Agriculture-informed Neural Networks for Predicting Nitrous Oxide Emissions

Agriculture and Agri-Food Canada, in its unwavering commitment to sustainable agriculture, has launched a program to reduce nitrous oxide (N 2 O) emissions from fertilizer utilization in farming practices. This initiative is a response to the pressing environmental and climate challenges we face. To achieve our goal, we must delve into the mechanism of N 2 O emission by measuring and predicting the flux of N 2 O. This study proposes a novel architecture for neural network models, namely the agriculture-informed neural network (AINN) model, consisting of recurrent neural networks and a process-based ecosystem model, the Dynamic Land Ecosystem Model (DLEM), to predict N 2 O emissions from farming. During the 2021 and 2022 growing seasons, field data on the flux of N 2 O, soil temperature, and soil moisture were collected. However, the amount of nitrate in the soil was missing since collecting accurate data on nitrate quantities from the soil was challenging. Therefore, assumptions about the nitrate quantity in the soil were made when training and testing AINN with the data collected from the 2021 and 2022 growing seasons. In 2024, from January to April, an indoor experiment under controlled conditions was successfully executed to collect data on nitrate quantity in the soil. This experiment demonstrated that nitrate quantity is an essential factor for predicting the emission of N 2 O. To demonstrate the versatility of the AINN across various neural networks, we conduct a comprehensive comparison with four state-of-the-art models: multilayer perceptron, convolutional neural network, long short-term memory, and Transformer. Our experiment and simulation results unequivocally demonstrate that the performance of AINN is superior to single neural network models. The DLEM component of the AINN acts as a regularizer, facilitating the training process of the AINN. This mathematical formulation transforms the problem of N 2 O emission into a constrained optimization issue, minimizing the explicit objective function and satisfying the constraints of the parameters fed into the DLEM in the AINN. The empirical results show that by incorporating information from the agricultural field, the AINN significantly reduces the generalization error compared to the corresponding neural network, underscoring its potential to revolutionize the field of neural network modeling.