## 1 Introduction  
The carbon sequestration of terrestrial ecosystems, which have provided a net carbon sink for about 30% of CO\({}_{2}\) emitted by human activities, plays a significant role in mitigating climate warming caused by rising global average temperature [1]. Since the majority of estimated carbon sequestration occurs in forests, forests are considered to be the main non-coenic force slowing the rate of CO\({}_{2}\) accumulation; thus, accurately estimating forest GPPhas been a research hotspot of carbon cycle for decades [2; 3]. During the past two decades, gross carbon sequestration by global forests were about 15.6 \(\pm\) 49 Gt CO\({}_{2}\) equivalent per year [4]. It is hard to achieve the climate change mitigation goal without the contribution from forests in atmospheric greenhouse gas (GHG) removal. The models for estimating terrestrial gross primary production (GPP) developed in past decades include process-based methods and empirical methods [5; 6; 7; 8; 9; 10]. Process-based models such as Biome-BGC require meteorological, eco-physiological, and soil input data because these algorithms involve physical and biological processes which control the exchanges of mass and energy, which makes it hard to drive these process models at large scales given data availability [11]. Empirical methods could reach higher accuracy with limited input data but are limited by the number and representativeness of training examples with no rigorous foundation of ecological theory, while suffering from poor generalizability [7]. The LUE model is a kind of process model which has relatively few parameters, enables easy data acquisition, and has low computational requirements and is thus commonly used to simulate GPP and seasonal variations at global or regional scales [8; 12; 13; 14; 15; 16; 17; 18]. LUE is defined as the efficiency of the vegetation photosynthesis system to use absorbed solar energy to assimilate CO\({}_{2}\). In this type of model, GPP is treated as a dependent variable of the APAR (Absorbed Photosynthetically Active Radiation) and the efficiency of carbon uptake [6; 9]. LUE models can be written as:  
\[GPP=\varepsilon_{g}\times APAR \tag{1}\]  
\[APAR=fPAR\times PAR \tag{2}\]  
where \(fPAR\) is the fraction of incident \(PAR\) (Photosynthetically Active Radiation, MJm\({}^{-2}\)) absorbed by the vegetation canopy at daily or monthly scales. \(fPAR\) could be calculated by linear regression of remote sensing indices. The actual light use efficiency \(\varepsilon_{g}\) is down-regulated from its theoretical maximum LUE \(\varepsilon_{0}\) (gCm\({}^{-2}\)day\({}^{-1}\)M]\({}^{-1}\)) by environmental conditions including water and temperature stress. It can be calculated as:  
\[\varepsilon_{g}=\varepsilon_{0}\times f(T,W,\dots\dots) \tag{3}\]  
where \(f(T,W,\dots\dots)\) is a scalar in the range (from zero to one) that describes the reduction in theoretical LUE for the reason of environmental conditions. The key point lies in how to define the environmental stress functions and integrate them to compute GPP, which is also the difference between different LUE models. Representative LUE models such as EC-LUE (Eddy Covariance-Light Use Efficiency) [19], GLO-PEM (GLObal Production Efficiency Model) [12], and VPM (Vegetation Photosynthesis Model) [20] differ in the structure of the regulation function, Equation (3). For example, VPM and GLO-PEM use the multiplicative method to integrate water and temperature stress, while EC-LUE takes only the most serious stress factor according to [PERSON]'s law. As a practical technology in scientific research and commercial use, machine learning has experienced rapid development in the past twenty years [21], and a series of machine learning methods has been developed and applied in many fields such as natural language processing, medical diagnosis, computer vision, remote sensing, and other interdisciplinary fields [22; 23; 24; 25].