dataesr/scientific-paragraphs-categorization huggingface dataset:
Beyond all the PolSAR data filtering techniques presented in this section, there exist a wide variety of similar approaches in the related literature, where a comparison among some of them has been presented in  (Foucher et al. 2012 ). Nevertheless, it may be concluded that reaching an optimal compromise of a joint preservation of the polarimetric and the spatial information, in the case of PolSAR data filtering, is still today a problem without an adequate solution. Consequently, the selection of a particular filtering alternative for PolSAR data must take into consideration the final application of the PolSAR data in order to determine the optimum filtering according to that application.
Before discussing the performance of the MLP models, we will introduce the chosen models while briey overviewing the Fig. 1  Schematic classification of popular molecular machine learning potentials (MLPs). Representative models on the scheme (models tested here in bold): (1) kernel methods with global descriptor (KM-GD: KREG, 18 KRR-CM,  41  and sGDML  20  ), (2) kernel method with fixed local descriptor (KM-fLD: GAP  42  -SOAP,  43  KRR-FCHL,  44  and KRR-aSLATM  45  ), (3) neural networks with fixed local descriptor (NN-fLD: ANI,  46  DPMD,  47  and BPNN  48  ), (4) neural networks with learned local descriptor (NN-lLD: PhysNet,  36  SchNet,  49, 50    main aspects of these different classes of ML algorithms and descriptors. We refer the reader to ref. 52 describing technical aspects of the MLPs, which we tested here using our soware package MLatom.
Finally, the global descriptors' dimensionality grows with the number of atoms. Although this is not an issue for the PES of small systems like those we discuss here, it may be a problem when dealing with chemically diverse datasets. Thus, special solutions with global representations have been suggested. 62, 68, 69 cal descriptors Alternatively to global descriptors, one can construct a suitable vector representation for MLPs based on an atom-centered approach. Such a molecular representation is designed to encode the local chemical environment around each atom through a set of basis functions that vanish outside of a cutoff sphere. These representations are called local descriptors (LDs). Following the concept of many-body expansion, MLPs with local descriptors model the interatomic interactions by decomposing them into n-body terms, typically expressed as a combination of radial and angular distribution functions.
Individual feed-forward NNs are designed and trained for each chemical element in the system so that the sum of atomic contributions approximates the total energy. 48 This NN-fLD model inspired a progressive and systematic improvement in the architecture and accuracy of NN potentials reported in the literature. 47, 50 A notable example of such advancement is the ANI family of MLPs. 2, 46, 86 Many ANI models, trained on a chemically diverse dataset spanning both congurational and conformational spaces, are available and can be used out-of-thebox. A similar concept but with different descriptors is used in DPMD, another successful example of an NN-fLD MLP. 47 DPMD belongs to the rst generation of deep learning models for molecular simulations, which have been continuously improved from both an efficiency  87  and accuracy  75  perspective.
For all kernel-based models, we optimized hyperparameters using default settings as described elsewhere. 52 Due to the high cost of training the NN-based models, we did not optimize their hyperparameters. Given the plethora of available MLPs and the different technical details related to their implementation and application, it is rather challenging to assess their performance systematically and on equal footing. Although the accuracy of these MLPs has been reported for different datasets, the data types (congurational, compositional) and the size of the training and validation sets are oen not the same, hindering a direct comparison between results. Furthermore, it is insuf-cient to compare just models trained on the same, specic number of points. An essential aspect that must be considered is how the models' accuracy changes with the training set size, i.
e. , one should compare the learning curves 100 of different models. To facilitate comparing different MLP model performances, we have recently extended the MLatom package with a modularized Python interface to popular third-party ML programs. The package offers researchers a unied platform with a standardized input/output structure to perform ML simulations for atomistic systems. 52 This integrated platform allows for automatic generation of the learning curves for errors in energies and forces and their standard deviations. It also allows for hyperparameter optimization and recording performance metrics such as the training and prediction times and their standard deviations. All the numerical results reported here are openly available together with the sample MLatom input les on DOI: 10.
