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LatticeVision: image to image networks for modeling non-stationary spatial data

Sikorski, Antony
; 
Ivanitskiy, Michael
; 
Lenssen, Nathan
; 
Nychka, Douglas
; 
McKenzie, Daniel
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2026-04
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2026 Graduate Research And Discovery Symposium (GRADS) posters and presentations
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Sikorski_Antony_GRADS2026.pdf
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https://hdl.handle.net/11124/182015
 https://doi.org/10.25676/11124/182015
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Abstract
In many applications, we wish to fit a parametric statistical model to a small ensemble of spatially distributed random variables ('fields'). However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.
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