dataesr/scientific-paragraphs-categorization huggingface dataset:
2a ). However, instead of using the rate modifiers for soil temperature and moisture used in the soil carbon module, daily decomposition rates (F POC_i , g C d -1 ) of each POC pool (S POC_i , g C) are simulated to vary with water temperature based on the Arrhenius term, which is used to simulate the DOC decomposition in ORCHILEAK  (Hanson et al. , 2011; Lauerwald et al. , 2017) : F POC_i = S POC_i 1. 073 (T water -28. 0) τ poc_i , (25) where T water ( • C) is the temperature of water reservoirs and is calculated from local soil temperature using an empirical function  (Lauerwald et al. , 2017). For the POC stored in bed sediment, the temperature of the stream reservoir is used to calculate the decomposition rate. τ POC_i is the turnover time of the i (active, slow, and passive) POC pool. We assumed that the base turnover times of active (0.
Model application and evaluation In this study, ORCHIDEE-C lateral was applied over Europe and parts of the Middle East (-30 • W-70 • E, 34-75 • N), where extensive observation datasets are available to calibrate and evaluate our model (Table  1 ). The return period of daily bankfull flow (P flooding , year), which represents the average interval between two flooding events, is used in this study to produce the forcing file of S rivmax from a pre-run of ORCHILEAK. Note that P flooding is generally shorter than the return period of real flooding events, as the flooding may occur on several continuous days and all the flooding waters occurring on these continuous days are generally regarded as belonging to the same flooding event (Fig. S2  in the Supplement). To our knowledge, existing observational data on P flooding are still very limited.
Therefore, following  Schneider et al. (2011) , we also use a constant P flooding to simulate the bankfull flows from European rivers and the observed long-term  average bankfull flow rate (m 3 s -1 ) at 66 sites obtained from  Schneider et al. (2011)  to calibrate P flooding (the optimized value is 0. 1 year, Table  2 ). To our knowledge, there are still no large-scale observation data on the sediment delivery rates from land to river networks in Europe. Therefore, following  Zhang et al. (2020) , the parameters a, b, c, and d in Eqs. (  1 ) and (2) (Table  2 ) were calibrated for 57 European catchments (Fig. S3d ) against the modeled sediment delivery data obtained from the European Soil Data Centre (ESDAC,  Borrelli et al. , 2018). The sediment delivery data from the ESDAC product were derived from Wa-TEM/SEDEM model simulations using high-resolution data for topography, soil erodibility, land cover, and rainfall.
In the "spin-up" simulation, the PFT maps, atmospheric CO 2 concentrations, and meteorological data during 1901-1910 were used repeatedly as forcing data. The final simulated water discharge rates in European rivers were evaluated using observation data at 93 gauging sites (locations see Fig. S3a ) from the Global Runoff Database (GRDC, Table  1 ). The simulated bankfull flows were evaluated against observed long-term  average bankfull flows at 66 sites (Fig. S3b ) from  Schneider et al. (2011). The simulated riverine sediment discharge rate is evaluated using observation data from the European Environment Agency and existing publications (see Table  1 ) at 221 gauging sites (Fig. S3c ). The riverine total organic carbon (TOC), POC, and DOC concentrations provided by the GLObal RIver Chemistry Database (GLORICH,  Hartmann et al.
, 2019)  at 346 sites (Fig. S3d ) were used to evaluate the simulated riverine POC and DOC concentrations. Note that observations in the GLORICH database, which are measured at gauging sites with drainage area <1. 0 × 10 4 km 2 , were excluded from our model evaluation because these small catchments cannot be represented by the coarse river network scheme at 0. 5 • (ca. 55 km at the Equator). Among the retained 346 gauging sites, TOC concentrations were measured at 188 sites, and DOC was measured at 314 sites. POC was measured at only two sites (Bad Honnef with 51 measurements and Bimmen with 78 measurements) in the Rhine catchment and one site (Rheine, 36 measurements) in the Ems catchment (Fig. S3d ).