6084/m9. gshare. c. 2878631. We adopted the extended version of the popular MD17 benchmark database  20, 58  to evaluate the performance of the chosen MLP models because molecular dynamics is one of the main applications of MLPs. This database is composed of independent congurational datasets generated through quantum-chemical molecular dynamics (with T ¼ 500 K) for ten organic molecules with sizes ranging from 9 (ethanol and malonaldehyde) to 24 atoms (azobenzene). Thus, this database also allows us to investigate how molecular complexity inuences the ML model's performance. As target quantities for predictions, the MD17 database includes potential energies and forces determined with van der Waals-corrected density functional theory with the PBE functional (DFT/PBE + vdW-TS). 101, 102 n the following, we evaluate the performance of MLPs trained either only on energies or simultaneously on energies and forces considering all MD17 datasets.
g. , very long molecular dynamics. The prediction times for KM-GDs models such as KREG and KRR-aXYZ trained with up to 50k points are again much lower than for other models (Fig. 2f ). The prediction time with NNs does not depend on the number of training points as expected from its parametric denition. GAP-SOAP delivers the best accuracy for ethanol (but not for all other molecules; see below). Nevertheless, its particularly bad training-time and prediction-time scaling with the increasing number of training points makes it quickly computationally intractable (Fig. 2d  and f ). One can speed up GAP-SOAP using approximation techniques (applying smaller Fig. 3  Performance of MLPs trained only on energies. Root-mean squared error (RMSE) calculated for energies with different ML potentials for all molecules of the MD17 database.
2c  and d ). The same general conclusions-drawn here for ethanolalso hold for other molecules. However, keeping track of the learning performance of MLPs across the compositional chemical space (i. e. , considering different molecules) becomes more challenging since we add one more dimension to the learning curve analysis. One possible way to analyze the model's accuracy for the whole MD17 database is to look at a slice through the learning curves at 1000 points, focusing on how the different models perform with increasing molecular complexity (Fig. 3 ). All models decrease their accuracy for larger and more exible molecules, requiring more training points to achieve the desired accuracy (results for other training-set sizes are available at DOI: 10. 6084/m9. gshare. c. 2878631). Nevertheless, the impact of complexity is different for different models, and, e.
g. , GAP-SOAP is no longer the best model for salicylic acid (where KREG is the best) and aspirin (where ANI and KRR-CM are better). Other examples are DPMD, which is more accurate than PhysNet for half of the molecules, and ANI, which has accuracy comparable to that of kernel methods in many cases. Alternatively, an overall picture of the learning performance of different MLPs can also be obtained by representing the (sparse) learning curves as box plots  105  characterizing the distribution of the RMSE values for all molecules of MD17 database (Fig. 4 ). The wide error bars obtained for models trained on 1000 points clearly demonstrate the dependence of the MLP's performance with respect to the molecular complexity. Although GAP-SOAP shows the smallest error bar for 1000 training points, the RMSE of energy predictions for azobenzene, paracetamol, and aspirin (3.
4, 3. 8, and 4. 5 kcal mol À1 , respectively) appears as outliers in the box plot, suggesting that the model's hyperparameters or the SOAP descriptor might not be well suited for these molecules. The size of the error bars quickly decreases for most MLPs (except for DPMD) when the training set is augmented by adding more geometries. In terms of accuracy, the tiny error bars (varying below 1 kcal mol À1 for 10k training points) obtained for both kernel methods, KRR-CM and KREG, and the NN model ANI indicate that these models are competitive in consistently predicting the total energies with high accuracy for the different molecules of the MD17 database when only energies are available for training.
