Automation of Data Acquisition Strategies in Model Calibration for System Models: Sensor Placement

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Model calibration is a challenging process for large-scale system models with a non-trivial number of variables. Although domain heuristics are often called for to guide the model calibration process, in particular, the scheduling of data acquisition on model variables, there lacks a general automatic framework for this strategic task. This problem points to the well-known sensor placement problem in physical dynamic systems, and existing approaches are ready to be translated to system models in social and economic sciences. The sensor placement problem on system models addresses the following question: with the model at hand and a pre-existing data availability, what are the (next) k model variables that would bring the largest utility to model calibration, once their datasets are acquired? In this study, we first translate two established solution approaches of this optimization problem, the information entropy approach and the miss probability approach, from physical dynamic systems to social science system models. Next, based on the idea of Data Availability Partition and drawing on the insights of the two existing solutions, we propose a new objective function for this optimization problem, constructed from the individual utilities of model variables, which could be understood from the entropy perspective. The new solution could essentially be embedded in the broader theoretical framework of the evaluation of side information. On the basis of graph theory, analytical results of the optimal placement solution under the new objective function are derived for binary and multi-ary trees; for a general tree structure with n nodes, an algorithm to determine the optimal placement is devised, with complexity upper bounded by O(nlog2(n)). For arbitrary model structures, approximate solution schemes for this combinatorial problem are pinned down. Our new solution scheme is compared with the two translated approaches on a sample model structure, and results suggest the advantages of our solution. In this study, in-depth discussions on the design of data acquisition strategies for system models are carried out, which may bring important insights for system modeling practice in social and economic sciences.