A combined model of shoot phosphorus uptake based on sparse data and active learning algorithm

The soil ecosystem has been severely damaged because of the increasingly severe environmental problems caused by excessive application of phosphorus (P) fertilizer, which seriously hinders soil fertility restoration and sustainable farmland development. Shoot P uptake (SPU) is an important parameter for monitoring crop growth and health and for improving field nutrition management and fertilization strategies. Achieving on-site measurement of large-scale data is difficult, and effective nondestructive prediction methods are lacking. Improving spatiotemporal SPU estimation at the regional scale still poses challenges. In this study, we proposed a combination prediction model based on some representative samples. Furthermore, using the experimental area of Henan Province, as an example, we explored the potential of the hyperspectral prediction of maize SPU at the canopy scale. The combination model comprises predicted P uptake by maize leaves, stems, and grains. Results show that (1) the prediction accuracy of the combined prediction model has been greatly improved compared with simple empirical prediction models, with accuracy test results of <i>R</i> ² = 0.87, root mean square error = 2.39 kg/ha, and relative percentage difference = 2.71. (2) In performance tests with different sample sizes, two-dimensional correlation spectroscopy i.e., first-order differentially enhanced two-dimensional correlation spectroscopy (1Der-2DCOS) and two-trace 2DCOS of enhanced filling and milk stages (filling-milk-2T2DCOS)) can effectively and robustly extract spectral trait relationships, with good robustness, and can achieve efficient prediction based on small samples. (3) The hybrid model constrained by the Newton-Raphson-based optimizer's active learning method can effectively filter localized simulation data and achieve localization of simulation data in different regions when solving practical problems, improving the hybrid model's prediction accuracy. The practice has shown that with a small number of representative samples, this method can fully utilize remote sensing technology to predict SPU, providing an evaluation tool for the sustainable use of agricultural P. Therefore, this method has good application prospects and is expected to become an important means of monitoring global soil P surplus, promoting sustainable agricultural development.