dataesr/scientific-paragraphs-categorization huggingface dataset:
6. 7 7 Testing of transformation overfitting This section tests the classification of transformed signals when the models are trained with different transformations (individual or chains). The aim is to demonstrate that the training with one individual transformation produces overfitting to the transformation of the training. Using 13 different transformations, Figure 3 compares the classi fication of original and transformed signals when the training is performed with original or transformed datasets. Note that the σ parameter is optimised once for each row of Figure3, and 25 repetitions are performed for each cell. For sake of simplicity, only the mean accuracy is displayed.
The formation of large quantities of ammonia has consequences for several aspects of the ITER plant operation in terms of gas reprocessing and duty cycle. It is therefore important to assess early on what fraction of ammonia may be found in the ITER gas exhaust when N 2 seeding is used. The design of the ITER divertor and estimates of the required fuel throughput have relied for many years on simulations performed with the SOLPS plasma edge modeling suite  [5] , a new version of which, SOLPS-ITER  [6, 7] , containing a more complete physics model, was launched in 2015 by the ITER Organization. The code uses the Monte Carlo neutral kinetic code EIRENE (www. eirene. de) as its main workhorse for solving the transport equations related to neutral atomic and molecular species, as well as for radicals and molecular ions.
A first conclusion of this literature analysis was that building a comprehensive database for an NH 3 production scheme requires taking into consideration the global N 2 /H 2 plasma chemistry. Nevertheless, some assumptions can be made by considering plasma conditions in the divertor area, which are summarized in Table  1. Thus, the following hypotheses have been put forward: • The species to be taken into consideration in the model are H, H • Considering the very low pressure, three-body collision processes were excluded. • Except molecular nitrogen that is present in the feed gas, species containing more than 2 nitrogen atoms were not considered, which means that second order processes in nitrogen were not considered. Following these assumptions, a database containing 130 reactions and 21 species was built up.
This database has been implemented in the SOLPS-ITER code suite formalism under the new acronym AMMONX and contains the following processes: • Ionization by collision between neutrals and electrons • Neutrals dissociation by electron impact • Dissociative recombination between ions and electrons • Ion-neutral processes • N 2 , N and H 2 metastable-states chemistry • Neutral/neutral chemistry. The source of kinetic data used for these processes have been verified and evaluated regarding explored plasma conditions. Among the most used databases one can mention: • the LxCat database [18], whose main references for cross-sections of collisional processes with electrons  [19] [20] [21]  are consistent with the values used by D. Reiter for processes involving N 2 9 • the Anicich reviews [22,23] and Umist database [24] for ions/ neutral processes • the work of Capitelli et al.
First simulations of ND 3 formation in Eirene Once our reduced mechanism was validated by the experiments available in the literature, we implemented it in the SOLPS-ITER package and we used it to predict the N x and NH X species concentrations for an N 2 gas injection into the ITER divertor. Tests cases are based on the test case ITER_2588_D+He+N and they are solved with code version SOLPS-ITER 3. 0. 6-51 (also known as the "SOLPS-ITER 3. 0. 6 master"). In order to illustrate the impact of nitrogen chemistry, we consider four test cases: • Test Case 1: only N and N + species are included in the EIRENE chemistry, and we use the standard AMJUEL set of reactions (ALL-He_el. amd file), plus neutral-neutral elastic collisions, • Test Case 2: only the molecular N 2 species and its chemical reactions are added compared to Case 1 (ALL-He_el.
The lowest N density close to the X-point is found with Case 4. Fig. 5  shows the particle density of N 2 molecules (in m -3 ) for test Cases 2, 3 and 4. The AMMONX database (test Cases 3 and 4) predicts less diffusion of N 2 above the divertor. Taking into account the metastable species, as for N, reduces the N 2 diffusion above the divertor even further. Fig. 6  illustrates the ND 3 formation for test Cases 3 and 4, in which N and H initial amounts are close. Results clearly show ammonia formation under the divertor, but the total amount seems too high, certainly due to the strong wall chemistry assumption made above. Different test cases (not shown here) where only homogeneous phase ND 3 formation reactions in the divertor volume are considered and wall chemistry is neglected yield only negligible amounts of ammonia formation.
