Spatio-temporal DeepKriging for Interpolation and Probabilistic Forecasting

TL;DR

This paper introduces a deep neural network approach for spatio-temporal interpolation and forecasting that overcomes the limitations of traditional Gaussian process models, offering computational efficiency and probabilistic predictions for large-scale data.

Contribution

The authors propose a two-stage deep learning model using basis functions and LSTM architectures that handles non-Gaussian, nonstationary data without requiring covariance specification.

Findings

Effective imputation of missing PM2.5 data at over 200,000 locations.

Provides probabilistic forecasts with quantile-based loss.

Outperforms traditional Kriging in computational efficiency and flexibility.

Abstract

Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure. However, processes in real-world applications often exhibit non-Gaussianity and nonstationarity. Moreover, likelihood-based inference for GPs is computationally expensive and thus prohibitive for large datasets. In this paper we propose a deep neural network (DNN) based two-stage model for spatio-temporal interpolation and forecasting. Interpolation is performed in the first step, which utilizes a dependent DNN with the embedding layer constructed with spatio-temporal basis functions. For the second stage, we use Long-Short Term Memory (LSTM) and convolutional LSTM to forecast future observations at a given location. We adopt the quantile-based loss function in the DNN to provide probabilistic forecasting. Compared to Kriging, the proposed method does not require specifying covariance functions or making stationarity assumption, and is computationally efficient. Therefore, it is suitable for large-scale prediction of complex spatio-temporal processes. We apply our method to monthly $PM_{2.5}$ data at more than $200,000$ space-time locations from January 1999 to December 2022 for fast imputation of missing values and forecasts with uncertainties.