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We present a method of constructing low-dimensional nonlinear modelsdescribing the main dynamical features of a discrete 2D cellular fault zone,with many degrees of freedom, embedded in a 3D elastic solid. A given faultsystem is characterized by a set of parameters that describe the dynamics,rheology, property disorder, and fault geometry. Depending on the location inthe system parameter space we show that the coarse dynamics of the fault can beconfined to an attractor whose dimension is significantly smaller than thespace in which the dynamics takes place. Our strategy of system reduction is tosearch for a few coherent structures that dominate the dynamics and to capturethe interaction between these coherent structures. The identification of thebasic interacting structures is obtained by applying the Proper OrthogonalDecomposition (POD) to the surface deformations fields that accompanystrike-slip faulting accumulated over equal time intervals. We use afeed-forward artificial neural network (ANN) architecture for theidentification of the system dynamics projected onto the subspace (model space)spanned by the most energetic coherent structures. The ANN is trained using astandard back-propagation algorithm to predict (map) the values of the observedmodel state at a future time given the observed model state at the presenttime. This ANN provides an approximate, large scale, dynamical model for thefault.Comment: 30 pages, 12 figure

Dynamical System Analysis and Forecasting of Deformation Produced by an Earthquake Fault