Conclusions A new database named AMMONX including NH X formation processes has been achieved based on the AMJUEL formalism, for inclusion in the SOLPS-ITER code suite and as a stand-alone tool. Two reduced schemes of 42 and 53 processes respectively are proposed to model NH 3 /ND 3 formation in plasma edge conditions under the divertor and have been validated by model/experiment comparison. We demonstrate the use of these new nitrogen chemistry datasets in EIRENE runs on a fixed SOLPS-ITER plasma background for typical ITER radiative divertor conditions. First simulations clearly predict ammonia formation in significant amounts under the divertor, however they are very sensitive to the details of the wall chemistry model used. Further refinements of the EIRENE wall chemistry capabilities are planned to improve the predictive power of such simulations.
A software framework was developed to facilitate the development of retrieval models from at-sensor TOA radiance data. As a proof of concept, maps of these biophysical variables have been generated for both TOA (L1C) and bottom-of-atmosphere (L2A) Sentinel-2 data by means of a hybrid retrieval scheme, i. e. , training GPR retrieval algorithms using the RTM simulations. Obtained maps from L1C vs L2A data are consistent, suggesting that vegetation properties can be directly retrieved from TOA radiance data given a cloud-free sky, thus without the need of an atmospheric correction.
g. , as studied in  [16] [17] [18]. It implies that biophysical variables retrieval from TOA radiance data have so far been restricted to experimental studies. With the purpose of democratizing these approaches to the broader community, what is lacking is a freely available, streamlined and generic processing framework that enables to automate retrieval applications directly from TOA radiance data. At-sensor spectral TOA radiance is the combination of radiometric effects from surface reflectance, atmospheric effects and target surroundings convolved with the sensor spectral and spatial response functions  [19]. Consequently, the identification of the key input variables that drive TOA radiance is a first mandatory step to retrieve biophysical variables directly from at-sensor TOA radiance data.
Based on these GSA results, biophysical variables retrieval strategies applicable directly to an at-sensor TOA radiance dataset will be developed. From past experiences where different retrieval methods have been compared for S2 data at TOC scale  [38] , the so-called hybrid retrieval methods, i. e. , where RTM data is used for training machine learning methods, are particularly promising in terms of accuracy and processing speed  [2, 39]. Here, the developed retrieval algorithms should eventually be applicable to S2 L1C products, thereby avoiding the uncertainties of the atmospheric correction process  [40]. Altogether, this study boils down to the following objectives: (1) to develop emulators to approximate the coupled PROSAIL-MODTRAN RTMs for a set of input variables and TOA radiance output; (2) to apply the emulator into a GSA in order to identify the driving variables; and finally, as a proof of concept, (3) develop hybrid retrieval models for biophysical variables from S2 L1C (TOA radiance) and L2A (bottom-of-atmosphere reflectance) data.
Imaging principle Pushbroom-grating Spectral range  [nm]  400-2200 nm Geolocation accuracy <12. 5 m SNR @L re f  50  The S2 MSI data is freely available from Copernicus Open Access Hub. From mid 2018 onwards, two reflectance products are provided: L1C and L2A. The L1C product refers TOA reflectances (i. e. , TOA radiance normalized by incident solar irradiance). The L2A product refers to bottom-of-atmosphere (BOA) reflectance, which is achieved by means of the Sen2Cor atmospheric correction scheme (version 2. 4. 1) [5]. Sen2Cor processing scheme is based on state-of-the-art algorithms that include cirrus cloud correction and scene classification  [43, 44]. Sen2Cor relies on the Dark Dense Vegetation algorithm for the retrieval of aerosol type (rural/continental by default) and optical thickness value at 550 nm (AOT 550 )  [45].
Materials and Methods The general work flow is presented in Figure  2. In order to analyze the feasibility of retrieving biophysical variables from TOA radiance, we performed three parallel studies. First, a GSA using an emulator was carried out to determine the relative influence of each biophysical and atmospheric variable in the TOA radiance signal. Secondly, a set of synthetic test scenarios were generated to assess the performance of biophysical variables retrieval under controlled conditions. Three different retrieval scenarios were implemented: (1) ideal surface reflectance data (i. e. , without errors from atmospheric correction), (2) TOA radiance, and (3) realistic surface reflectance data (i. e. , affected by error propagation from atmospheric correction). Finally, retrieval strategies were applied to a real S2 data at L1C (TOA radiance) and L2A (BOA reflectance).
