Title: An Ensemble Quadratic Echo State Network for Nonlinear Spatio-Temporal Forecasting,
Abstract: Spatio-temporal data and processes are prevalent across a wide variety of
scientific disciplines. These processes are often characterized by nonlinear
time dynamics that include interactions across multiple scales of spatial and
temporal variability. The data sets associated with many of these processes are
increasing in size due to advances in automated data measurement, management,
and numerical simulator output. Non- linear spatio-temporal models have only
recently seen interest in statistics, but there are many classes of such models
in the engineering and geophysical sciences. Tradi- tionally, these models are
more heuristic than those that have been presented in the statistics
literature, but are often intuitive and quite efficient computationally. We
show here that with fairly simple, but important, enhancements, the echo state
net- work (ESN) machine learning approach can be used to generate long-lead
forecasts of nonlinear spatio-temporal processes, with reasonable uncertainty
quantification, and at only a fraction of the computational expense of a
traditional parametric nonlinear spatio-temporal models.