deepspat: An R package for modeling nonstationary spatial and spatio-temporal Gaussian and extremes data through deep deformations

2025-12-08

AI Summary

Environmental data frequently exhibit spatial and spatiotemporal nonstationarity, yet existing statistical software lacks effective tools for modeling such complexity. To address this, we introduce *deepspat*, an open-source R package that pioneers the application of deep multi-layer domain warping to nonstationary spatial modeling, enabling flexible fitting and prediction for both Gaussian and extreme-value processes. Methodologically, the framework leverages TensorFlow’s backend for gradient-based optimization, incorporates custom loss functions, and utilizes automatic differentiation for end-to-end parameter estimation. Empirical evaluation—across synthetic experiments and real-world Nepalese temperature data—demonstrates substantial improvements in model fit accuracy and spatial predictive reliability compared to conventional approaches. *deepspat* thus provides a scalable, user-friendly, and theoretically coherent deep learning–enhanced solution for environmental statistical modeling.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Nonstationarity in spatial and spatio-temporal processes is ubiquitous in environmental datasets, but is not often addressed in practice, due to a scarcity of statistical software packages that implement nonstationary models. In this article, we introduce the R software package deepspat, which allows for modeling, fitting and prediction with nonstationary spatial and spatio-temporal models applied to Gaussian and extremes data. The nonstationary models in our package are constructed using a deep multi-layered deformation of the original spatial or spatio-temporal domain, and are straightforward to implement. Model parameters are estimated using gradient-based optimization of customized loss functions with tensorflow, which implements automatic differentiation. The functionalities of the package are illustrated through simulation studies and an application to Nepal temperature data.

Problem

• Models nonstationary spatial and spatio-temporal Gaussian and extremes data
• Addresses scarcity of software for nonstationary environmental processes
• Uses deep deformations and gradient-based optimization for implementation

Innovation

• Uses deep multi-layered deformation for nonstationary modeling
• Implements gradient-based optimization with TensorFlow for estimation
• Provides R package for Gaussian and extremes data analysis