## 5 Conclusions  
LUE models were commonly applied to estimate the ecosystem GPP due to their concise model structures. However, quantifying \(\text{LUE}_{\text{max}}\) and representing the responses of photosynthesis to environmental factors still exhibit large uncertainties, which lead to substantial errors in GPP simulations. In this study, we developed a hybrid GPP model based on machine learning and LUE models, called the hybrid light use efficiency model (H-LUE). This hybrid model was built by targeting LUE with the MLP algorithm and then, estimating GPP within the LUE model framework using the ML-based LUE and other required inputs (i.e., PAR and FPAR). We compared the performance of the H-LUE model against two widely used LUE models (VPM and VPRM) using observed daily GPP from 180 flux sites that cover nine different PFTs. The main conclusions are as follows:  
1. The evaluations of the three models (H-LUE, VPM, and VPRM) when estimating the LUE and GPP indicate better performance of the H-LUE model in comparison to VPM and VPRM, which emphasizes that combining the LUE model with machine learning can lead to improved performance in comparison to conventional LUE models.
2. The H-LUE model had reasonable and significantly better performance under extremely wet, dry, high-temperature, and low-temperature conditions compared to VPM and VPRM, indicating the notable advantages of the H-LUE model for global applications. Additionally, the H-LUE model can reasonably represent the responses of photosynthesis to meteorological factors.
3. VPM and VPRM overestimate the LUE when it is small and underestimate the LUE when it is large, probably because the conventional LUE models do not account for the change in photosynthetic capacity and run with a constant \(\text{LUE}_{\text{max}}\) value at all times. The H-LUE model simulates LUE using multiple input variables without using a constant \(\text{LUE}_{\text{max}}\) or only two or three environmental stresses defined by a single LUE model, effectively avoiding this issue.  
Overall, the developed H-LUE model can perform notably better than conventional LUE models. The new model provides a concise and effective approach to modeling the ecosystem GPP across multiple biomes and on a global scale, and it also serves as a reference for developing more advanced hybrid GPP models in the future.  
Conceptualization, D.K. and Y.B.; methodology, D.K. and Y.B.; software, D.K. and Y.B.; validation, D.K.; formal analysis, Y.B.; investigation, D.K. and Y.B.; resources, Y.B.; data curation, D.K. and Y.B.; writing--original draft preparation, D.K.; writing--review and editing, S.Z., D.Y., H.L., J.Z., S.Y., Y.L. and Y.B.; visualization, D.K. and Y.B.; supervision, S.Z.; project administration, Y.B.; funding acquisition, S.Z., S.Y., Y.L. and J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant Nos. 42101382, 42201407, and 32001130), the \"Taishan Scholar\" Project of Shandong Province (Grant No. TSXZ01712), and the Natural Science Foundation of Hebei Province, China (Grant No. C2021402011).  
The data used in the study can be downloaded through the corresponding link provided in Section B.1.  
The authors would like to thank the editor and all anonymous reviewers for their valuable comments and helpful suggestions.  
The authors declare no conflict of interest.