Modeling nonstationary spatial processes with normalizing flows

2025-09-16

AI Summary

Modeling high-dimensional nonstationary spatial processes faces challenges in designing spatial warping functions, and existing methods are largely restricted to two dimensions. Method: This paper proposes an invertible spatial deformation framework based on Neural Autoregressive Flows (NAF). It employs invertible neural networks to construct explicit, parametric spatial warping mappings over high-dimensional domains, and integrates probability density transformation theory to jointly characterize nonstationarity and anisotropy within the warped space. Contribution/Results: Unlike conventional approaches, the framework lifts dimensional constraints, enabling flexible modeling of spatial processes in arbitrary dimensions. Evaluations on synthetic data and real-world 3D Argo float observations demonstrate substantial improvements in predictive accuracy and generalization performance, confirming its strong representational capacity and adaptability to complex spatial structures.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Nonstationary spatial processes can often be represented as stationary processes on a warped spatial domain. Selecting an appropriate spatial warping function for a given application is often difficult and, as a result of this, warping methods have largely been limited to two-dimensional spatial domains. In this paper, we introduce a novel approach to modeling nonstationary, anisotropic spatial processes using neural autoregressive flows (NAFs), a class of invertible mappings capable of generating complex, high-dimensional warpings. Through simulation studies we demonstrate that a NAF-based model has greater representational capacity than other commonly used spatial process models. We apply our proposed modeling framework to a subset of the 3D Argo Floats dataset, highlighting the utility of our framework in real-world applications.

Problem

• Modeling nonstationary spatial processes with neural networks
• Overcoming limitations in spatial warping function selection
• Extending warping methods beyond two-dimensional spatial domains

Innovation

• Neural autoregressive flows for spatial warping
• Invertible mappings for high-dimensional domains
• Modeling nonstationary anisotropic spatial processes