Visual comparison of dynamical systems

Master Thesis

Description

Observing the geometry of dynamical systems is anticipated to provide mathematical domain scientists with a significant understanding of the dynamics, and potentially, of underlying modeled biological processes. New visualization tools to support domain scientists to understand, analyze, and illustrate trajectories of dynamical systems are available, but they do not support the visual comparison thereof [1,2]. To compare multiple trajectories emerging from different initial conditions, techniques from ensemble visualization could be incorporated, e.g., contour boxplots [3] and curve boxplots [4] or approaches from weather forecast ensemble visualization [5], or concepts from flow visualization [6].

Tasks

We are interested in developing novel visual analytics techniques, which will support the comparison of a large ensemble of particle trajectories, resulting from different initial conditions of dynamical systems. 

Requirements

•    Interest and knowledge in visualization and visual analytics.
•    Good programming skills (C++, OpenGL).
•    Creativity and enthusiasm.

Environment

C++, OpenGL (you will be building on top of an existing system [1])

References

[1] Amirkhanov, Aleksandr, Ilona Kosiuk, Peter Szmolyan, Artem Amirkhanov, Gabriel Mistelbauer, M. Eduard Gröller, and Renata G. Raidou. "ManyLands: A Journey Across 4D Phase Space of Trajectories." In Computer Graphics Forum, vol. 38, no. 7, pp. 191-202. 2019.
[2] Bartolovic Nemanja, Markus Gross, and Tobias Günther. "Phase Space Projection of Dynamical Systems." In Computer Graphics Forum, vol. 39, no. 3, pp. 253-264. 2020.
[3] Whitaker, Ross T., Mahsa Mirzargar, and Robert M. Kirby. "Contour boxplots: A method for characterizing uncertainty in feature sets from simulation ensembles." IEEE Transactions on Visualization and Computer Graphics 19, no. 12 (2013): 2713-2722.
[4] Mirzargar, Mahsa, Ross T. Whitaker, and Robert M. Kirby. "Curve boxplot: Generalization of boxplot for ensembles of curves." IEEE transactions on visualization and computer graphics 20, no. 12 (2014): 2654-2663.
[5] Ferstl, Florian, Mathias Kanzler, Marc Rautenhaus, and Rüdiger Westermann. "Time-hierarchical clustering and visualization of weather forecast ensembles." IEEE transactions on visualization and computer graphics 23, no. 1 (2016): 831-840.
[6] Von Funck, Wolfram, Tino Weinkauf, Holger Theisel, and Hans-Peter Seidel. "Smoke surfaces: An interactive flow visualization technique inspired by real-world flow experiments." IEEE Transactions on Visualization and Computer Graphics 14, no. 6 (2008): 1396-1403.

Responsible

For more information please contact Renata Raidou, Aleksandr Amirkhanov.