S6b ). This explains why the simulated water discharge rate at the outlet of the Danube catchment is larger than the observation at the Ceatal gauging station, Romania (identification number in the GRDC database is 6742900, Fig. S5m ), where only the main stream discharge was measured. With the calibrated return period (0. 1 year) of the daily flooding rate (see Sect. 2. 3), the simulated bankfull flow rates compare well to observations at the 66 sites for which data were available (Fig. 3b ). Overall, the simulation result explained 75 % of the inter-site variation of the observed bankfull flow rates. Relative biases of the simulated bankfull flow rates are generally lower than 30 %, although the relative bias may be larger than 100 % at some sites.
Organic carbon transport Simulation of the riverine carbon discharge rate at large spatial scale is an even bigger challenge than simulating sediment discharge, as the riverine carbon discharge is controlled by many factors, such as upland topsoil SOC concentrations, soil erosion rate, the transport and deposition rate of the clay fraction in the river channel and on the floodplain, and the decomposition of POC in transit and in aquatic sediments. As described above, the simulated water discharge rate, bankfull flow, and sediment discharge rate are overall comparable to observations (Figs. 3  and 4 ). The simulated total SOC stock in the top 0-30 cm soil layer in Europe of 107 Pg C is close to the value extracted from the HWSD database (106 Pg C) but significantly lower than the values extracted from some other databases, such as GSDE (249 Pg C), SoilGrids (202 Pg C), S2017 (148 Pg C) and landGIS (226 Pg C) (Fig.
S7a ). We noticed that the SOC stocks extracted from these observationbased soil databases show considerable difference (vary from 106 to 249 Pg C), as they have been produced using different clusters of site-level SOC measurements and different interpolation methods to produce global gridded SOC stocks from the site-level measurements  (Shangguan et al. , 2014; Hengl et al. , 2014; Sanderman et al. , 2017). Distributions of the simulated SOC stock along the latitude gradients (30-75 • N) are overall comparable to those extracted from the HWSD and S2017 databases (Fig. S7 ). But even compared to these two databases, our model still underestimated the SOC stock in southern Europe (30-41 • N). Comparison of the simulated concentrations of riverine organic carbon and the observations obtained from the GLO-RICH database  (Hartmann et al.
In Europe, the GLORICH database only provides POC concentrations measured at three gauging stations in northwestern Germany (Figs. 7, S3d ). The simulated POC concentrations and discharge rates in the Ems river at Rheine are overall comparable to the observations (Fig. 7e, f ). However, at the two gauging sites at the river Rhine, the POC con-centrations have been significantly underestimated (Fig. 7ad ). We noticed that the stream routing scheme of the Rhine catchment at 0. 5 • obtained from the forcing data STN-30p  (Vörösmarty et al. , 2000)  differs significantly from the stream routing scheme extracted based on the high-resolution (3") DEM (Fig. S6 ). Thus, besides the errors in simulated  SOC stocks, soil erosion rate, stream discharge rate, and sediment transport and deposition rate, the inaccurate stream routing scheme used in this study might also be an important reason for the underestimation of POC concentration in the Rhine river.
e. , no soil aggregates break down). The acceleration of POC decomposition rate due to the breakdown of soil aggregates can thus slightly affect the estimate of the regional landatmosphere carbon flux. Moreover, the riverine POC and DOC can be transported over a long distance and finally settle or infiltrate floodplains or river channels (especially estuarine deltas) where the local environmental conditions might be quite different from those encountered in the uplands from where these C pools originate. These changes in environmental conditions can affect the decomposition rate of the laterally redistributed organic carbon  (Abril et al. , 2002). Comparison between the simulation results from ORCHIDEE-C lateral with activated and deactivated erosion and river routing modules indicates that ignoring lateral carbon transport processes in LSMs may lead to significant biases in the simulated land carbon budget  (Figs.
