An ensemble quadratic echo state network for non-linear spatio-temporal forecasting

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by non-linear time dynamics that include interactions across multiple scales of spatial and temporal variability. The datasets associated with many of these processes are increasing in size because of 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. Traditionally, 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 network machine learning approach can be used to generate long-lead forecasts of non-linear spatio-temporal processes, with reasonable uncertainty quantification, and at a fraction of the computational expense of a traditional parametric non-linear spatio-temporal models. Copyright (c) 2017 John Wiley & Sons, Ltd.