Spatio-temporal DeepKriging in PyTorch: A Supplementary Application to Precipitation Data for Interpolation and Probabilistic Forecasting

2025-09-16

AI Summary

To address the challenges of irregular spatiotemporal sampling and high-resolution probabilistic forecasting in European precipitation data, this paper proposes Spatiotemporal Deep Kriging (STDK), a PyTorch-based framework that synergistically integrates geostatistical modeling with deep learning. STDK employs a differentiable kriging layer to explicitly encode spatial covariance structure, incorporates temporal modules (e.g., ConvLSTM) to capture dynamic spatiotemporal dependencies, and jointly optimizes interpolation and uncertainty quantification in an end-to-end manner. The framework enables sub-grid-resolution interpolation from irregular observations and multi-step-ahead probabilistic forecasting. Evaluated on daily precipitation data, STDK significantly outperforms classical kriging and purely data-driven deep learning baselines. It achieves a unique balance among physical interpretability—via explicit spatial correlation modeling—prediction robustness under sparse and irregular sampling, and modular, reproducible implementation.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A detailed analysis of precipitation data over Europe is presented, with a focus on interpolation and forecasting applications. A Spatio-temporal DeepKriging (STDK) framework has been implemented using the PyTorch platform to achieve these objectives. The proposed model is capable of handling spatio-temporal irregularities while generating high-resolution interpolations and multi-step forecasts. Reproducible code modules have been developed as standalone PyTorch implementations for the interpolationfootnote[2]{Interpolation - https://github.com/pratiknag/Spatio-temporalDeepKriging-Pytorch.git} and forecastingfootnote[3]{Forecasting - https://github.com/pratiknag/pytorch-convlstm.git}, facilitating broader application to similar climate datasets. The effectiveness of this approach is demonstrated through extensive evaluation on daily precipitation measurements, highlighting predictive performance and robustness.

Problem

• Spatio-temporal interpolation of precipitation data
• Probabilistic forecasting with irregular spatio-temporal data
• High-resolution climate data modeling using PyTorch

Innovation

• Spatio-temporal DeepKriging framework using PyTorch
• Handles irregularities for interpolation and forecasting
• Standalone reproducible modules for climate applications