, 2017) , an approach that is incompatible with large-scale simulations like those performed here. Without such calibration, the simulated geometrical properties of the river channel and runoff are prone to large uncertainties, thus rendering the simulation of sediment transport at continental or global scale using physically based algorithms a more challenging task. Given the difficulty of simulating the detailed hydraulic dynamics of streamflow at large spatial scale, we thus apply a simple approach (Eq. 8) to calculate the sediment transport capacity. Overall, we encourage future studies to produce large-scale databases on the geomorphic properties of global river channels (e. g. , river depth and width) and to develop large-scale sediment transport models capable of producing more realistic and accurate simulations of sediment deposition, re-detachment, and transport processes, as well as including the exchanges of water, sediment, and carbon between river streams and floodplains.
In addition, it is still unknown whether our model can satisfactorily simulate intermediate processes such as sediment deposition in river channels and floodplains, as well as the rate of river channel erosion. It is also unknown whether our model would perform satisfactorily in regions with very different climates than Europe such as the tropical region. Thus, in the future, an important aim will be to further calibrate our model against more detailed observation data (e. g. , sediment deposition rate in river channels and floodplains) and extend the model application to regions of contrasting climate, vegetation, and topography. Moreover, the GLORICH database  (Hartmann et al. , 2019)  only provides instantaneous observations of riverine organic carbon concentrations, and it is therefore difficult to evaluate the model's ability to reproduce temporal trends.
5 %. In regions experiencing high soil erosion or high sediment deposition rate, lateral carbon transport also changes the total SOC stock significantly, by more than 8 %. We recognize that ORCHIDEE-C lateral still has several limitations and significant uncertainties. To address those, we plan to enhance our model with additional processes, such as sediment deposition at downhill areas or the regulation of lateral transport by dams and reservoirs. We also plan to calibrate and further evaluate our model by extending the observational dataset to regions outside Europe.
INTRODUCTION In mobile robotics, state estimation is often a tedious problem [see, e. g. ,  Rohou et al. (2019) ]. Indeed, estimating especially the position and the attitude of a robot is a common task usually handled nowadays by off-the-shelf AHRS/INS [Attitude and Heading Reference System/Inertial Navigation System, such as SBG Systems (2021) and iXBlue (2021)] or autopilots [cf. Meier et al. (2011) ; Dronecode (2021); ArduPilot (2021a); Paparazzi  UAV (2021) ], but the best of them run proprietary fusion algorithms that are often not extensively described, while the cheapest of them may run simple ones from the literature. Since there are more and more internal and external sensors that could be easily available to fuse data and estimate the attitude, and whenever possible, the position, different fusion methods can be used to try to estimate the true but unknown values as closely as possible taking into account numerous of the following limitations or criteria: • Cost, dimension, weight, mutual disturbances, etc.
g. , multipaths as well as increasing the heading output rate compared with a dual GPS without IMU aid. However, it should be possible to detect easily the gyrometer saturations and to choose in that case automatically to trust more the GPS data as long as they seem to be correct (e. g. , distance between antennas still consistent with what was evaluated previously and with what was specified by the user as the initial value), as it was the case in this experiment. Figure  6  shows the results of the experiment for the Pixhawk. The fused heading and the GPS heading coincide (except the update rate of the GPS is 5 Hz, while the fused heading is determined at a frequency of 50 Hz) until the gyrometers are saturated. At this point, the fused heading seems off but converges slowly toward the GPS value, until the IMU is moved back in the same direction of the GPS, when the gyrometers detect the rotation even though the fused heading seems again to converge finally toward the GPS value.
Tracer tests are derived numerically by solving the forward problem to obtain the corresponding concentration data that feed the training. The trained networks accurately map the transmissivity fields, of which the accuracy relies on the volume and nature of the heterogeneities of training models, as well as the number of piezometers used to monitor the concentration changes. Reconstruction quality, on the other hand, is less influenced by data noise. Effective training requires a large dataset, but the time required for dataset generation is only on the order of the Gauss-Newton algorithm in a conventional inversion, while the trained network performs inference instantly.
