Strong connections between the leaf photosynthetic capacity and reflectance spectra have been reported, although their underlying mechanisms remain unclear in most cases. A range of studies have also demonstrated that leaf reflectance spectra can be used to accurately estimate leaf photosynthetic capacity in several different ways, ranging fromsimple linear regression to machine learning techniques , even though the capacity varies greatly due to multiple biotic and environmental variables . Considering some examples in detail, multiple vegetation indices, such as the normalized difference vegetation index, enhanced vegetation index, photochemical reflectance index, simple ratio, double difference, and chlorophyll index, have been used to predict photosynthetic parameters and to reveal photosynthetic productivity .

Similarly, partial least squares regressions have also been widely applied to estimate Vcmax and Jmax from leaf reflectance spectra , due to their advantages in handling the problems of both collinearity and more predictors than observations, although obvious variations in the performance of partial least squares regressions for estimating photosynthetic traits are found across different plant species and environmental conditions, or different years and growing periods . Furthermore, machine learning techniques, including the support vector machine, least absolute shrinkage and selection operator, and random forests, have also been used to estimate leaf photosynthetic capacity . Deep learning is a recent advanced data-oriented analytical approach, which can be described as a model that represents nonlinear processing composed of a multilayer artificial neural network, and it employs multiple neurons. Examples include the deep neural network, convolutional neural network , recurrent neural network , etc. . Previous studies have reported that deep learning can be used to process large-scale and multi-feature data by using a hierarchical learning capacity to characterize input and target data, which usually leads to better performance and generalization ability.

Accordingly, the deep learning model has a powerful ability to capture highly abstracted features with deeper layers and could be used to mine effective information better and to estimate the target parameters accurately.A deep learning model will thus consider the relationships between each spectrum and the plant characteristics more comprehensively and could provide an accurate estimation of plant properties from leaf spectra. To date, deep learning has been widely employed for big data analysis with remote sensing , and has also been applied to speech recognition and object detection , surface parameters , yield prediction , stress and disease detection , and other fields using different types of deep neural network architectures. However, the approach has not yet been thoroughly explored in terms of photosynthetic capacity estimation. To the best of our knowledge, only Fu et al. reported the potential of an artificial neural network regression in estimating photosynthetic capacities in tobacco genotypes. Thus, it is necessary to explore the potential of powerful deep learning techniques to estimate photosynthetic capacity. Unfortunately, deep learning models with complex multi-layer structures have a fundamental limitation for practical applications due to the need for a large training dataset and the connections among the input, hidden, and output layers, which lead to uncertainties and fluctuations in predictions, particularly for limited samples.

However, increasing evidence has indicated that an ensemble of deep learning models with the application of the bootstrap sampling approach provides a potential solution to increase the robustness and accuracy and has obtained satisfactory results in the fields of species distribution and complex diseases and medicine . Including the bootstrap sampling approach in the deep learning models may thus be necessary for handling unknown complexity in a given dataset. Among current deep-learning-based techniques, deep neural network models have recently gained wide attention across various fields; for example, they have been used for the prediction of soil properties , biomass estimation , and forecasting . In general, the DNN has been proposed to overcome the shortcomings of the traditional ANN and, because it has more complexity, it can efficiently learn from training samples, with high accuracy . Although most available studies focused on the field of classification , the applications of DNN models in regression problems have increased in recent years. For example, Cai et al. obtained promising results using a DNN-based regression model to predict soil moisture from meteorological variables and initial mois-ture data. Similarly, Elbeltagi et al. used a DNN model to estimate and predict crop evapotranspiration from recorded historical and future meteorological data, with good results.