for one–dimensional blood Flow. Journal of computational physics, 294, 96.
• T. Adams, S. Wagner, M. Baldinger, I. Zellhuber, M. Weber, D. Nass and R. Surges (2022). Accurate detection of heart rate using in-ear photoplethysmography in a clinical setting. Frontiers in Digital Health, 4, 909519.
• L. Formaggia, D. Lamponi,  M. Tuveri and A. Veneziani (2006). Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart. Computer methods in biomechanics and biomedical engineering, 9(5), 273-288.

1.1.15. S4: Optimization of artificial neural networks (ANN)

An ANN is a system of nodes which are referred to as artificial neurons, since they can be compared to neurons in a brain. A connection or edge between two nodes, like the synapses in a biological brain, can send a signal to other nodes. A node receiving a signal can send it to other nodes which are connected to it. Within an ANN the signal is a real number, and the output of each node is provided by a combination of non-linear functions and its inputs. To each node (neuron) and edge one assigns a weight that is adjusted during a training process. According to the weight the strength of the signal at a connection can be strengthened or weakened. Nodes typically have also a threshold such that signals received by the node such that they are only transmitted if they exceed this threshold. Typically, nodes are grouped together in form of layers. The different layers are connected by edges. Signals enter the network at the first layer (input layer) and leave the last layer (output layer) corresponding to quantities of interest. ANNs have successfully been used as simple surrogate models for complex relationships. For a learning process a sufficient amount of training data is required to determine the different weights. However, it is in general not quite clear how many nodes or neurons and layers have to be chosen to obtain an accurate ANN. The goal of this project is to find algorithms and estimates that can help to design an optimal structure for ANNs. In this context, the term optimal indicates that an ANN contains a minimal number of layers and neurons.

Required programming skills: Python (AI libraries in Python), C++ or MATLAB

Sub-tasks:

•     Study the literature on optimization algorithms for ANNs.
•     Study approximation theorems for neural networks.
•     Implement an algorithm optimizing the topology of an ANN.
•     Apply your optimized ANNs to appropriate data sets.

Literature:

• https://www.adagos.com
• Description of a patent: https://patents.justia.com/patent/12124779
• A. Baldominos, Y. Saez, and P. Isasi. On the automated, evolutionary design of neural networks: past, present, and future. Neural Computing and Applications 32, no. 2 (2020): 519-545.
• K. Yotov, E. Hadzhikolev, S. Hadzhikoleva and S. Cheresharov  (2023). Finding the optimal topology of an approximating neural network. Mathematics, 11(1), 217.
• E. Schiessler, R.  Aydin, K. Linka, K and C. Cyron (2021). Neural network surgery: Combining training with topology optimization. Neural networks, 144, 384-393.