  We present a method of constructing low-dimensional nonlinear models
describing the main dynamical features of a discrete 2D cellular fault zone,
with many degrees of freedom, embedded in a 3D elastic solid. A given fault
system is characterized by a set of parameters that describe the dynamics,
rheology, property disorder, and fault geometry. Depending on the location in
the system parameter space we show that the coarse dynamics of the fault can be
confined to an attractor whose dimension is significantly smaller than the
space in which the dynamics takes place. Our strategy of system reduction is to
search for a few coherent structures that dominate the dynamics and to capture
the interaction between these coherent structures. The identification of the
basic interacting structures is obtained by applying the Proper Orthogonal
Decomposition (POD) to the surface deformations fields that accompany
strike-slip faulting accumulated over equal time intervals. We use a
feed-forward artificial neural network (ANN) architecture for the
identification of the system dynamics projected onto the subspace (model space)
spanned by the most energetic coherent structures. The ANN is trained using a
standard back-propagation algorithm to predict (map) the values of the observed
model state at a future time given the observed model state at the present
time. This ANN provides an approximate, large scale, dynamical model for the
fault.
