Bartolovic, NemanjaGross, MarkusGünther, TobiasViola, Ivan and Gleicher, Michael and Landesberger von Antburg, Tatiana2020-05-242020-05-2420201467-8659https://doi.org/10.1111/cgf.13978https://diglib.eg.org:443/handle/10.1111/cgf13978Dynamical 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.Attribution 4.0 International LicenseHuman centered computingVisualization techniquesScientific visualization10.1111/cgf.13978253-264