dataesr/scientific-paragraphs-categorization huggingface dataset:
Characteristic dimensions Pore, strut, and node dimensions (d p ,d s ,l s ,d n ) were extracted directly from the 2D micro-CT images. In order to estimate the pore diameter (d p ), we first accurately evaluated the area of each pore (cross-sectional area of the void space) using the FijiImageJ software, then the diameter of an equivalent circle was determined (Fig. 2. A). As reported in our previous work (Moncada  Quintero et al. , 2021a) , the circular pore shape assumption can be perfectly adopted for the analysis of foams as catalytic supports, even if the structures present mostly oval pores. As for the strut, because during the manufacturing process the ceramic precursor slurry is deposited mostly at the nodes instead of being homogeneously distributed along the length, the strut exhibits a variable cross-section with diameter values that reach a maximum at the intersections (nodes) and a minimum at the center of its length.
Funding sources This work was supported by the  Italian Ministry of University and Research (MUR, Italy) , via the  ERANETMED network (SOLCARE project , grant number  ENERG-065 ). The stay of C. W. M. Q. at  IFP Energies Nouvelles , site of Solaize (France) was funded by the  Erasmus+  traineeship from the  Politecnico di Torino  ( European Charter  for Higher Education  28995-LA-1-2014-1-IT-E4AKA1-ECHE ).
At least six liquid phase samples are routinely analyzed to ensure reproducibility at the equilibrium pressure and temperature. The equilibrium pressure inside the HP cell does not change, due to the small sample amounts. Utilizing the proper chromatographic syringes and known dosages of each chemical, the TCD is calibrated for carbon dioxide and 2,4-dimethylpentane. In order to determine the component's mole number in relation to the chromatographic area, calibration data are correlated to quadratic polynomials. The gas chromatograph calibration curves have the Pearson coefficients of 0. 9999 for CO 2 and 0. 9986 for 2,4-DMP. It was previously explained how to estimate the uncertainty in all variables and properties  [51, 52]. The platinum temperature sensor attached to a device with digital display was calibrated at the Romanian Bureau of Legal Metrology using a digital accurate thermometer with a PT 100 sensor.
The critical parameters as well as the acentric factors of the two pure compounds utilized in the computations are presented in Table  2. In recent papers  [1, 2, 48] , it was shown that the choice of critical parameters and acentric factors of pure compounds are important, but in this case the values for the 2,4-DMP branched alkane are similar in different databases. Therefore, we chose the values given in the DIPPR database  [58] , as recommended in other papers  [59, 60]. The modeling approach for the carbon dioxide + 2,4-DMP was threefold steps. Firstly, the experimental data at each temperature were correlated with all three EoSs, coupled with one-parameter conventional mixing rules, 1PCMR. The optimized values of binary interaction parameter k ij calculated for each of the four measured temperatures were averaged and this value was then used to model the critical curves.
The critical curve was also calculated with the PPR78 model  [38]  and compared with the SRK, GEOS, and PR results. Secondly, the experimental data were fitted with GEOS, PR, and SRK and two-parameter conventional mixing rules, 2PCMR. The binary interaction parameters (BIPs), k ij and l ij , are calculated by minimizing the next objective function: F ob = ∑ N i=1 ( P exp i -P calc i P exp i ) 2 (35) The optimized values of the binary interaction parameters, k ij and l ij , at each temperature and for each model were averaged and the median values were used to model the critical curves. For the Peng-Robinson model, we compared both bubble point pressures  [51]  and flash calculations. In the latter case, phase diagrams were generated by successive T, P-flash calculations, using the Peng-Robinson equation of state, combined with a two-parameter van der Waals-type mixing rule as the underlying thermodynamic model.
The computations were made using our internal software tool entitled "Phase Equilibria Database and Applications -PHEQ"  [65]  and with "Global Phase Equilibrium Calculations -GPEC" software  [64, [66] [67] [68]. The critical lines were calculated with the CRITHK dedicated module of PHEQ, in which the technique given by Heidemann and Khalil  [69]  with the numerical derivatives provided by Stockfleth and Dohrn  [70]  is implemented, the in-house software developed by  [71] , and GPEC.
