A physically informed multi-scale deep neural network for estimating foliar nitrogen concentration in vegetation

This study introduces a Physically Informed Deep Neural Network (PINN) that leverages spectral data and Radiative Transfer Model insights to improve nitrogen concentration estimation in vegetation, addressing the complexities of physical processes. Utilizing a comprehensive spectroscopy dataset from various species across dry/ground (n = 2010), leaf (n = 1512), and canopy (n = 6007) scales, the study identifies 13 spectral bands key for chlorophyll and protein quantification. Key bands at 2276 nm, 755 nm, 1526 nm, 2243 nm, and 734 nm emerged vital for accurate N% prediction. The PINN outperforms partial least squares regression and standard deep neural networks, achieving an R 2 of 0.71 and an RMSE of 0.42 (%N) on an independent validation set. Results indicate dry/ground data performed best (R 2 = 0.9, RMSE = 0.24 %N), with leaf and canopy data showing lower efficacy (R 2 = 0.67, RMSE = 0.45 %N; R 2 = 0.65, RMSE = 0.46 %N, respectively). This multi-scale approach provides insights into spectral and N% relationships, enabling precise estimation across vegetation types and facilitating the development of transferable models. The PINN offers a new avenue for analyzing remote sensing data, demonstrating the significant potential for accurate, scale-spanning N% estimation in vegetation. Further enriching our analysis, the inclusion of seasonal data significantly enhanced our model's performance in field spectroscopy, with notable improvements observed across summer, spring, autumn, and winter. This adjustment underlines the model's increased accuracy and predictive capability at the field spectroscopy scale, emphasizing the vital role of integrating environmental factors, including climatic and physiological aspects, in future research.