Optimization of Recurrence Plot Generation by Differentiable Programming
In this master thesis the potential of differentiable programming on a basic concept of nonlinear physics will be explored. The generation of recurrence plots from a time series will be re-implemented into an coding environment that allows for automatic differentiation (e.g., RTorch, PyTorch, TensorFlow, Enzyme.jl). In the forward calculation, a recurrence matrix will be calculated from a given time series under the choice of parameters, such as embedding dimension, delay and recurrence distance threshold. The automatic differentiation capabilities of the differentiable programming environment of choice will then allow to generate a respective backward calculation of the above procedure (cf. https://docs.pytorch.org/tutorials/beginner/basics/autogradqs_tutorial.html) resulting in gradients in the parameters. In the end, the goal is to optimize the previously hand-chosen parameters iteratively with respect to suitable requirements of the recurrence plot (e.g., line density, mode separation etc.). The student will not only learn a key programming technique with a very wide range of potential applications. She/he also has to creatively overcome some challenges as the differentiation of choosing discrete parameters (e.g., the embedding dimension) and inequality operators (e.g., ≤ in combination with the recurrence distance threshold).
[Joint project with Dr. J. Saynisch-Wagner, GFZ Helmholtz Centre for Geosciences]
Fractal dimension of solution structures in a gypsum cave
Gypsum caverns in the old copper-shale mines of the Mansfeld region exhibit solution structures at a wide range of scales. How are the sizes of these structures distributed? Do we observe scale free behaviour, self-similar features, and can we characterise them by a fractal dimension? High-resolution spatial data from LiDAR and SfM measurements are available.
Spatial statistics of speleothem ensembles from structure-from-motion data
Sodastraws are fragile speleothems in caves and respond to environmental changes, e.g., to flooding of cave parts. The spatial orientation of sodastraws is completely unexplored, but could help to understand their response to environmental changes. In this project, structure-from-motion data of ensembles of sodastraws from two different sites in a cave in Thuringia will be analysed. It combines image processing (segmentation) and statistical analysis.
[Joint project with the Remote Sensing and Earth Surface Processes group, University of Potsdam]
Assessing Discretization Effects in Climate Networks Using Hexagonal Grids
Climate networks based on gridded data (e.g., from reanalysis data) are susceptible to spatial discretisation bias, particularly due to the higher sampling density at the poles. This bias significantly distorts network measures and, consequently, the interpretation of results. Alternative discretisation schemes, such as the hexagonal or HEALPix approaches, may mitigate these issues. In this project, the influence of different spatial discretisation approaches on global climate network analyses will be investigated. Specifically, the aim is to determine how network measures are affected when replacing the commonly used latitude–longitude grid with alternative grid approaches.
Recurrence analysis and Hurst exponents
Recurrence analysis is a modern method for non-linear time series analysis. New developments combine non-linear approaches with those from fractal geometry. In this Master's thesis, the properties of the method are compared with alternative approaches such as "Detrended Fluctuation Analysis" and "Hurst Exponent".
Improving phase sync measure using τ-recurrence rate
τ-recurrence rate can be used to study phase synchronisation. Comparing τ-recurrence rates of different systems was originally introduced by Pearson correlation coefficient, but other measures seem better suited. τ-recurrence rate is actually a probability of recurrence, therefore, measures to compare probabilities should be tested and compared.
Development of Sonification Framework for Palaeoclimate Data
Are you interested in exploring how data can be transformed into sound? This project involves developing a framework to convert palaeoclimate data, such as Milankovitch cycles and various proxy records (e.g., ice cores, sediment layers, tree rings), into an auditory experience. By sonifying complex data patterns, the aim is to create an intuitive way to understand long-term climate changes and enhance the interpretation of cyclical phenomena like orbital forcing. This project combines climate science, data analysis, and digital audio processing, offering a unique opportunity to bridge scientific research and creative technology. Ideal for students with a background in environmental science, data science, or digital media.
