MPS-APO: a rapid and automatic parameter optimizer for multiple-point geostatistics

Abstract

Multiple-point statistics (MPS) have been widely used in Earth and environmental sciences because of their ability to generate realistic stochastic realizations of complex natural processes. The spatial patterns and statistical information required for MPS modeling are represented by a training image. However, each MPS algorithm has a specific set of parameters that have a direct impact on the quality of pattern reproduction and should be chosen prior to the modeling. While there are some general guidelines for some MPS algorithms, a general parameter interference methodology is currently lacking. To date, the common practice for finding optimal parameters is to carry out a sensitivity analysis, which can be cumbersome especially in complex applications. In this study, we propose the MPS Automatic Parameter Optimizer (MPS-APO), a generic method based on stochastic optimization to rapidly approximate optimal parameters for any MPS method and different types of settings. The MPS-APO formulates an objective function that quantifies spatial pattern reproduction for each set of parameters. The Simultaneous Perturbation Stochastic Approximation (SPSA) optimization method is used because of its computational efficiency, and also its ability to cope with the stochastic nature of the objective function. The optimization proceeds in two steps. The first step aims to optimize the parameters for the best quality regardless of computational cost. When no more improvement can be achieved, the second step minimizes the CPU cost without degrading the spatial structures reproduction attained in the first step. In this study, MPS-APO is performed on different pixel-based and patch-based MPS methods: SNESIM, FILTERSIM, Direct Sampling and Image Quilting. Test cases show that MPS-APO is a useful heuristic to automatically approximate optimal parameters for good patterns reproduction with minimal computational cost. Therefore, it can help non-expert users and increase the usability of MPS methods for practical applications.