## 1 Introduction  
Forest ecosystems play a critical role in sequestering atmospheric carbon dioxide [1; 2]. The magnitude of carbon sequestration in different forest stands at various timescales ranging from hour to inter-annual is seriously influenced by global environmental change, such as climate, land use, CO\({}_{2}\) enrichment, nitrogen deposition and biotic invasions. In addition, the substantial impacts of climate extreme events (e.g., droughs, precipitation, wind storms, heat waves, frosts and fires) on the terrestrial carbon cycle have been revealed by a few recent studies [3, 4]. These effects may alter the growth patterns of pine species and biodiversity as well as the structure and functioning of forest ecosystems [5, 6], which will lead to a major impediment in our understanding of the underlying mechanisms causing the ongoing seasonal variation in carbon fluxes, mainly including gross primary production (GPP), ecosystem respiration (\(R\)) and net ecosystem exchange (NEE). Therefore, quantification of the carbon exchanges between the forest ecosystems and the atmosphere is challenging for current modeling techniques, due to the complex interactions and feedbacks involved in biological, physical and chemical processes across various spatial and temporal scales. Mechanism-based land surface models have been extensively used for estimating the terrestrial carbon fluxes from site to regional scales. However, the modeling ability of land surface models is limited because of lacking the flexibility and robustness to capture the nonlinear characteristics. Moreover, to a large extent, the fixed parameters within the models pose a challenge for the interpolation and extrapolation of the well-established models, maybe owing to the inherent variability of model parameters at various temporal and spatial scales. Therefore, considering the constantly varying statistical features in natural ecosystems, mechanism-free models were strongly recommended by [PERSON] [7] and [PERSON] et al. [8], as a useful paradigm to handle the nonlinear interactions of non-equilibrium dynamical and complex ecological systems. Inspired by this as well as the recent availability of a great deal of data obtained by the eddy covariance (EC) technique from three different flux towers, we here used the mechanism-free machine learning techniques to simulate and predict the carbon fluxes of terrestrial forest ecosystems. Over the past two decades, machine learning techniques have been growingly utilized to deal with the different issues involved in carbon flux estimates [9, 10, 11, 12, 13], such as filling the missing data of carbon fluxes and climatic driving factors based on the flux tower measurements [14, 15], reducing the predictive errors of carbon fluxes from the land surface models [16, 17] and upscaling the carbon fluxes of terrestrial ecosystems from site to regional scale on the basis of multi-source remote sensing data [18, 19]. In particular, several lines of evidence have demonstrated that machine learning techniques, mainly including two traditional artificial neural network (ANN) and support vector machine (SVM) methods, have sufficiently strong ability to elucidate the nonlinear relationship between ecosystem-based carbon fluxes and environment variables based on EC measurements [13, 20]. For example, [PERSON] and [PERSON] [21] utilized the ANN approach to estimate the carbon flux in three different ecosystems (grassland, cropland and forest) using the air temperature, soil temperature and several energy fluxes as input data and found that ANN could be successfully applied in simulating the ecosystem-based carbon fluxes. [PERSON] et al. [22] used the ANN method to map different carbon and water fluxes in three Douglas-fir Stands in the Pacific Northwest based on long-term measurements and found that the use of ANN could be effective to determine the responses of three different carbon fluxes (GPP, \(R\) and NEE), evapotranspiration and water use efficiency to nitrogen fertilization.