Experimental results VLE data (P-X, Y) for the CO 2 + 2,4-DMP binary mixture were experimentally determined at four temperatures (323. 15 K, 343. 15 K, 363. 15 K, and 383. 15 K), and in the pressure range spanning from 10. 4 to 120. 4 bar. The isotherms are shown in Table  3 , and mole fractions are represented with four significant figures, as resulted from the uncertainties calculation  [4, 51, 53]. The critical curve was also examined beginning at the CO 2 critical point and continuing up to 422. 35 K. The greatest pressure, which corresponds to the critical pressure maximum (CPM), was 121. 4 bar. The results are shown in Table  4  together with their standard uncertainties evaluated as explained in ref. [72]. Fig. 1  illustrates the isotherms determined in this study located in the supercritical region of CO 2 , while Fig.
Modeling results with GEOS/1PCMR, SRK/1PCMR, and PR/ 1PCMR The isothermal data were correlated with SRK, GEOS, and PR/ 1PCMR using the critical parameters and acentric factors provided Standard uncertainties: u(T) = 0. 1 K, u(P) = 0. 1 bar, u(X 1 ) = 0. 001; a DIPPR  [58]  values; b interpolated values. DIPPR database  [58]  (Table  2 ) and the results are presented in Table  5. The average absolute deviations in bubble-point pressures (AADP, %) and the average absolute deviations in the vapor-phase compositions (AADY, %) are determined using the following equations: AADP ( % ) = 1 N exp ∑ Nexp i=1 ⃒ ⃒ ⃒ ⃒ P exp i -P calc i P exp i ⃒ ⃒ ⃒ ⃒ × 100 (25) AADY ( % ) = 1 N exp ∑ Nexp i=1 ⃒ ⃒ Y exp i -Y calc i ⃒ ⃒ × 100 (26) The smallest errors both in bubble-point pressures and vapor-phase compositions are achieved with SRK/1PCMR, followed closely by PR/ 1PCMR, and the largest ones are obtained with the GEOS/1PCMR model (Fig.
The enlargement of Fig. 6 (a ) is shown in the Supplementary Information as Fig. 14S , while Fig. 7  depicts the comparison of the critical experimental data and the SRK equation of state with the average values of BIPs (k ij = 0. 0569; l ij = 0. 0388). In Fig. 7 (c ), the projection of the LLV line is also shown. The AADP, % and AADY, % are slightly larger for the average values of the BIPs, as can be seen in Table  7 , compared with the regression results. The isothermal experimental data, the correlation results, and the calculations with the average values of the BIPs are compared and plotted in Figs. 15S (GEOS), 16S (PR), and 17S (SRK). The differences between the representations with the optimized values of the BIPs and their average values are very small and therefore hardly visible.
Conclusions Vapor-liquid equilibrium data at constant temperatures and VL critical data are reported for the first time for the CO 2 + 2,4-DMP binary system. The experiments were performed in a visual HP static-analytic installation. Pressurecompositions diagrams were measured at 323. 15 K, 343. 15 K, 363. 15 K, and 383. 15 K and pressures ranging between 10. 4 and 120. 4 bar. The vapor-liquid critical curve (pressures, temperatures, CO 2 compositions) was measured up to the maximum critical pressure of 121. 4 bar and the greatest temperature of 422. 35 K. The GEOS, Peng-Robinson, and Soave-Redlich-Kwong EoSs together with one-and two-conventional parameters mixing rules were used to successfully model the phase behavior of the CO 2 + 2,4-DMP system.
X-ray structural analyses A single crystal of each compound was mounted under inert perfluoropolyether at the tip of a glass fiber and cooled in the cryostream of a Rigaku Oxford-Diffraction XCALIBUR Gemini EOS diffractometer for H 2 L1, a Nonius Bruker APEXII diffractometer for 4⋅CHCl 3 and a Bruker APEXII for 5. The structures were solved by using the integrated space-group and crystal structure determination SHELXT software  [57]  and refined by least-squares procedures on F 2 using SHELXL-2014  [58]. All H atoms attached to carbon or oxygen atoms were introduced in the calculations at idealised positions and treated according to the riding model. Compound 4⋅CHCl 3 is a dinuclear complex arranged around an inversion centre, with half a molecule within the asymmetric unit. The two tertbutyl groups (C18 and C28) are statistically disordered.
Acknowledgements The authors thank the  Agence Nationale de la Recherche, France  (Grant  ANR-19-CE07-0031-01 ,  POLYSWITCH ) for support of this work. Additional support by the  Ministère de l'Enseignement Supérieur et de la Recherche Scientifique, France (PROFAS B+  fellowship to Y. K. R), the  Centre National de la Recherche Scientifique (CNRS, France)  and the  Institut Universitaire de France  ( IUF, France ) are also gratefully acknowledged.
