###### Abstract
The different LUE\({}_{\text{max}}\) values between various LUE models can result in significant differences in GPP estimates [12]. Secondly, taking into account the variability and uniqueness of various ecosystems in primary production, most current LUE models rely on look-up tables to determine vegetation specific model parameters including LUE\({}_{\text{max}}\)[5]. However, this parameterization strategy needs high-quality maps of vegetation cover. There are large uncertainties in current large area vegetation cover datasets, which can propagate into regional and global GPP estimates [11]. In addition, LUE\({}_{\text{max}}\) can also vary within a single biome type [13; 14; 15] and is a primary source of the uncertainty associated with GPP estimation [14]. Moreover, the differences in the descriptions and calculations of environmental stress between different LUE models can also cause differences in GPP simulations. [PERSON] et al. [16] found that the correlations of GPP simulations among seven LUE models were lower than that of simulated potential GPP without considering any environmental stress (i.e., \(PAR\times FPAR\times LUE_{max}\)), which indicated that the difference in the environmental stresses between different LUE models was one of the major sources of uncertainty in GPP simulation. [PERSON] et al. [17] found that most of the LUE models they investigated found a strong positive correlation between the water availability and GPP estimates across large areas, different LUE models suggested that different areas exhibited this positive correlation, which indicates that different LUE models give varied GPP estimates due to varied projections of the ecosystem water balance. The problem in estimating the LUE could be addressed by incorporating machine learning (ML) approaches, such as random forests (RF) and artificial neural network (ANN), which were applied to simulate various ecosystem processes [18; 19; 20]. Machine learning is powerful for dealing with large-scale datasets with multiple variables, especially when complex relationships exist among the predictors [21; 22; 23; 24]. To decrease the uncertainties introduced by LUE\({}_{\text{max}}\) and environmental stresses in GPP simulations, we consider building a hybrid model based on ML and LUE models for GPP estimates. This hybrid model targets LUE with machine learning and then estimates the GPP within the LUE model framework with simulated LUE and other required inputs. LUE is affected by multiple environmental factors and has complex relationships with a series of variables [2; 25; 26; 27], and thus, ML could potentially be useful for characterizing the variations in LUE across a wide range of environmental gradients and ecosystem types. Compared to the existing LUE models, such a hybrid model is expected to reduce the uncertainties introduced by LUE\({}_{\text{max}}\) and environmental stresses in GPP simulations and improve GPP simulation accuracies by directly simulating LUE with ML. In fact, a number of studies applied machine learning methods to estimate purely empirical GPP models [25; 28; 29; 30]. For example, [PERSON] et al. [29] trained a support vector machine (SVM) to predict vegetation GPP using explanatory remote sensing variables, such as land surface temperature, enhanced vegetation index (EVI), land cover, and ground-measured climate variables. Based on support vector regression (SVR) and RF, [PERSON] et al. [30] first simulated a LAI time series directly using meteorological variables as inputs, and further modeled the GPP time series using modeled LAI time series and meteorological variables. However, compared to a hybrid model, purely empirical methods showed weaker adaptability to extreme environmental conditions [20].