Topics for Bachelor's or Master's Theses

We offer a wide range of possible Bachelor and Masterthesis projects as well as Praktika. If you are interested in any of these topics, or something in the direction of the below, please contact us. (hellmann@pik-potsdam.de or nora.molkenthin@pik-potsdam.de).
 

Further topics are offered in cooperation with our partners at TU Berlin.

Power Grid Topics

Machine Learning with Networks

Machine learning tools allow us to study complex systems in novel ways. A defining feature of many complex systems are the underlying interaction networks. A crucial challenge in the application of machine learning tools to complex systems science is the development of ML methods that are network aware. A frist significant and active step in this direction is the ongoing rapid development of Graph Neural Networks. We offer BA/MA thesis topics that investigate GNNs in the context of power grids and complex system science, but also contribute novel architectures that arise out of network science.

ML with Networks 2

The above topic deals with understanding networked systems through ML. Complimentary is the task to define them from data using ML.

Develop and implement intermediate complexity models

The methods developed for the analysis of networked systems are in principle applicable to arbitrary models. In order to investigate actual power grids it is necessary to implement intermediate level complexity models of real and realistic power grids in a way that is amenable to sampling based methods. This will be done in the context of PowerDynamics.jl in the programming language Julia. This involves both, numerical and analytical work to find appropriate simplifications of detailed engineering models.

Further numerical work

While a set of tools for numerical investigations of complex systems already exists, there is still a great need for further developing the software ecosystem and implementing well written libraries for these investigations, particularly in the rather young Julia ecosystem.

Optimizing nonlinear properties of power grids

By using semi-analytic approximations of non-linear stability measures, we will investigate the performance of standard optimization algorithms for optimizing the non-linear behaviour of high dimensional power grids. A more far reaching project (MA only) is to investigate the use of sensitivity analysis to develop novel gradient descent algorithms for optimizing sampling based non-linear properties directly.

Mobility Topics

Effective Topology

The efficiency and operation of on-demand ride-sharing depends on many factors including the layout of the street network and the distribution of requested rides on it. It seems plausible that these two factors could be combined into an effective topology, by weighing edges and/or nodes based on their request frequency. The task at hand is to analytically and in simulations analyze different combinations of demand patterns and simple topologies to derive this relationship.

Pricing and Efficiency

Ride-sharing is most efficient in a regime of high request rate and many buses, however, operating many buses is costly for the operator and/or the environment. Furthermore, the number of requests is limited in reality. We offer a BA/MA thesis on analytically and numerically optimizing the fleet size with different cost functions and pricing variants.

Optimized stop pooling

To improve the number of sharable rides, as well as the efficiency of the resulting routes, it can be beneficial to require some amount of walking from potential customers. In this thesis the aim is to optimize amount and location of pooled stops using Monte Carlo methods and analyze the characteristics of pooled stops and resulting networks.

Social Network Topics

Modeling social network restructuring

Generating models of social networks could improve the understanding of many processes on such networks (e.g. opinion formation, information spreading, disease spreading). Moreover, the mechanism of generating them itself can give insights into which processes are at work behind the scenes. Building on existing models of social network growth and restructuring we offer BA/MA thesis topics exploring

- Node-based reformulation of a social network rewiring model for easier interpretability

- Studying the effects of altered preferential attachment rules ranging from nonlinear functions of the node degree to random walk distances.

- Analyze real social networks and find out why offline networks tend to be close to the critical transition while online networks are widely distributed in the supercritical regime.

General Network and Theory Topics

MCMC (and other advanced sampling methods) for investigating non-linear emergent network properties

While naive sampling approaches can reveal the dominant behavior of a complex system, they do not allow us to efficiently understand rare events. This project will develop and test advanced optimization and sampling methods that purposefully drive the system towards rare failure modes. Such methods will allow us to efficiently investigate and model complicated emergent phenomena such as cascading failures in power grids and other networks.

A secondary challenge for analytically inclined MA students is to develop new MCMC methods for this context.

Clustering trajectories in dynamical systems, unsupervised machine learning (MA)

In order to understand the behavior of high dimensional systems under parameter change, their bifurcation structure, we need novel methods. Monte-Carlo basin bifurcation studies the bifurcation structure from the point of view of changes in the basin volume. At the core of this method is the clustering of trajectories, a challenging problem in unsupervised ML. There is considerable scope for more analytic and semi-analytic work in this context.

Quasi-local loop base control

Loops or cycles play a fundamental role in the behavior of networked systems. A basis of the possible flow states in a networked system is given by a basis of cycles. This project will investigate the potential of controlling a networks dynamical behaviors through the cycle flows.

Another component here is to look at complex formulations of flow networks and study the solution spaces using algebraic methods.

Low dimensional approximations to oscillator networks

For many phenomena observed in high dimensional systems we can find simplified low dimensional models. We will explore the behavior of some of these models analytically and semi-analytically and develop new ones.


Last updated on 27.05.2020.