Parallel Multiple-Point Statistics Algorithm Based on List and Tree Structures

Abstract

Multiple-point statistics are widely used for the simulation of categorical variables because the method allows for integrating a conceptual model via a training image and then simulating complex heterogeneous fields. The multiple-point statistics inferred from the training image can be stored in several ways. The tree structure used in classical implementations has the advantage of being efficient in terms of CPU time, but is very RAM demanding and then implies limitations on the size of the template, which serves to make a proper reproduction of complex structures difficult. Another technique consists in storing the multiple-point statistics in lists. This alternative requires much less memory and allows for a straightforward parallel algorithm. Nevertheless, the list structure does not benefit from the shortcuts given by the branches of the tree for retrieving the multiple-point statistics. Hence, a serial algorithm based on list structure is generally slower than a tree-based algorithm. In this paper, a new approach using both list and tree structures is proposed. The idea is to index the lists by trees of reduced size: the leaves of the tree correspond to distinct sublists that constitute a partition of the entire list. The size of the indexing tree can be controlled, and then the resulting algorithm keeps memory requirements low while efficiency in terms of CPU time is significantly improved. Moreover, this new method benefits from the parallelization of the list approach.

HYPPS: A hybrid geostatistical modeling algorithm for subsurface modeling

“…Even though the SNESIM algorithm benefits from search tree, it is still computationally inefficient for the real multimillion cells applications . Several other methods were later proposed to improve the efficiency and quality of the SNESIM algorithm [Straubhaar et al, 2013;Cordua et al, 2015].…”

Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research

“…These acceleration methods can be combined, bringing drastic improvement in simulation times, with synthesis speeds of up to 15.5 million pixels per second (Han et al, 2008). In contrast, recent multiple-point algorithms report computation times orders of magnitude slower, with commercial implementations reporting about 5000 nodes per second (Straubhaar et al, 2013;Zhang et al, 2012).…”

Simulation of braided river elevation model time series with multiple-point statistics

“…F can be dealt with in two ways. The first efficient MPS approaches -implemented for instance by Strebelle (2002) in SNESIM or by Straubhaar et al (2011Straubhaar et al ( , 2013 in IMPALA -rely on computing an histogram of the patterns present in the TI and compatible with the local data event d.Theseap-proaches are limited to categorical variables and with fixed search neighborhood templates. The use of successive multigrid simulation allows us, in that case, to capture and reproduce the structures from the TI at different scales while using small search templates,but may create some artifacts.…”