Visual Analysis of Multi-run Multi-field Simulation Data

时空现象的数值模拟在科学和工程中广泛应用于检验理论模型和进行预测。这种模拟通常依赖于许多输入参数或初始条件。由于输入参数的精确设置通常是未知的，或者它们的影响需要调查，研究人员使用不同的参数设置进行了大量的模拟运行。因此，模拟运行的总体结果通常是多运行多变量时变体积模拟数据（或简称多运行多字段数据）。由于这些数据的结构复杂，具有多个方面（即多运行、多变量、时空），而且它们的大尺寸大大超出了主要存储容量，因此对这些数据的分析是一项挑战。在第一个资助期，我们开发了一个通用的概念，用于对考虑所有方面的多运行多领域数据进行交互式可视化分析。在第二个资助期，我们努力在几个方面扩展这个概念：为了研究输入参数的相互作用，我们希望将它们的分析推广到更高维度的参数空间。此外，由于生成新的模拟运行通常很耗时，我们希望（近似地）预测新的模拟运行的结果，其中预测的不确定性应该被估计和可视化，这允许计算转向。除了时空模拟运行的全球比较外，人们还对空间局部相关性和因果关系感兴趣，其对整个集合的分析也是我们现在的目标。最后，我们还希望将整个模拟集合与实测数据进行比较分析。这些扩展建立在已经开发的交互式可视化分析方法的基础上，但允许新的见解，并将显著增加我们的多运行多字段数据分析概念的影响。

Numerical simulations of spatio-temporal phenomena are widely used in science and engineering to test theoretical models and make predictions. Such simulations, frequently, rely on a number of input parameters or initial conditions. Since the precise settings for the input parameters are often unknown or their influence is subject to investigation, researchers execute a larger number of simulation runs with different parameter settings. Hence, the overall outcome of the simulation runs is, commonly, multi-run multi-variate time-varying volumetric simulation data (or multi-run multi-field data for short). The analysis of such data is a challenge due to their complex structure with their multiple facets (i.e., multi-run, multi-variate, spatio-temporal) and also due to their large sizes going significantly beyond primary storage capacities. In the first funding period, we developed a general concept for the interactive visual analysis of multi-run multi-field data that considers all facets. In the second funding period, we strive for extending the concept in several aspects: To investigate the interplay of the input parameters, we want to generalize their analysis to higher-dimensional parameter spaces. Moreover, since the generation of new simulation runs is often time-consuming, we want to (approximately) predict the outcome of new simulation runs, where the uncertainties of the prediction shall be estimated and visualized, which allows for computational steering. Besides the global comparisons of spatio-temporal simulation runs, one is also interested in the spatially local correlations and causalities, whose analysis for the entire ensemble is what we also aim for now. Finally, we also want to integrate a comparative analysis of the entire simulation ensemble with measured data. These extensions build upon the already developed interactive visual analysis methods, but allow for new insights and will significantly increase the impact of our concept for multi-run multi-field data analysis.