Training PES on energies and forces When reference forces are available, one can include this information in the training to improve the MLP accuracy. 43, 48 ndeed, our tests also clearly conrm a signicant reduction in prediction error for all MLPs (Fig. 5 ). Learning curves for MLPs evaluated on the ethanol dataset are shied to higher errors for models trained only on energies (Fig. 2 ) in comparison to those trained on energies and forces (Fig. 5 ). Note that KREG, KRR-CM, and KRR-aXYZ are not evaluated because learning on energies and forces is not implemented for these models. However, to answer whether it is worth including forces in the training set, we must consider the additional computational cost due to the quantum-chemistry calculations of forces and the substantially longer training time.
Training set sampling and conformational analysis Another critical point is that the accuracy of machine learning can quickly achieve lower error than the inherent error of the Fig. 8  Box plot representation of the MLPs' learning performance across the compositional space of MD17 database. All ML models were trained using energies and forces information. Each box plot represents the distribution of the root-mean squared error (RMSE) for the total energies of all molecules in the MD17 database calculated with respect to the true labels of a test set consisting of 20 000 geometries. The mean value of RMSE calculated for all different molecules is represented as white dots, while black markers represent outliers. typical quantum-chemistry approaches used to generate the training data. Thus, in many cases, we can expect that simulations with different MLPs would lead to similar results, but to what extent the error in ML inuences the nal result is yet to be explored.
Finally, maybe the most critical question in MLP model development is not improving the models themselves but the efficient generation of good training data, which is, therefore, a topic of intensive ongoing research. 9 These data should be balanced because signicant undersampling of a region in the conformational space may lead to a drastic drop of accuracy for this region, introducing a bias in the ML potential and, as a result, quantitatively wrong conclusions from simulations with such a potential. For example, aspirin has many different conformational isomers, and training data sampled from molecular dynamics will probe each of them differently. If we focus on the two conformations formed by rotation around the Ph-C bond of the carboxylic acid, the ratio between points populating them in the entire MD17 dataset is 1 : 3.
Thus, the researcher choosing an MLP may follow them for a quick qualitative assessment, but they should benchmark MLPs in the view of their own applications as it is common while choosing a quantum-chemical method. Although kernel methods tend to outperform NNs in small training-set scenarios when trained on energies and forces, the computational overhead for training a kernel-based potential may become an issue in applications requiring many data points. Such would be the case of constructing PES for isomeric molecular datasets (e. g. , ISO17 dataset 49 ), describing complex dynamical reaction processes,  26  or tting PESs in the full chemical (compositional and congurational) space with a single MLP model. Therefore, a detailed benchmark study to elucidate these issues would close a critical gap in the literature by providing helpful, evidence-based, and numericallysupported guidelines for selecting and developing efficient ML potentials.
Methods All machine learning potentials were trained with default settings of MLatom 2. 0. 3 as described in ref. 52. The GAP-SOAP model was trained without cutoff and sparsication to avoid arbitrariness in choosing these hyperparameters. The rst geometry in each data set was used as the reference geometry for calculating the RE descriptor in the KREG models. In the case of the neural network models (ANI, DPMD and PhysNet), the ethanol dataset was used as the basis to calibrate hyperparameters when the values were not available in the original publication. Once we have found the hyperparameter settings that better reproduce the testing error reported in the literature, we use the same settings for the remaining molecules of the MD17 database. These hyperparameters are used as the default in the MLatom interface module.
Therefore, further improvements in the NN model predictions provided in this work might be achieved by ne-tuning the hyperparameters to each specic dataset. The early stopping method was used in the training process to prevent overtting, either in its original implementation when available (TorchANI) or through our own implementation in the MLatom interface with other packages (DeePMD-kit and PhysNet). To generate aXYZ descriptors, rst, we dened the coordinate origin at the molecule's centroid. Then, the Kabsch algorithm  109  was applied to align their orientations with respect to the rst geometry of the reduced data set with 20k test points of each molecular PES. Finally, the aligned geometries were attened to 1D arrays as the X input of MLatom. No weights for different atoms were used in the alignment.
