A reverse engineering approach to optimal design of site investigation schemes and monitoring networks

实验设计的目标是调查一个系统，以便从给定的有限的调查预算中获得最大的信息。将地下水视为一种饮用水水源，其质量和安全很难评估和预测，主要是因为地下物质是非均质的，而且数据太少，无法解决这种异质性并提取系统必要的关键属性。试验设计有助于优化地下勘探，在勘探预算有限的情况下，最大限度地提高地下水质量和安全的预期预测置信度。然而，目前的实验设计受到计算机需求的严重限制，特别是在随机地下水水质模型等复杂的大尺度问题中。本项目将从新的信息论角度重新阐述最优设计理论。与传统上繁琐地搜索所有可能的测量地点以找到信息最丰富的地点不同，分析的方向将被逆转，以在单一步骤中直接确定信息最丰富的地点。这将极大地减少计算负荷，允许对更大、更复杂、因此更现实的问题应用优化设计。同时，这避免了在分析中损害数据集的信息含量的简化或线性化。新方法不会屈服于计算限制，而是允许处理当前的、面向目标的和应用驱动的研究任务。首先在地下水角度内开发和应用新方法，然后将其作为许多科学学科的宝贵工具输出，这些科学学科在非均质或复杂的动力系统中面临类似的不确定性。

The goal of experimental design is to investigate a system such that maximum information is achieved from a given, limited budget for investigation. Looking at groundwater as a drinking water resource, its quality and safety is hard to assess and predict mainly because subsurface materials are heterogeneous, and there are too few data to resolve this heterogeneity and extract the necessary key properties of the system. Experimental design can help to optimize subsurface exploration, maximizing the desired prediction confidence of groundwater quality and safety in spite of limited exploration budgets. However, experimental design is currently heavily limited by its computer demands, especially in complex large-scale problems such as stochastic groundwater quality models. The current project will re-formulate optimal design theory within a new information-theoretic perspective. Instead of traditionally and tediously searching through all possible measurement locations to find the most informative ones, the direction of analysis will be reverted to directly identify the most informative ones in a single step. This will dramatically reduce the computational load, allowing to apply optimal design for larger, more complex and hence more realistic problems. At the same time, this avoids simplifications or linearizations that compromise the information content of data sets in the analysis. Instead of giving in to computational restrictions, the new method will allow tackling current, goal-oriented and application- driven research tasks. At first developed and applied within the groundwater perspective, the new method will then be exported as a valuable tool for many scientific disciplines that face similar uncertainties in heterogeneous or complex dynamic systems.