Deep Echo State Networks with Uncertainty Quantification for Spatio-Temporal Forecasting

TL;DR

This paper introduces a deep ensemble echo state network (D-EESN) for spatio-temporal forecasting that provides both predictions and uncertainty quantification, applicable to complex environmental data.

Contribution

It develops a novel deep ensemble ESN model with two uncertainty quantification frameworks, enhancing forecasting of high-dimensional nonlinear spatio-temporal processes.

Findings

Successfully applied to simulated non-Gaussian multiscale Lorenz-96 data

Demonstrated effectiveness in long-lead U.S. soil moisture forecasting

Provides both forecasts and uncertainty measures

Abstract

Long-lead forecasting for spatio-temporal systems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often highly parameterized and thus, challenging to implement from a computational perspective. One potential parsimonious solution to this problem is a method from the dynamical systems and engineering literature referred to as an echo state network (ESN). ESN models use so-called {\it reservoir computing} to efficiently compute recurrent neural network (RNN) forecasts. Moreover, so-called "deep" models have recently been shown to be successful at predicting high-dimensional complex nonlinear processes, particularly those with multiple spatial and temporal scales of variability (such as we often find in spatio-temporal environmental data). Here we introduce a deep ensemble ESN (D-EESN) model. We present two versions of this model for spatio-temporal processes that both produce forecasts and associated measures of uncertainty. The first approach utilizes a bootstrap ensemble framework and the second is developed within a hierarchical Bayesian framework (BD-EESN). This more general hierarchical Bayesian framework naturally accommodates non-Gaussian data types and multiple levels of uncertainties. The methodology is first applied to a data set simulated from a novel non-Gaussian multiscale Lorenz-96 dynamical system simulation model and then to a long-lead United States (U.S.) soil moisture forecasting application.