Phase Space Projection of Dynamical Systems
| dc.contributor.author | Bartolovic, Nemanja | en_US |
| dc.contributor.author | Gross, Markus | en_US |
| dc.contributor.author | Günther, Tobias | en_US |
| dc.contributor.editor | Viola, Ivan and Gleicher, Michael and Landesberger von Antburg, Tatiana | en_US |
| dc.date.accessioned | 2020-05-24T13:00:38Z | |
| dc.date.available | 2020-05-24T13:00:38Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | Dynamical systems are commonly used to describe the state of time-dependent systems. In many engineering and control problems, the state space is high-dimensional making it difficult to analyze and visualize the behavior of the system for varying input conditions. We present a novel dimensionality reduction technique that is tailored to high-dimensional dynamical systems. In contrast to standard general purpose dimensionality reduction algorithms, we use energy minimization to preserve properties of the flow in the high-dimensional space. Once the projection operator is optimized, further high-dimensional trajectories are projected easily. Our 3D projection maintains a number of useful flow properties, such as critical points and flow maps, and is optimized to match geometric characteristics of the high-dimensional input, as well as optional user constraints. We apply our method to trajectories traced in the phase spaces of second-order dynamical systems, including finite-sized objects in fluids, the circular restricted three-body problem and a damped double pendulum. We compare the projections with standard visualization techniques, such as PCA, t-SNE and UMAP, and visualize the dynamical systems with multiple coordinated views interactively, featuring a spatial embedding, projection to subspaces, our dimensionality reduction and a seed point exploration tool. | en_US |
| dc.description.number | 3 | |
| dc.description.sectionheaders | Dimension Reduction and Projections | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 39 | |
| dc.identifier.doi | 10.1111/cgf.13978 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 253-264 | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.13978 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.1111/cgf13978 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.rights | Attribution 4.0 International License | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | ] |
| dc.subject | Human centered computing | |
| dc.subject | Visualization techniques | |
| dc.subject | Scientific visualization | |
| dc.title | Phase Space Projection of Dynamical Systems | en_US |