Visual Parameter Space Exploration in Time and Space

Abstract

Computational models, such as simulations, are central to a wide range of fields in science and industry. Those models take input parameters and produce some output. To fully exploit their utility, relations between parameters and outputs must be understood. These include, for example, which parameter setting produces the best result (optimization) or which ranges of parameter settings produce a wide variety of results (sensitivity). Such tasks are often difficult to achieve for various reasons, for example, the size of the parameter space, and supported with visual analytics. In this paper, we survey visual parameter space exploration (VPSE) systems involving spatial and temporal data. We focus on interactive visualizations and user interfaces. Through thematic analysis of the surveyed papers, we identify common workflow steps and approaches to support them. We also identify topics for future work that will help enable VPSE on a greater variety of computational models.

Keywords: parameter space analysis; visual analytics; visualization.

Figure 1

The themes identified as part of our survey describe common actions in a workflow for visual parameter space exploration (VPSE). The relation of our themes to a simplified data flow model in VPSE based on Sedlmair et al. [SHB*14] (left) and the InfoVis pipeline by Card et al. [CMS99] (right) is shown on top. We focus on models where either parameters or outputs reference space and/or time.

Figure 2

Several examples for models in our survey. (a) Flood simulation: The model takes a parameter (barriers) and produces a output (water volume). (b) Physics: The model takes a parameter (3D model) and produces an output (whether or not the shape is balanced). (c) Biochemistry: The model takes several parameters and produces a output (number of species over time).

Figure 3

Flow diagram outlining our collection process.

Figure 4

Statistics of the surveyed papers.

Figure 5

Sub‐themes of Finding Parameter Settings illustrated on a polygon ( parameter). The two left images contain manual approaches, while automatic approaches are in the right two. Other than their counterparts, unconstrained and unsupervised approaches do not limit which parameter settings may be obtained.

Figure 6

Forward and inverse design with direct manipulation of a canule ( parameter); stress on surface ( output) is shown embedded (Section 6.3) to the design. [CLEK13] © 2013 IEEE

Figure 7

Steer by Rating: The parameter space is continually shrinked by selecting preferred solutions at its borders. [KGS19] © 2019 Pergamon

Figure 8

Supervised automatic search for flood barrier settings ( parameter). The perimeter is continually shrinked (a–d) when water touches it. [KWS*14] © 2014 IEEE

Figure 9

Sub‐themes of Input/Output Visualization. The grids refer to coordinate systems of visualizations, where red is generally the input and blue the output.

Figure 10

Example for combination of Input/Output Visualization sub‐themes on parameter, static input and output: Superposition, Embedding, Alignment, Explicit Encoding. [BHR*19] © 2019 Wiley

Figure 11

Examples for Juxtaposition (Section 6.1). (a) Dimensionally‐reduced views of a parameter (left) and a time series ( output, right) support sensitivity analysis. (b) Coordinated multiple views showing parameters (top) and accuracy (bottom, right) of a precipitation forecasting model ( outputs) support uncertainty analysis.

Figure 12

Examples for Superposition (Section 6.2) to support an optimization task. (a) Radiation seed positions ( parameter), organs at risk (static input) and radiation dose ( output) of brachytherapy plan shown on axis‐aligned slices (top row). (b) Original ( input) and rastered time series ( output) as well as raster size ( parameter) shown on common time axis in top left part of the layout.

Figure 13

Examples for Embedding (Section 6.3). (a) View quality ( output) out of a skyscraper's ( parameter) windows (“refined design”) to support optimization. (b) Aggregated water heights ( output) indicate sensitivity to breach location ( parameter, yellow horizontal lines).

Figure 14

Examples for Alignment (Section 6.4). (a) Spreadsheet‐like visualization with parameter on the left and output on the right shows output sensitivity to parameter settings. (b) Particle trajectory glyphs ( output) are aligned in a grid pattern according to initial position of the particle ( parameter), thus supporting partitioning.

Figure 15

Examples for Sequential Superposition (Section 6.5) and optimization/sensitivity tasks. (a) parameters (left) and volume visualization ( output, right) of an ocean simulation. (b) output space is divided into Pareto‐optimal sections, parameter setting (lamp designs) is shown to the side.

Figure 16

Examples for Overloading (a, Section 6.6) and Integration (b, Section 6.7). (a) Detected edges ( feature) in images scanned with 3D X‐ray computed tomography ( output) and different scan parameters (optimization, sensitivity). (b) Integration of parameter and derived feature with trapezoids—comparing side lengths of the trapezoid enables sensitivity analysis.

Figure 17

Examples for Explicit Encoding (a, Section 6.8) and Nesting (b, Section 6.9). (a) Residual plots (4a, 4b) utilize Explicit Encoding to show if any seasonal patterns persist between the original and modelled time series (), an optimization task in time series modelling. (b) Correlation to feature of output (matrix) nested into visualization of parameter value intervals (tree) showing sensitivity of parameter range to output feature.

Figure 18

Sub‐themes of Data Case Organization illustrated on a time series.

Figure 19

Examples for Focusing (Section 7.1). (a) Focus on individual data cases (time series) by selection. (b) Focus on multiple data cases by filtering.

Figure 20

Examples for Derivation (Section 7.2). (a) Two measures of similarity between segmented image ( output, bottom) and reference segmentation in a HyperSlice visualization of an parameter (top right Response View). Dark areas mark high quality of outputs, hence supporting parameter optimization. (b) Parallel Coordinates Plot showing correlations (Y position) between a parameter (line) and the number of segments with a given label (axes), a derived feature from the output of a time series segmentation model. It is visible that the Obs parameter influences the number of labelled segments most (sensitivity).

Figure 21

Examples for Aggregation (Section 7.3). (a) A density plot in a spacetime cube shows the distribution of particle trajectories ( output) with identical initial location but varying velocity and size (, , parameters). The blue spiral marks small particles of size $100\mu m$, and the red blob around it particles of size $300\mu m$, thus highlighting common behaviour within each particle size (partitioning). (b) Plot of median time series and quantiles shows most frequent temporal behavior of outputs.

Figure 22

Example for Sorting theme (Section 7.4): Ranking of derived output features of a flood simulation in the form of a list. Only top‐ranked solutions ( parameter settings) are relevant for the optimization task as they protect many buildings and may be constructed in time. [WKS*14] © 2014 Wiley

Figure 23

Examples for Grouping (Section 7.5). (a) Clustering (right) by outputs was used for a 3D cup generator. Associated parameter settings for clusters are shown to the left in the Parallel Coordinates Plot, supporting sensitivity analysis. (b) Analysts may group time series ( outputs) by simulation parameter, thus carrying out a partitioning task.