A detailed description of the used processing tools and simulated datasets is provided in Sections 3. 1 and 3. 2. The used GSA and emulation algorithms are described in Sections 3. 3 and 3. 4. Further information about the implemented method for retrieving the various biophysical variables from the simulated data and evaluating their accuracy is described in Section 3. 5. The method to assess the performance on a real S2 image is then described in Section 3. 6.
• Atmospheric Look-up table Generator (ALG)  [19]  is an independent software tool that can be plugged into ARTMO and allows generating and analyzing LUTs based on a suite of atmospheric RTM, i. e. , MODTRAN, 6SV, libRadtran. • A new so-called "TOC2TOA" toolbox has been developed to enable coupling surface reflectance simulations with atmospheric simulations, i. e. , to reach TOA radiance data. The TOC2TOA toolbox couples the atmospheric transfer functions with canopy reflectance simulations or observations to enable TOA radiance data, thereby ensuring that consistent geometry at canopy and atmosphere is preserved. Either canopy LUTs, surface reflectance data, e. g. , from a field spectroradiometer, or a BOA reflectance image can be coupled with atmospheric transfer functions to enable uppscaling to TOA radiance data.
Description of Simulated Datasets The training and performance assessment of biophysical parameters retrieval from at-sensor TOA radiance is based on simulated data of surface reflectance and TOA radiance. The use of RTMs allows us to test the retrieval accuracy under controlled conditions. On the one hand, surface reflectance datasets are based on the combination of PROSPECT-4  [20]  and SAIL  [21]  RTMs, also known as PROSAIL. PROSPECT-4 is one of the most widely used RTMs that simulates leaf optical properties. The model calculates directional-hemispherical reflectance and transmittance measured from 400 nm to 2500 nm at 1 nm spectral sampling. SAIL solves the radiative transfer equation for scattering and absorption of four upward/downward fluxes at the canopy scale. In combination with PROSPECT-4 leaf optical properties, SAIL provides top-of-canopy (TOC) reflectance in the 400-2500 nm spectral range at 1 nm sampling.
The generation of the simulated datasets (analysis, reference and retrieval) is represented in Figure  3  and further described in the paragraphs below. The first dataset (further referred to as analysis) functions to train an emulator that allows running a GSA to evaluate the relative contribution into TOA radiance of various leaf-canopy and atmospheric properties. Thus, this dataset combines PROSAIL and MODTRAN into a database of TOA radiance spectra. The first step was to generate the LUT of directional reflectance (ρ) derived from the combination of the PROSPECT-4 and SAIL. A set of 10,000 samples of the six input leaf-canopy variables were distributed according to a Latin Hypercube Sampling (LHS) distribution  [61]  (see Table  2 ). The hot-spot, soil brightness coefficient, and the sun-target senor geometry variables have been excluded from the analysis in order to facilitate the coupling between the vegetation and atmospheric RTMs.
Simulations were carried out in the 400-2500 nm spectral range at 1 nm sampling. The second step involves generating MODTRAN simulations. The analysis dataset contains 10,000 MODTRAN simulations sampled with a LHS distribution (see Table  3 ). These simulations were carried out in the same spectral range as PROSAIL simulations with a sampling of 15 cm -1 (0. 3-9 nm in the covered spectral range of 400-2500 nm). Input variables were selected so that they have an impact in the entire wavelength range (400-2500 nm) and include typical variability  [8, [62] [63] [64]  in: (1) the AOT 550 ; (2) the spectral dependency of the extinction coefficient, through the Ångström exponent; (3) the phase function, through the HG asymmetry parameter; (4) the single scattering albedo; and column-integrated concentrations of (  5 ) ozone (O3C) and (  6 ) vapor (CWV).
