LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data

2025-05-14

AI Summary

Maximum likelihood estimation (MLE) for nonstationary spatial fields—such as climate sensitivity fields—in few-shot settings suffers from prohibitive computational cost and poor scalability. Method: We propose an end-to-end deep regression framework for parameter estimation, treating the gridded parameters of a nonstationary spatial autoregressive (SAR) model as 2D images and directly regressing them from input field images using image-to-image (I2I) architectures (e.g., U-Net). Contribution/Results: Our approach entirely bypasses iterative MLE optimization, achieving over 100× speedup on synthetic climate field modeling while preserving physical consistency and statistical fidelity. It delivers high accuracy without sacrificing interpretability or domain alignment. This work establishes a scalable, high-fidelity paradigm for complex nonstationary spatial modeling, enabling efficient few-shot inference in geoscientific and environmental applications.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

In many scientific and industrial applications, we are given a handful of instances (a 'small ensemble') of a spatially distributed quantity (a 'field') but would like to acquire many more. For example, a large ensemble of global temperature sensitivity fields from a climate model can help farmers, insurers, and governments plan appropriately. When acquiring more data is prohibitively expensive -- as is the case with climate models -- statistical emulation offers an efficient alternative for simulating synthetic yet realistic 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.

Problem

• Estimating parameters for non-stationary spatial data efficiently
• Avoiding costly MLE for large spatial field modeling
• Using image-to-image networks for SAR model parameter estimation

Innovation

• Image-to-image networks for parameter estimation
• Modeling non-stationary spatial autoregressive data
• Efficient SAR parameter inference without MLE