These relationships are determined using networks consists of multiple layers in which a set of linear and nonlinear operations are performed sequentially on the neurons of these layers. This process involves the use of multidimensional coefficients, known as weights and biases, to ensure the connectivity between two successive layers  (Zhang et al. , 1998; Tahmasebi et al. , 2020; Marçais & de Dreuzy, 2017). The identification of the weights and biases is based on the optimization process, i. e. their selection is made according to their ability to connect the input data with their corresponding outputs which are considered to be known and referred to as training dataset  (Hassoun, 1995). The accuracy of the predictions provided by the learned network depends strongly on the size of this training dataset  (Zhang et al.
, 2017). However, in this paper, the network is adapted to perform a regression task to associate concentration data with hydraulic transmissivity fields. To our knowledge, this is the first time such an advanced network has been performed in a tracer test inversion problem. The first part of this paper introduces the theoretical background of the tracer test -the forward problem -used to generate the training data. The principle of inversion is then introduced, followed by a brief explanation of the proposed encoder-decoder architecture, its built-in layers, and operations for establishing the relationship between the concentration data and hydraulic transmissivity fields. In the implementation process, the network is tested with 5000 models after being trained with synthetic datasets. After that, the algorithm accuracy is assessed under a variety of data conditions in a monitoring field, including the effects of data size, low resolution, and observation noise.
Theoretical background In this section, we first describe the theoretical concept of the forward problem used for the numerical simulation of spatiotemporal concentration data of a tracer injected into an aquifer with a heterogeneous transmissivity field. This forward problem is based on a coupling of the steady-state groundwater flow equation and the transient transport equation and is employed to build a database in which the concentration data and its corresponding transmissivity field are used in the network training phase. In the second section, we introduce the concept of inversion problem with the convolutional neural network with an encoder-decoder structure.
In this paper, the groundwater flow and transport equations are solved numerically using the finite element method with Comsol software. These equations constitute the direct problem of the tracer test in which the concentration of conservative tracer is connected in a nonlinear manner to the transmissivity field: c = f (m), withT = 10 -m , ( 8 ) As mentioned earlier, the forward problem will be served to create the training dataset by computing concentration data for thousands of geostatistically generated transmissivity fields.
m is the negative of logarithm of transmissivity field. In the learning phase, the inverse operator is built with an optimization process for finding the best weights and biases that connect the concentration and transmissivity of the training data set. This operation can be expressed as follows: Θ = argmin { ∑ N 1 ⃦ ⃦ m i -f -1 (c i , Θ) ⃦ ⃦ } , ( 10 ) where (mi, c i ) refers to the transmissivity model and its corresponding concentration data determined numerically with the forward problem, and N is the size of training data used to train the network. The quality of the approximation of the inversion function depends on the amount of data used in the training phase. To get an accurate estimate, we need to build a large training database from repeated solving of the forward problem, making this step the most timeconsuming in the process.
Construction of training data This section is dedicated to the construction of the training dataset to train the Segnet network. To accomplish, we use a geostatistical code to generate 25,000 transmissivity fields in which the distribution of log 10 T is constructed randomly using a Gaussian variogram. Variogram properties vary 0. 1-2. 5 for sill, 3-5 for mean, and 3-15 m for range. The values of the generated transmissivity models range from 10 -6 to 10 m 2 /s in six orders of magnitude. We assign these models to a confined aquifer with dimensions of (20 m × 10 m) and 5 m for thickness (Fig. 2 ). On this aquifer, we have set up 49 wells, 3 of which are dedicated to the injection of the tracer and the others to the monitoring of the evolution in time of the tracer concentration. Then, the set of transmissivity fields is used in the forward problem described in the previous sections to numerically calculate the concentration data associated to the tracer tests conducted sequentially on the three wells.
