Supporting the integrated visual analysis of input parameters and simulation trajectories

• Combined view of parameters and simulation trajectories by multi-scale visualization.
• Independent exploration of parameters and trajectories along chosen scale sequences.
• Visual guidance towards finer scales through interscale heterogeneity metrics.
• Exploration across scales increases understanding of and confidence in the result.

The visualization of simulation trajectories is a well-established approach to analyze simulated processes. Likewise, the visualization of the parameter space that configures a simulation is a well-known method to get an overview of possible parameter combinations. This paper follows the premise that both of these approaches are actually two sides of the same coin; since the input parameters influence the simulation outcome, it is desirable to visualize and explore both in a combined manner. The main challenge posed by such an integrated visualization is the combinatorial explosion of possible parameter combinations. It leads to insurmountably high simulation runtimes and screen space requirements for their visualization. The Visual Analytics approach presented in this paper targets this issue by providing a visualization of a coarsely sampled subspace of the parameter space and its corresponding simulation outcome. In this visual representation, the analyst can identify regions for further drill-down and thus finer subsampling. We aid this identification by providing visual cues based on heterogeneity metrics. These indicate in which regions of the parameter space deviating behavior occurs at a more fine-grained scale and thus warrants further investigation and possible re-computation. We demonstrate our approach in the domain of systems biology by a visual analysis of a rule-based model of the canonical Wnt signaling pathway that plays a major role in embryonic development. In this case, the aim of the domain experts was to systematically explore the parameter space to determine those parameter configurations that match experimental data sufficiently well.

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