The surface (PROSAIL) and the atmospheric (MODTRAN) simulations were randomly one-to-one combined (10'000 simulations) and propagated to TOA radiance following Equation (  1 ) with the Lambertian and homogeneous surface assumption: L = L 0 + E tot T tot ρ π(1 -Sρ) (1) where T tot = T dir + T di f is the total target-to-sensor transmittance and T tot = E dir cos θ il + E di f is the total at-surface irradiance for a solar zenith angle θ il. Here, the 1 nm sampling surface reflectance (ρ) was interpolated by cubic splines to the MODTRAN wavelength grid. For the sake of simplicity, the spectral dependency of all terms in the Equation (  1 ) has been omitted. A random subset of 1000 cases is then used to train an emulator for further GSA calculation. The second dataset (further referred to as reference) aims at representing realistic S2 observations over land surfaces for broad atmospheric conditions and is used for validation.
The reference dataset is divided into three subsets to validate the retrieval strategies under three different scenarios (see Figure  3 ): (1) retrieval from an ideal surface reflectance data, (2) retrieval from TOA radiance, and (3) retrieval from surface reflectance after a non-perfect atmospheric correction. The first subset (reference_toc) corresponds to a reference surface reflectance dataset composed of a random subset of 5000 samples extracted from the analysis dataset previously described in Table  2. This scenario should be taken as the ideal case, since there are no radiometric perturbances due to atmospheric scattering and absorption. This surface reflectance data is combined with other 5000 MODTRAN simulations to create the second subset of reference TOA radiance (reference_toa).
This second scenario refers to the goal of this paper i. e. , to validate the performance of retrieving biophysical variables directly from TOA radiance. In this case, MODTRAN simulations were run with varying conditions of CWV, O3C, AOT 550 and aerosol type with an LHS distribution (see Table  4 ) and in the same spectral range and sampling as in the analysis dataset. With respect the aerosol type, the following 9 models were included: MODTRAN's rural, urban and navy-maritime (with 3 air mass values identifying coastal to strong land influence), and OPAC's continental (clean, average and polluted) and urban  [62]. Both the reference_toc and the reference_toa subsets were convolved by S2 instrument spectral response function (ISRF, f c ) for each spectral channel c (1 to 13)  [42]  following Equation (2): L c = L • f c dλ f c dλ (2) The third subset (reference_atm) aims to represent surface reflectance spectra obtained after a non-perfect atmospheric correction as would be from Sen2Cor algorithm.
Instead of implementing an atmospheric correction process on the reference_toa subset, the reference_toc subset was perturbed in order to reproduce the expected error propagation from the Sen2Cor algorithm  [50]. Accordingly, the reference_atm surface reflectance spectra (ρ atm ) is created from the reference_toc spectra (ρ toc ) following Equation (3): ρ atm = ρ toc + ε ρ (3) where ε ρ is the expected wavelength-dependent error from Sen2Cor shown in Figure  4. See Table  VIII  in  [50]  for detailed information. Finally, the third dataset (further referred to as retrieval) is used to train the retrieval algorithms for each of the biophysical variables (see Section 3. 5). The retrieval dataset consists of two subsets of surface reflectance (retrieval_toc) and TOA radiance (retrieval_toa), both generated with the same process as for the construction of the reference dataset.
Regarding the retrieval_toc subset, this is constructed from the remaining 50% samples from the analysis dataset that were not used in the reference_toc subset. The TOA radiance subset uses a new set of 5000 MODTRAN simulations with the same input variables as in Table  4  but only using MODTRAN's rural aerosol type. In this way, the retrieval of biophysical variables from TOA will carry along errors due to uncertainties in aerosol optical properties.
Global Sensitivity Analysis (GSA) In order to identify the driving vegetation and atmospheric variables having an impact on TOA radiance, we first conducted a global sensitivity analysis (GSA) of the TOA radiance simulations from the analysis dataset. Most GSA methods are variance-based methods, which decomposes the variance of the model output into fractions that can be attributed to inputs or sets of inputs  [28, 65]. While the Sobol' method  [66]  pioneered in developing a variance-based GSA method, a modified version was proposed by  [67] , which proved to be effective in identifying the so-called Sobol's sensitivity indices. These indices quantify both the main sensitivity effects (first-order effects: S i , i. e. , the contribution to the variance of the model output by each input variables) and total sensitivity effects (S Ti , i.
