Non-Linear Model-Based Sequential Decision-Making in Agriculture
Authors: Sakshi Arya, Wentao Lin
Organizations: Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA · CTrees, Pasadena, CA 91105, USA
Abstract
Agricultural decision-making faces a dual challenge: sustaining high yields to meet global food security needs while reducing the environmental impacts of input use, including fertilizer losses and other agrochemical applications such as herbicides, insecticides, and fungicides. Nitrogen inputs are central to this tension. They are indispensable for crop growth yet major drivers of greenhouse gas emissions, nutrient runoff, and escalating production costs. Addressing these intertwined pressures requires adaptive decision-support tools that are statistically principled, economically sustainable and interpretable for practitioners. We develop nonlinear model-based bandit algorithms as a framework for adaptive fertilizer management under uncertainty. Building on classical mechanistic yield-response models, our approach links algorithmic exploration-exploitation strategies directly to interpretable biological processes such as maximum yield and nutrient efficiency. This grounding makes recommendations transparent for practitioners while supporting cost-effective and sustainable input use. Methodologically, we establish regret and sample complexity results for the well-specified nonlinear case, examine robustness under misspecification, and evaluate the proposed methods through profit-oriented simulations and an offline replay case study on publicly available multi-site corn nitrogen field trials from the U.S. Midwest. The results show that incorporating biologically meaningful mechanistic structure enables faster learning and higher profit as evidence accumulates, with flexible nonparametric baselines providing a competitive alternative in pooled and heterogeneous settings. Our findings illustrate how interpretable, uncertainty-aware sequential decision rules can support economically sustainable fertilizer recommendations and contribute to more efficient agricultural input use.
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.
To understand complex system dynamics in dairy farming, it is essential to use modeling tools that capture farm heterogeneity, social interactions, and cumulative environmental impacts. This study proposes an agent-based modeling (ABM) framework to simulate nitrogen management and the adoption of low-emission fertilizer across 295 Irish dairy farms over a 15-year period. Using empirical data, the model represents farm communication through a social network, capturing peer influence and discussion group dynamics, where adoption probabilities are driven by social contagion, farm-scale characteristics, and policy interventions such as subsidies and carbon taxes. The framework estimates sectoral greenhouse gas emissions, cumulative abatement, and private-social cost trade-offs, using Monte Carlo simulation and sensitivity analysis to quantify uncertainty. The model shows strong agreement with observed adoption trajectories (R2=0.979, RMSE = 0.0274) and is validated against empirical data using a Kolmogorov-Smirnov test (D = 0.2407, p < 0.001), indicating its ability to reproduce structural patterns in adoption behavior. Adoption dynamics are further characterized using a logistic diffusion model consistent with Rogers' innovation diffusion theory, capturing progression from early adoption to a saturation level of approximately 91%. By framing decarbonization as a socio-technical diffusion process rather than a purely economic optimization problem, this study provides an in silico policy laboratory for evaluating the robustness and diffusion speed of climate mitigation strategies prior to implementation.
Surya Jayakumar, Kieran Sullivan, John McLaughlin +2