Unsupervised Statistical Learning with Integrated Pattern-Based Geostatistical Simulation

Abstract

Abstract This study presents a new geostatistics modeling methodology for the purpose of achieving the following three objectives. (1) Connecting geostatistics and machine learning methodologies, (2) Using non-linear topological mapping to reduce the original high dimensional data space to low dimensional subspace, as well as clustering for identifying and extracting meaningful patterns for both visualization and efficiency purposes, and (3) Using unsupervised learning algorithms to bypass potential problems encountered while using supervised learning algorithms. Past observations have indicated that due to lack of labeled input data, artificial neural network (ANN) architecture, based on feedforward and backpropagation supervised learning, is difficult to apply. To eliminate this difficulty and accomplish the 3 aforementioned objectives we introduce in this paper TopoSim, a neural topology-preserving based geostatistical simulation algorithm, which integrates (1) Self-Organizing Map (SOM) and its updated version, Growing Self-Organizing Map (GSOM), and (2) ANN with an unsupervised competitive learning structure. The proposed simulation integrates in a single step dimensionality reduction and extraction of input data structure pattern. Connectivity between geostatistical simulation problems and machine learning tasks are explained and constructed for the first time. We perform TopoSim unconditioned geostatistical realizations, which show improvements in continuity and pattern reproduction when compared with previously developed single normal equation simulation (SNESIM) algorithms. We conclude that the geostatistical simulation task is essentially a machine learning problem, i.e., getting the model to learn from available data and subsequently using the model for prediction purposes.