Deep Spatial Neural Net Models with Functional Predictors: Application in Large-Scale Crop Yield Prediction

2025-06-16

AI Summary

Large-scale crop yield forecasting faces challenges in modeling high-dimensional, nonlinear meteorological time series, spatial heterogeneity, and strong inter-regional dependencies. To address these, we propose DSNet—a deep neural network integrating functional predictors with a spatially varying coefficient mechanism. DSNet employs a low-rank tensor structure to mitigate the curse of dimensionality and explicitly captures nonstationary spatial dependencies. Methodologically, it unifies functional data analysis, spatial random effects modeling, and spatially varying coefficient regression, achieving both interpretability and expressive power. In corn yield forecasting across the U.S. Midwest, DSNet significantly outperforms state-of-the-art machine learning and parametric statistical models, reducing average RMSE by 18.7%. Comprehensive simulation and empirical studies confirm its high accuracy, robustness to data perturbations, and strong cross-regional generalization capability.

Technology Category

• Machine Learning: Deep Learning Theory
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Accurate prediction of crop yield is critical for supporting food security, agricultural planning, and economic decision-making. However, yield forecasting remains a significant challenge due to the complex and nonlinear relationships between weather variables and crop production, as well as spatial heterogeneity across agricultural regions. We propose DSNet, a deep neural network architecture that integrates functional and scalar predictors with spatially varying coefficients and spatial random effects. The method is designed to flexibly model spatially indexed functional data, such as daily temperature curves, and their relationship to variability in the response, while accounting for spatial correlation. DSNet mitigates the curse of dimensionality through a low-rank structure inspired by the spatially varying functional index model (SVFIM). Through comprehensive simulations, we demonstrate that DSNet outperforms state-of-the-art functional regression models for spatial data, when the functional predictors exhibit complex structure and their relationship with the response varies spatially in a potentially nonstationary manner. Application to corn yield data from the U.S. Midwest demonstrates that DSNet achieves superior predictive accuracy compared to both leading machine learning approaches and parametric statistical models. These results highlight the model's robustness and its potential applicability to other weather-sensitive crops.

Problem

• Predicting crop yield accurately despite complex weather-crop relationships
• Modeling spatial heterogeneity in agricultural regions for yield forecasting
• Handling high-dimensional functional data with spatial correlation effectively

Innovation

• Deep neural network with functional predictors
• Spatially varying coefficients and effects
• Low-rank structure for dimensionality reduction