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Deep neural networks (DNNs) are the go-to model for learning functions from data, such as image classifiers or language models.

Abstract Spatial processes with nonstationary and anisotropic covariance structure are often used when modeling, analyzing, and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in “space-folding.” Here, we propose modeling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework. We conside...