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Deep echo state networks with uncertainty quantification for spatio‐temporal forecasting

计算机科学 不确定度量化 贝叶斯概率 回声状态网络 高斯过程 非线性系统 集合预报 数据同化 人工智能 数据挖掘 高斯分布 人工神经网络 机器学习 循环神经网络 量子力学 物理 气象学
作者
Patrick L. McDermott,Christopher K. Wikle
出处
期刊:Environmetrics [Wiley]
卷期号:30 (3) 被引量:56
标识
DOI:10.1002/env.2553
摘要

Abstract Long‐lead forecasting for spatio‐temporal systems can entail complex nonlinear dynamics that are difficult to specify 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 reservoir computing to efficiently compute recurrent neural network forecasts. Moreover, multilevel (deep) hierarchical 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 those we often find in spatio‐temporal environmental data). Here, we introduce a deep ensemble ESN (D‐EESN) model. Despite the incorporation of a deep structure, the presented model is computationally efficient. We present two versions of this model for spatio‐temporal processes that 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. Across both applications, the proposed methodology improves upon existing methods in terms of both forecast accuracy and quantifying uncertainty.
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