Physically motivated scale interaction parameterization in reduced rank quadratic nonlinear dynamic spatio‐temporal models

2017

Stat

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. Nonlinear 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 (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.

Section: Application: Long‐lead Forecasting Of Pacific Sea Surface Tementioning

confidence: 58%

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

McDermott

2017

Stat

“…The first 10 EOFs, which account for over 80% of the variability in the data, are retained for both the input and response. This same number of EOFs has been used in multiple previous SST studies, i.e., [ 4 , 63 ]. Note, the first two EOFs account for almost

of the variation in the data.…”

Section: Applicationsmentioning

confidence: 99%

Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

McDermott

2019

Entropy

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data.The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications

“…This is particularly the case in nonlinear models (e.g., there are

O ((), n_{α}^{3})

parameters to estimate in a GQN model). Again, one can make use of mechanistically‐motivated models and scientific knowledge to parameterize the dynamical evolution . Various model selection approaches can also be used to reduce the parameter space, such as stochastic search variable selection in the low‐rank GQN context …”

Section: Dynamic Spatio‐temporal Modelsmentioning

confidence: 99%

“…Again, one can make use of mechanistically-motivated models and scientific knowledge to parameterize the dynamical evolution. 20 Various model selection approaches can also be used to reduce the parameter space, such as stochastic search variable selection in the low-rank GQN context. 21 Finally, note that for extremely complicated processes for which large deterministic simulation models are available, it may be easier to incorporate the associated mechanistic information by building emulators (i.e., surrogate models) for the deterministic computer output and using those to inform the DSTM of interest (typically through a prior distribution in a hierarchical setting as described below).…”

Section: Parameter Reductionmentioning

confidence: 99%

Modern perspectives on statistics for spatio‐temporal data

WIREs Computational Stats

2014

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially explicit processes that evolve over time. Although descriptive models that approach this problem from the second-order (covariance) perspective are important, many real-world processes are dynamic, and it can be more efficient in such cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The challenge with the specification of such dynamical models has been related to the curse of dimensionality and the specification of realistic dependence structures. Even in fairly simple linear/Gaussian settings, spatio-temporal statistical models are often over parameterized. This problem is compounded when the spatio-temporal dynamical processes are nonlinear or multivariate. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters and science-based parameterizations. Such models are best considered from a Bayesian perspective, with associated computational challenges. Spatio-temporal statistics remains an active and vibrant area of research.