The objective is to benefit from a method allowing for performing multiple simulations to optimize burners and boilers, thanks to a CPU time kept to a minimum after training a set of neural networks to process the expensive time integration of the stiff chemical system of equations. Indeed, machine learning is now a standard ingredient of computational combustion  [11]. It is used for building sub-models from various databases used to train neural networks (including DNS or canonical problems) or to reduce CPU time by replacing specific costly numerical operations performed during the solving of the aerothermochemical equations. Pioneer works in the field have discussed an integrated probability density function/neural network approach for simulating turbulent reacting systems  [12]. Artificial neural networks were also used in the 90's to model the temporal evolution of reduced combustion chemistry  [13].
The influence of kinetic uncertainties on the accuracy of numerical modeling of an industrial flameless furnace fired with NH 3 /H 2 blend was addressed in a combined experimental and numerical study  [36, 37] , also examining the role of mixing models in MILD combustion  [38]. The specific aspect of internal recirculation and how it impacts on modeling accuracy was carefully examined  [39]  along with strategies for hydrogen-enriched methane flameless combustion  [40]. Here we start by devising a procedure to build, from a detailed chemical combustion kinetics, a database representative of the thermochemical conditions which can be expected in a flameless furnace. The method relies on stochastic micro-mixing, including the specific high-dilution rates and heat-losses as observed in the UMONS furnace studied experimentally  [8] [9] [10].
From this database, a set of neural networks are trained to return the increment in species mass fractions and temperature for a given thermochemical state. These networks are then introduced in a Large-Eddy Simulation (LES) flow solver to be combined with a simple formulation of turbulence/chemistry interaction modeling, in order to simulate the furnace and results are compared against experimental measurements. The subsequent section reports on the flow configuration, the numerical methods and turbulence modeling. After that, the focus is on the structures of the networks and their training in view of combustion chemistry integration in LES. The training database is presented and verified, with a discussion on the compromise between multiplying the Fig. 2. UMONS furnace configuration and mesh.
Flow solver and modeling The Navier-Stokes equations (momentum, energy and species mass fractions) are solved using the open source software Code_Saturne  [44]. It relies on a co-located second order accurate cell-centered finite volume approach operating over unstructured grids. The full volume of the furnace is meshed, including the 12 exhaust cylinders, with a non-uniform mesh of 12 million cells, featuring tetrahedrons and hexahedrons (Fig. 2 ). On the bottom wall where gases are injected, the mesh is so that 𝑦 + is just below unity, while 7 < 𝑦 + < 15 on the lateral walls. The mesh is strongly refined in the shear layers developing downstream of jet injection with a resolution down to 0. 2 mm. From previous RANS simulations  [10] , the integral length scales in the shear layers are about 10 mm and 5 mm in the air and the gas jets.
Training database The strategy for building the neural networks training database relies on previous works  [19, 57]. Stochastic micromixing modeling is combined with complex chemistry to generate, prior to any flow simulation, the variety of thermochemical conditions expected in the combustion system. In this approach, the fraction of flow rate injected through a given inlet defines the number of stochastic particles taking  the thermochemical properties of that inlet at initial time. Each particle carries information on the species mass fraction vector and enthalpy. From this non-premixed initial condition, the stochastic particles evolve in time according to 2   𝜕𝑌 𝑝 𝑘 (𝑡) 𝜕𝑡 = MIX 𝑝 (𝜏 T ) + ω𝑝 𝑌 𝑘 , ( 4 ) 𝜕ℎ 𝑝 𝑠 (𝑡) 𝜕𝑡 = MIX 𝑝 (𝜏 T ) + ω𝑝 ℎ 𝑠 + 𝛼 𝑙𝑜𝑠𝑠 (𝑇 𝑝 -𝑇 𝑤𝑎𝑙𝑙 ). ( 5 ) 𝑌 𝑝 𝑘 (𝑡) is the mass fraction of the 𝑝th particule, MIX 𝑝 (𝜏 T ) denotes the Euclidian Minimum Spanning Tree micromixing model  [60]  and ω𝑝 𝑌 𝑘 is the chemical source.
