Optimierte Informationsverarbeitung in Methoden zur stochastischen Simulation und zur Abschätzung von Parameterwerten: Unsichere zeitabhängige Strömungs- und Transportvorgänge im Untergrund

地下水量和水质的预测通常采用数值模型。它们的参数具有未知的空间分布，可以使用地质统计反演技术从现场数据估计这些分布。现场数据通常包括来自油井测试或示踪剂实验的时间序列，由于它们的时间自相关性而传递了冗余信息，导致参数估计的计算成本过高。相反，使用时间序列的时间矩可以更快地计算，这是一种总结信息的有效方法。遗憾的是，时间矩仍然不构成独立的信息，导致精度问题，仍然允许进一步改进。在这个项目中，时间矩将被时间序列的广义泛函取代，包括矩的比率。这将产生一组独立的信息单元，为大规模时变系统的参数估计和随机模拟中的快速和准确的信息处理提供基础。第一次，优化设计的概念将被用来优化信息处理和确定最优泛函集。此外，还将开发一种从这些泛函重建时间序列的方法。来自实际现场的测量数据将被用来测试所开发的方法，并应用于参数估计和随机建模。

Subsurface water quantity and quality is usually predicted using numerical models. Their parameters have unknown spatial distributions which can be estimated from site data using geostatistical inversion techniques. Site data often include time series from well tests or tracer experiments which convey redundant information due to their temporal auto-correlation, leading to excessive computational costs in parameter estimation. Much quicker calculations are possible using temporal moments of time series instead, which is an efficient method to summarize information. Unfortunately, temporal moments still do not constitute independent information, leading to accuracy problems and still allowing further improvement. In this project, temporal moments will be replaced by generalized functionals of time series, including ratios of moments. This is expected to result in a set of independent information units, yielding a basis for rapid and accurate information processing in parameter estimation and stochastic simulation of largescale time-dependent systems. For the first time, concepts from optimal design will be used to optimize information processing and to identify optimal sets of functionals. Also, a method to reconstruct time series from these functionals will be developed. Measured data from a real site will be used to test the developed methods, with applications to parameter estimation and stochastic modeling.