AutoQS v1: automatic parametrization of QuickSampling based on training images analysis

Abstract

Multiple-point geostatistics are widely used to simulate complex spatial structures based on a training image. The practical applicability of these methods relies on the possibility of finding optimal training images and parametrization of the simulation algorithms. While methods for automatically selecting training images are available, parametrization can be cumbersome. Here, we propose to find an optimal set of parameters using only the training image as input. The difference between this and previous work that used parametrization optimization is that it does not require the definition of an objective function. Our approach is based on the analysis of the errors that occur when filling artificially constructed patterns that have been borrowed from the training image. Its main advantage is to eliminate the risk of overfitting an objective function, which may result in variance underestimation or in verbatim copy of the training image. Since it is not based on optimization, our approach finds a set of acceptable parameters in a predictable manner by using the knowledge and understanding of how the simulation algorithms work. The technique is explored in the context of the recently developed QuickSampling algorithm, but it can be easily adapted to other pixel-based multiple-point statistics algorithms using pattern matching, such as direct sampling or single normal equation simulation (SNESIM).