The DFT single-point calculations (PBE0/6-311G*) were performed with ORCA. 110 The energies and forces were calculated using a dense integration grid (given by the Grid5 and NoFi-nalGrid keywords, corresponding to 434 points in the Lebedev grid), and also using a very tight criteria for the self-consistent eld (SCF) as given by the VeryTightSCF keyword (tolerance of 10 À9 hartrees for energy change and 2. 0 Â 10 À6 for orbital gradient rotation angle convergence). available as a part of the program for calculating root-meansquare deviation between two molecular geometries at https:// github. com/charnley/rmsd.
Acknowledgements P. O. D. acknowledges funding by the  National Natural Science Foundation of China  (No. 22003051 ) and via the  Lab  project of the  State Key Laboratory of Physical Chemistry of Solid Surfaces. M. B. and M. P. J. acknowledge the support of the  European Research Council (ERC)   Advanced grant SubNano  (grant agreement  832237 ). The  Centre de Calcul Intensif d'Aix-Marseille  is acknowledged for granting access to its highperformance computing resources. The authors thank  Prof. Stefan Grimme  for helpful suggestions.
Code availability MLatom package is available free of charge for non-commercial and non-prot uses at http://MLatom. com. MLatom with the settings used to perform the simulations in this study is available as an open-source code and executables on the aforementioned website and can be also installed using the command pip install MLatom¼¼2. 0. 3. List of programs interfaced in MLatom and their versions used in this work are provided in Table 1. Scripts for aligning XYZ (aXYZ descriptor) and forces are available at http://MLatom. com/MLPbenchmark1 and DOI: 10. 6084/ m9. gshare. c. 2878631. The code with the Kabsch algorithm is Table 1 List of programs interfaced in MLatom and used in this work ML potential Program Version Repository ANI TorchANI 2. 2 https://github. com/aiqm/torchani DPMD DeePMD-kit 1.
2. 2 https://github. com/deepmodeling/deepmd-kit PhysNet PhysNet e243e2c https://github. com/MMunibas/PhysNet sGDML sGDML 0. 4. 4 https://sgdml. org GAP-SOAP GAP 1598976566 https://www. libatoms. org/gap/ gap_download. html QUIP 5c61598e4 https://github. com/libAtoms/QUIP.
Across-species data syntheses using sap flow data have mostly focused on maximum values extracted from publications  (Kallarackal et al. , 2013; Manzoni et al. , 2013; Wullschleger et al. , 1998). Multi-site syntheses have focused on the environmental sensitivity of sap flow, using site means of plant-level sap flow or sap-flow-derived stand transpiration  (Poyatos et al. , 2007; Tor-ngern et al. , 2017). Because data sharing is only incipient in plant ecophysiology, sap flow datasets have not been traditionally available in open data repositories. Open data practices are now being implemented in databases, which fosters collaboration across monitoring networks in research areas relevant to plant functional ecology  (Falster et al. , 2015; Gallagher et al. , 2020; Kattge et al. , 2020)  and ecosystem ecology  (Bond-Lamberty and Thomson, 2010).
The success of the data sharing and data re-use policies within the FLUXNET global network of ecosystemlevel fluxes has shown how these practices can contribute to scientific progress  (Bond-Lamberty, 2018). Here we introduce SAPFLUXNET, the first global database of sap flow measurements built from individual community-contributed datasets. We implemented this compilation in a data structure designed to accommodate time series of sap flow and the main hydrometeorological drivers of transpiration, together with metadata documenting different aspects of each dataset. We harmonized all datasets and performed basic semi-automated quality assurance and quality control (QC) procedures. We also created a software package that provides access to the database, allows easy visualization of the datasets, and performs basic temporal aggregations.
Data compilation SAPFLUXNET was conceived as a compilation of published and unpublished sap flow datasets (Appendix, Table  A1 ), and thus the ultimate success of the initiative critically depended on the contribution of datasets by the sap flow community. An expression of interest showed that a critical mass of datasets with a wide geographic distribution could potentially be contributed, and the results of this survey were used to raise the interest of the sap flow community  (Poyatos et al. , 2016). The data contribution stage was open between July 2016 and December 2017, although a few additional datasets were updated during the data quality control process and contain more recent data. All contributed datasets had to meet some minimum criteria before they were accepted, in terms of both content and format.
