Show simple item record

dc.contributor.authorBartolovic, Nemanjaen_US
dc.contributor.authorGross, Markusen_US
dc.contributor.authorGünther, Tobiasen_US
dc.contributor.editorViola, Ivan and Gleicher, Michael and Landesberger von Antburg, Tatianaen_US
dc.description.abstractDynamical 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.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.subjectHuman centered computing
dc.subjectVisualization techniques
dc.subjectScientific visualization
dc.titlePhase Space Projection of Dynamical Systemsen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersDimension Reduction and Projections

Files in this item


This item appears in the following Collection(s)

  • 39-Issue 3
    EuroVis 2020 - Conference Proceedings

Show simple item record

Attribution 4.0 International License
Except where otherwise noted, this item's license is described as Attribution 4.0 International License