Modeling nonstationary spatial processes with normalizing flows

• URL: http://arxiv.org/abs/2509.12884v1
• Date: Tue, 16 Sep 2025 09:37:18 GMT
• Title: Modeling nonstationary spatial processes with normalizing flows
• Authors: Pratik Nag, Andrew Zammit-Mangion, Ying Sun,
• Abstract summary: We introduce a novel approach to modeling nonstationary, anisotropic spatial processes using neural autoregressive flows (NAFs)<n>Through simulation studies we demonstrate that a NAF-based model has greater representational capacity than other commonly used spatial process models.<n>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.
• Score: 4.5379917333739055
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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