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

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.

Accurate prediction of nitrous oxide (N2O) emissions from agriculture is important for assessing environmental impacts and supporting sustainable farming. However, prediction remains difficult because N2O emissions result from complex interactions among soil properties, climate, biochemical processes, and management practices, while high-quality observations are limited. Deep learning models can capture nonlinear relationships but often lack physical interpretability and may generalize poorly across environmental conditions. We propose the Knowledge-enhanced Agriculture-informed Neural Network (KAINN), a hybrid neural-mechanistic framework that extends the Agriculture-informed Neural Network by incorporating domain knowledge about fertilizer diffusion, soil respiration, and water-filled porosity. We evaluate KAINN using CNN, LSTM, and Transformer architectures across multiple growing seasons and input-feature configurations. The results show that KAINN generally provides lower root mean square error and mean absolute error and higher R-squared values than purely data-driven models and the original AINN. Analysis of the learned interfaces also shows smoother and more physically consistent parameter trajectories with reduced uncertainty. These findings demonstrate that incorporating environmental knowledge into neural networks can improve the reliability, interpretability, and generalization of agricultural N2O-emission predictions.

Crop recommendation systems in precision agriculture have long suffered from a fundamental modality gap: visual soil characterization and chemical nutrient profiling are typically treated as independent inference problems, with fusion often reduced to late-stage feature concatenation. AgroSense2.0 addresses this limitation through three architectural advances. First, we introduce continental-scale geospatial integration via a seven-band soil raster (india\_soil\_7bands.tif) spanning India, encoding Nitrogen, pH, SOC, Clay, Sand, Silt, and Bulk Density as $32\times32$ spatial patches, a modality entirely absent from prior work. Second, we replace naive feature concatenation with a cross-modal Transformer fusion module, where tabular nutrient features attend over image representations via multi-head attention, enabling richer inter-modal dependency modeling than shallow fusion. Third, we adopt a multi-task objective jointly optimizing soil classification and crop recommendation through a shared backbone, improving generalization via complementary cross-task signal. To enhance interpretability, we apply TreeSHAP to the tabular branch, revealing crop-conditioned nutrient sensitivity: humidity and rainfall emerge as the most influential features globally, while crop-specific profiles diverge meaningfully rainfall dominates rice, nitrogen and potassium dominate maize, and humidity and nitrogen dominate coffee. These explanations provide transparency into model decisions and surface both agronomically consistent patterns and dataset-specific divergences worth further study. Together, these contributions establish AgroSense2.0 as a more principled, interpretable, and geospatially grounded framework for precision agriculture.