Towards Data-driven Nitrogen Estimation in Wheat Fields using Multispectral Images

Andreas Tritsarolis; Tomaž Bokan; Matej Brumen; Domen Mongus; Yannis Theodoridis

cs.CVFeb 24, 2026

Towards Data-driven Nitrogen Estimation in Wheat Fields using Multispectral Images

Authors: Andreas Tritsarolis, Tomaž Bokan, Matej Brumen, Domen Mongus, Yannis Theodoridis

Organizations: Department of Informatics, University of Piraeus, Piraeus, Greece · Innovation Technology Cluster, Murska Sobota, Slovenia · Department of Electrical Enginnering & Computer Science, University of Maribor, Maribor, Slovenia

Abstract

The modernization of agriculture has motivated the development of advanced analytics and decision-support systems to improve resource utilization and reduce environmental impacts. Targeted Spraying and Fertilization (TSF) is a critical operation that enables farmers to apply inputs more precisely, optimizing resource use and promoting environmental sustainability. However, accurate TSF is a challenging problem, due to external factors such as crop type, fertilization phase, soil conditions, and weather dynamics. In this paper, we present TerrAI, a Neural Network-based solution for TSF, which considers the spatio-temporal variability across different parcels. Our experimental study over a real-world remote sensing dataset validates the soundness of TerrAI on data-driven agricultural practices.

Figures & tables

Fig. 1: Architecture overview of the proposed TerrAI framework.

Fig. 2: Estimation of the prescription map for two randomly selected test parcels from the ITC dataset using TerrAI. Left: input soil-health tensor (one spectral image); middle and right: actual and estimated prescription maps.

Model size	#Parameters	RMSE ( $\text{kg}\cdot\text{N}\cdot\text{ha}^{-1}$ )	MAPE (%)	SMAPE (%)	RMSE ( $\text{kg}\cdot\text{N}\cdot\text{ha}^{-1}$ )	MAPE (%)	SMAPE (%)	Energy consumption per run (J)	Annual savings vs. larger variant (kWh)	CO 2 equivalent (g CO 2 e)
		Metrics / Patch			Metrics / Prescription map			Green dimension of TerrAI
small	16,773	14.54	6.12	6.33	30.60	16.42	13.60	16,619	4.60 × 10 -3	0.76
baseline	207,421	12.31	5.31	5.23	21.26	9.72	9.16	33,172	5.44 × 10 -3	0.90
large	1,063,981	12.73	5.35	5.36	22.25	10.84	9.94	52,769	—	—

TABLE I: Comparison of three different TerrAI versions with respect to model size, prediction error, and energy consumption (lower is better).

Precision Agriculture

Precision agriculture uses spatial and temporal data, sensors, AI, and robotics to tailor crop monitoring and farm inputs to local conditions.

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May 29, 2026J/K move · Enter open · S save

Learning Parametric Nitrogen Fertilizer Response Curves Using Neuro Symbolic Regression

Giorgio Morales, John Sheppard

Aston Centre for Artificial Intelligence Research and Application, Aston University, Birmingham, UK · Gianforte School of Computing, Montana State University, Bozeman, US

Precision Agriculture Symbolic Regression

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Accurately modeling crop response to Nitrogen (N) fertilization is a fundamental challenge in precision agriculture, as it impacts both economic returns and environmental sustainability. Existing approaches either rely on predefined parametric forms or opaque machine learning models, limiting their ability to interpret or discover site-specific functional relationships from data. In this work, we propose a neuro symbolic regression (SR) approach to learn parametric N-response curves without assuming a predefined functional form. Our approach integrates a transformer-based Multi-Set Symbolic Skeleton Prediction strategy, enabling the discovery of shared functional structures across multiple subdomains or management zones (MZs). By constructing diverse input subsets and enforcing consistency across them, the method recovers robust symbolic skeletons that are subsequently fitted to observed data using a genetic algorithm. This framework was first evaluated on synthetic one-dimensional problems to assess its robustness under varying levels of epistemic uncertainty. The results demonstrate the ability of the proposed SR approach to recover correct expressions even in data-scarce regimes. In this work, we present the results of applying our method to real-world winter wheat data, learning distinct parametric N-response curves for different MZs within a field. The results show that the discovered expressions not only achieve lower fitting errors than traditional models such as quadratic-plateau and exponential functions, but also capture diverse functional behaviors across spatial regions. This demonstrates the potential that neuro SR has to enable the discovery of site-specific agronomic relationships and support informed decision-making in precision agriculture.

Abstract

Precision Agriculture

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