Learning and validation of the neural network As described in Section 2. 2, we build two architectures in this study, Net-1 and Net-2, to process the single-injection test and the multiinjection test respectively. For the first network (Net-1), it will be trained three times, one for each injection tests. The trainings of both networks are performed with the ADAM optimization algorithm implemented in MATLAB on a Dell Precision Tower 5810, single GPU NVIDIA Quadro K2200. For Net-1, the training is performed with 60 epochs in 82 min, with a learning rate initiated at 0. 01 and decreasing by 0. 1 for every 30 epochs. However, the second network Net-2 is trained in 35 min, using a constant learning rate of 0. 01 with 30 epochs. The number of epochs in both training is set manually to avoid the overfitting problem.
The Jacobian could be computed with the adjoint state method, which is faster than the finite difference method, but it is complex to implement  (Vu et al, 2019; Sun & Yeh, 1990). The process is repeated until a local minimum is reached that minimizes the objective function. This algorithm was applied on the three models used as reference in the previous sections and the inversion of each model took 3 days using a CPU (Intel Xeon 3. 5 GHz, 6 cores, 12 threads). The results of these inversions faithfully reproduce the main characteristics of the real models with the same degree of accuracy as the CNN-2T algorithm (see Fig. 12 ). Each inference of Gauss-Newton inversion method consumes the same time with building entire process of CNN-2T, including time for dataset generation and training network, while CNN-2T performs each inference only on few milliseconds.
Because in machine learning, the data processing is performed on the spatial analysis of several information instead of individual data as it is the case in deterministic algorithms. The results of the Gauss-Newton inversion are local minima, so they depend on the choice of the initial model. In contrast, machine learning provides a global solution. The machine learning method does not require any linearization of the forward Fig. 10. Distributions of the metric parameters R 2 and RMSE determined from the comparison between predicted and real models and used to evaluate the accuracy of predictions. We recall that these evaluations were made on 5000 models. problem, but it does require a large amount of forward problem computation to construct the training data. The time spent generating this training dataset can be the same or less than that needed to find a local minimum with Gauss-Newton code using the finite difference method.
Then, this network is trained with data of each tracer test performed separately. The transmissivity fields determined from the individual tracer data are then incorporated into the second network as input data, which is linked to the real transmissivity field to improve the reconstructions. This second network performs a joint inversion of data from multiple tracer tests and corrects the transmissivity fields determined separately from each individual tracer test. The networks were trained from a large synthetic database where the transmissivity fields were generated geostatistically and the concentration data by the coupled numerical solutions of the groundwater flow and transport equations. Several sensitivity analyses were conducted on these networks to evaluate the prediction accuracy, which was also compared with that achieved by a deterministic Gauss-Newton method.
Based on these results, we conclude that: The network succeeded in accurately reconstructing the heterogeneities of the transmissivity field. The reconstruction accuracy though shows a clear dependence on the scale of training datasets, whose generation is the hardest task in a deep learning approach. However, the time needed to generate datasets is of the same magnitude as that required in solving a local minimum in a Gauss-Newton algorithm which computes the Jacobian matrix using the finite difference method. In addition, the size of the training datasets to achieve a perfect approximation of the inverse function depends strongly on the nature of the heterogeneity of the target field. Learning can be achieved with a small number of training models if the generated models have a low degree of heterogeneity.
For the + -b b final state our MiNNLO PS predictions are compared against the NNLOPS results of ref. [126] , while for ± ν H production we validate our calculation against the NNLOPS results presented in ref. [84]  for on-shell Higgs bosons. The new MiNNLO PS implementation shall supersede those NNLOPS implementations in the future within the Powheg-Box framework  [129]. Finally, we present a complete study of NNLO+PS events for both ZH and W ± H production with H → b b decay, finding agreement with a recent LHC measurement from the ATLAS collaboration  [131]. This manuscript is organized as follows: in section 2 we introduce our calculation by discussing the processes (section 2. 1), sketching the MiNNLO PS method (section 2. 2), describing our practical implementation (section 2. 3) and recalling the combination of production and decay events (section 2.