We required that all datasets contained sub-daily, processed sap flow data, representative of whole-plant water use under different hydrometeorological conditions. This meant that both the processing from raw temperature data to sap flow quantities and the scaling from single-point measurements to whole-plant data had been performed by the data contributor responsible for each dataset. Time series of sap flow data and hydrometeorological drivers were required to be representative of one growing season, setting, as a broad reference, a minimum duration of 3 months. Sap flow could be expressed as total flow rate either per plant or per unit sapwood area. Contributors also needed to provide metadata on relevant ecological information of the site, stand, species, and measured plants as well as on basic technical details of the sap flow and hydrometeorological time series.
Data harmonization and quality control: QC1 Once datasets were received, they were stored and entered a process of data harmonization and quality control (Fig. 1 , Supplement Fig. S1 ). This process combined automatic data checks with human supervision, and the entire workflow was governed by functions and scripts in the R language (R Core Team, 2019), including other related tools, such as R markdown documents and Shiny applications. All R code involved in this QC process was implemented in the sapfluxnetQC1 package  (Granda et al. , 2016) ; see the package vignettes for a detailed description (https://github. com/ sapfluxnet/sapfluxnetQC1/tree/master/vignettes, last access: 8 June 2021). To aid in the detection of potential data issues throughout the entire process (Figs. 1, S1), we implemented several elements of control: (1) automatic log files tracking the output of each QC function applied, (2) automatic creation and update of status files tracking the QC level reached by each dataset, (3) automatic QC summary reports in the form of R markdown documents, (4) interactive Shiny applications for data visualization, (5) documentation of manual changes applied to the datasets using manually edited text files, (6) storage of manual data cleaning operations in text files, and (7) automatic data quality flagging associated with each dataset.
All these items ensure a robust, transparent, reproducible, and scalable data workflow. Example files for (2), (3), and (6) can be found in the Supplement. The first stage of the data QC (QC1) performed several data checks (Supplement Table  S1 ) on received spreadsheet files and produced an interactive report in an R markdown document, which signalled possible inconsistencies in the data and warned of potential errors. These data issues were addressed, with the help of data contributors if needed. Once no errors remained, the dataset was converted into an object of the custom-designed "sfn_data" class (Fig. S2 ; see also Sect. 2. 5), which contained all data and metadata for a given dataset (Tables A2-A6 list all variable names and units). Data and metadata belonging to all Level 1 datasets were further   and QC2 ).
Both QC1 and QC2 produce an. RData object of the custom-designed sfn_data S4 class storing all data, metadata, and data flags for each dataset. The progress and results of the QC processes are monitored through individual reports and log files. The final outcome is stored in a folder structure with a either single. RData file for each dataset or a set of seven csv files for each dataset. visually inspected using an interactive R Shiny application, and, if no major issues were detected, they were subjected to the second QC process, QC2.
Data harmonization and quality control: QC2 Datasets entering QC2 underwent several data cleaning and data harmonization processes (Table  S2 ). We first ran outlier detection and out-of-range checks; these checks did not https://doi. org/10. 5194/essd-13-2607-2021 Earth Syst. Sci. Data, 13, 2607-2649, 2021 delete or modify the data but only warned about any suspicious observation ("outlier" and "range" warnings). The outlier detection algorithm was based on a Hampel filter, which also estimates a replacement value for a candidate outlier  (Hampel, 1974). For the range checks, we defined minimum and maximum allowed values for all the time series variables, based on published values of extreme weather records and maximum transpiration rates  (Cerveny et al. , 2007; Manzoni et al. , 2013). The outcome of outlier and range checks were visually inspected on the actual time series being evaluated using an interactive R Shiny application (Fig.