When it comes to emulating RTM spectral outputs, however, the challenge lies in delivering a full spectrum. This implies that the MLRA should be able to generate multiple outputs to reconstruct a full spectral profile, which is not a trivial task. For instance, the contiguous spectral profile between 400 and 2500 nm consists of over 2000 bands when binned to 1 nm resolution. Only some MLRAs can obtain multi-output models, but that typically lead to highly complex models with long training time and certain risk of overfitting because of model over-representation, e. g. , as with neural networks. A workaround solution was developed that enables the regression algorithms to cope with large spectroscopy datasets by taking advantage of the so-called curse of spectral redundancy, i. e. , the Hughes phenomenon  [72].
Although its superior performance went somewhat at the expense of processing speed as opposed to other MLRAs, it runs numerous times faster than the original RTM  [31] [32] [33]. GPR is a probabilistic kernel method, and has been widely used for retrieval of biogeophysical variables and emulation applications  [79] [80] [81]. Kernel methods in machine learning owe their name to the use of kernel functions  [82] [83] [84]. These functions quantify similarities between input samples of a dataset. Similarity reproduces a linear dot product (scalar) computed in a possibly higher dimensional feature space, yet without ever computing the data location in the feature space. GPR generalize Gaussian probability distributions in function spaces  [78]. The prediction and the predictive variance of the model for new samples are given by: f(x q ) = n ∑ i=1 i k(x i , x q ) (10) V[ f(x q )] = k(x q , x q ) - * (K + σ 2 n I) -1 * (11) where k(•, •) is a covariance (or kernel function), * is the vector of covariances between the query point, x q , and the n or training points, and σ 2 n accounts for the noise in the training samples.
As one can see, the prediction is obtained as a linear combination of weighted kernel (covariance) functions, the optimal weights given by w = (K + σ 2 n I) -1 f(x). Many different functions can be used as kernels for  [85]. We used the automatic relevance determination squared exponential kernel for GPR, which has a separate length hyperparameter for each input dimension. Stochastic gradient descent algorithms maximizing the marginal log-likelihood are employed, which allow optimizing a large number of hyperparemeters in a computational effective way. Based on experience from earlier emulation exercises  [32, 33] , the TOA radiance data was first compressed into 20 PCA components. The GPR emulator was trained with 70% of the 1000 samples and the remaining dataset was kept for validation. Goodness-of-fit statistics were calculated to assess the emulator's capability to generate accurate TOA radiance data: the Pearson's correlation coefficient (R 2 ) and root-mean-square error (RMSE) are calculated according to Equations (  12 ) and (  13 ): R 2 = n ∑ n i=1 X re f ,i • X ret,i -∑ n i=1 X re f ,i • ∑ n i=1 X ret,i n ∑ n i=1 X 2 re f ,i -∑ n i=1 X re f ,i 2 n ∑ n i=1 X 2 ret,i -(∑ n i=1 X ret,i ) 2 , ( 12 ) and: RMSE = 1 n n ∑ i=1 X re f ,i -X ret,i 2 , ( 13 ) where X re f ,i and X ret,i are respectively the reference and retrieved values.
We assessed the performance on biophysical variable retrieval on the three reference scenarios previously described in Section 3. 2. The MLRA retrieval toolbox was first used to train and to validate an MRLA from the retrieval datasets and then to apply the trained model to retrieve biophysical variables from the reference datasets. Based on experience from earlier retrieval exercises  [32, 33] , the two retrieval databases were split into 70% for the training and 30% for the validation of the GPR retrieval algorithms. The retrieval_toc dataset was used to train and validate one GPR model for the retrieval of biophysical variables from surface reflectance. The retrieval_toa was instead used for the retrieval from TOA radiance. Goodness-of-fit statistics were calculated to assess the GPR models' capability to retrieve accurately biophysical variables.
Further, in an attempt to make the models better fit to process real S2 data, Gaussian noise was added to the retrieval TOC and TOA training datasets. The addition of noise to the RTM generated spectral bands has multiple purposes: it simulates errors of radiometric calibration, atmospheric noise and residuals from the atmospheric correction, but to some extent also bridge between the simplified representation of the RTM and the actual radiometric behaviour of the canopy [89]. Generally, noise prevents the retrieval model from over-fitting on the training database. However, an accurate quantification of all error terms in the sensing process remains difficult  [89]. While for the TOC training dataset noise levels can be obtained from S2 surface reflectance studies as in  [50] , for TOA that is not the case.