[not available] Einfluß der Quasi-biennial Oscillation auf die Europäischen Winter-Temperaturen
Oszillationen sind in der Natur allgegenwärtig und nehmen auch im Klimawandel eine Schlüsselrolle ein. Die Quasi-biennial Oscillation (QBO) ist eine zeitliche Veränderung der Richtung des zonalen Windes in der äquatorialen unteren Stratosphäre mit Perioden von etwas mehr als zwei Jahren (28 Monate). Diese Richtungsänderungen haben signifikanten Einfluss auf die vertikale Ausbreitung Planetarer Wellen in den mittleren Breiten der Winterhemisphäre und auf den Temperaturverlauf über Europa. Jedoch sind die Mechanismen nur unzureichend verstanden was die Abschätzung des Einflusses der globalen Erwärmung auf die QBO und die Wintertemperaturen erschwert. Um den Mechanismus dieses Zusammenhanges besser zu verstehen soll in einem Master-Projekt ein konzeptionelles Modell für dieses gekoppelte System entwickelt und damit Synchronisationsphänomene studiert werden. Anhand instrumenteller Beobachtungsdaten sollen die Kopplungsrichtungen und -stärken zwischen den atmosphärischen Teilsystemen mit modernen Verfahren (z. B. Tigramite) untersucht und quantifiziert werden.
[not available] New metrics for event recurrence analysis
New extensions in the recurrence plot framework allow their direct application on event data (highly discrete data). In this project, alternative metrics for recurrence analysis will be implemented and investigated with respect of their usability.
[not available] New metrics for spectral analysis of event data
Recent developments introduced the concept of spectral analysis for event data. In this project, alternative metrics for this analysis will be implemented and investigated with respect of their usability.
Coupled mechanical pendula as macroscopic analogue of qubit dynamics
Qubits are essential in quantum information applications, but their coherent temporal evolution cannot be continuously measured due to the wave function collapse inherent in quantum measurement. To overcome this limitation, a classical analogue system is highly valuable for visualization and studying the time evolution of a qubit. Arguing along the correspondence principle and wave mechanics, we can reconstruct the coherent dynamics of a driven qubit from the classical equation of motion of macroscopic physical pendula with modulated coupling. By mapping the classical equations of motion onto a Schrödinger-like equation, this system establishes a one-to-one analogue for a qubit, allowing for the direct visualisation of its dynamics. This setup provides a continuous monitoring of the state evolution in time, enabling demonstrations of full control of a qubit. In this master’s project, recurrence analysis is used to systematically investigate the complex time-evolution of a classical coupled-pendulum system, which acts as an analogue to a quantum qubit. The study aims to validate how recurrence plots reflect the characteristic dynamics of Rabi oscillations and Landau-Zener-Stückelberg-Majorana (LZSM) interference, and explores the potential for recurrence-based methods to uncover subtle, unmodeled dynamical effects.
[Joint project with PD Dr. Stefan Ludwig, Paul-Drude-Institut für Festkörperelektronik Berlin]
Efficient algorithm for recurrence quantification analysis
Recurrence quantification analysis (RQA) can be performed very efficiently by replacing the full recurrence matrix computation with a sampling scheme, in which only a random or systematic subset of recurrence points is evaluated to estimate RQA measures. While this approach already yields substantial computational savings, several avenues for further improvement remain open. These include testing for statistical convergence of the sampled estimates (i.e. determining when enough points have been sampled to guarantee a reliable result), and caching intermediate results to avoid redundant computation across multiple RQA measures or repeated analyses. A further open question is whether and how this sampling strategy can be adapted to recurrence-based network measures, such as recurrence networks, where the topology of the full recurrence matrix is in principle required – making naive sampling non-trivial. The goal of this project is to implement, test, and extend this sampling framework. The topic is well suited for physics students with a preference for practical, programming-oriented work, as well as for informatics students with an interest in applied algorithm design and scientific computing.
If you are interested, contact Norbert Marwan.
