TSCoNet: A Two-Stage Copula CNN-LSTM for Uncertainty-Aware Spatio-Temporal Forecasting

2026-07-11

AI Summary

This work addresses the challenge in multivariate spatiotemporal forecasting where existing methods often struggle to simultaneously achieve high point prediction accuracy and reliable uncertainty quantification due to strong inter-variable correlations. The authors propose a two-stage deep learning framework: first, a CNN-LSTM architecture learns a high-accuracy mean prediction; then, with the mean fixed, a Gaussian copula models the shared latent representation to estimate the covariance structure, combined with prediction interval calibration to produce well-calibrated uncertainty intervals. The approach maintains point forecast accuracy comparable to strong deterministic models while significantly improving the reliability of uncertainty estimates. Empirical validation on both non-stationary spherical field simulations and real-world monthly precipitation and temperature data from 50 cities (2000–2020) demonstrates its effectiveness.

Abstract

Reliable forecasting of several interrelated environmental variables - such as regional precipitation and temperature, or other correlated geophysical fields - across many locations calls for accurate predictions accompanied by trustworthy statements of their uncertainty. Modern deep-learning models forecast such variables accurately but usually report no uncertainty, and forcing them to output uncertainty through maximum likelihood tends to degrade their accuracy, especially when the variables are strongly correlated. Motivated by this tension, we develop TSCoNet, a two-stage convolutional-recurrent model coupled with a Gaussian copula that jointly forecasts multiple variables over space and time while quantifying predictive uncertainty. The method first learns accurate mean forecasts and then, holding the mean fixed, refines a shared representation to estimate the predictive variance, yielding calibrated prediction intervals after a standard recalibration, so that uncertainty is added without sacrificing point accuracy. We study the approach on simulated non-stationary spatial fields on the sphere and on a real dataset of monthly precipitation and temperature for fifty cities over 2000-2020. The model matches the accuracy of a strong deterministic forecaster while supplying calibrated prediction intervals that the deterministic model cannot, giving a single tool that provides both accurate point forecasts and reliable uncertainty for multivariate spatio-temporal data.

Problem

• spatio-temporal forecasting
• predictive uncertainty
• multivariate environmental variables
• calibrated prediction intervals
• correlated geophysical fields

Innovation

• Two-Stage Learning
• Gaussian Copula
• Uncertainty Quantification
• Spatio-Temporal Forecasting
• CNN-LSTM