The characteristic value of the micromixing time, 𝜏 𝑇 = 0. 3 ms, was determined from previous simulations of the furnace  [10]. Varying 𝜏 𝑇 in Eqs. (  4 )-(  5 ) around its nominal value was found to have a relatively weak impact for the purpose of database generation in view of chemistry reduction, at least as long as ignition occurs  [58]. To account for the non-adiabatic character of the flow, a linear heat loss term is added and calibrated with the variable coefficient 𝛼 𝑙𝑜𝑠𝑠 , the temperature of the particle 𝑇 𝑝 and the average wall temperature measured in the experiments 𝑇 𝑤𝑎𝑙𝑙 = 1259. 4 K. The parameter 𝛼 𝑙𝑜𝑠𝑠 is chosen so that the mean chemical equilibrium temperature of the ensemble of stochastic particles ranges between 1200 and 1500 K, as reported experimentally in the recirculating burnt gases.
The first training database is then composed of three set of stochastic particles evolving from their initial condition up to equilibrium, for 𝛼 𝑙𝑜𝑠𝑠 taking the values 3 ⋅ 10 5 , 5 ⋅ 10 5 and 7 ⋅ 10 5 W kg -1 K -1. Eqs. (  4 ) and (  5 ) are solved with routines from the Cantera package  [61]. Three inlets are imposed to build every set of time evolving stochastic particles. These inlets carry respectively the B50 gas, air and a given amount of recirculating equilibrium burnt products (Table  1 ). This third inlet is necessary because with separated jet injection, the reactants are mixed with recirculating burnt gases before they meet and this specific behavior must be included in the training thermochemical dataset. The estimated mass flow rate of recirculating burnt gases, as provided experimentally, is given in Table  1.
Clustering thermochemical data and ANN structure A single neural network cannot handle the large variety of chemical conditions seen by the gases during their evolution from injection up to chemical equilibrium. Following a previously develop approach  [57] , the dataset is first decomposed in clusters and a dedicated neural network will be affected to every cluster. Multiplying the numbers of ANN to secure precision does not increase significantly the CPU time of the flow simulation, as all the ANNs are implemented as subroutines in the computational fluid dynamics (CFD) solver and called according to the thermochemical composition space location of the mesh cell to be advanced in time. However, this considerably impacts on the CPU devoted to training, as discussed in the next subsection.
The decomposition of the dataset into subdomains implies the application of pre-treatments, such as centering, rescaling and clustering with K-means. [64]. More precisely, we use the K-means++ algorithm  [65] , which stands as a well-established unsupervised machine learning algorithm to group similar data into different clusters. The algorithm assigns randomly a first centroid, a second centroid is then chosen as farthest as possible to the first centroid, a third centroid is as farthest as possible to the first two centroids, and so on. Then, every data point is assigned to the cluster with the shortest Euclidean distance in the multi-dimensional composition space. The centroid locations are updated by averaging all data points in each cluster and the process is repeated until the centroid locations are converged by evaluating the shifting tolerance which is chosen at 10 -20.
During LES, from the input state vector composed of the species mass fractions and temperature, the Euclidean distance to each cluster centroid is calculated. The LES mesh point is then assigned to the cluster located at the minimum distance. The ANN regression structure (Table  2 ) is similar to previous works  [19]  (Table  2 ). Every ANN consists of 1 input layer, 4 dense hidden layers with the rectified linear activation function (ReLU) and 1 output layer. The total number of parameters (weights and biases) is 179851. The database is split into training set (81%), validation set (9%) and test set (10%) for model verification. The training is performed for a fixed time-step of 5 ⋅ 10 -7 s. The training process is performed using Tensorflow 2 with GPU support (NVIDIA GeForce GTX 1080 Ti) and the Adam optimizer in default setting.
ANNs verification and database blurring The ANNs are trained to return the increments, or source terms, for the species mass fractions and temperature, knowing the vector of species mass fractions and temperature (ANN input). To verify the quality of the training, the evolution of the stochastic particles is simulated again from Eqs. (  4 ) and (  5 ), but replacing the computation of the chemical sources from the detailed mechanisms by the ANNs output. The strategy reported in previous works  [19]  is applied to fully insure mass conservation after the removal of the less influential species. The mass imbalance in the source of atom A is measured for reduced set of species 𝛥 ωA = 𝑁 𝑟 𝑠 ∑ 𝑖=1 𝛽 A,𝑖 𝑊 A 𝑊 𝑖 ω𝑖 , (6) where 𝑊 A and 𝑊 𝑖 are molar weights and 𝛽 A,𝑖 the number of atom 'A' in the 𝑖th species.
As a matter of fact, within the UMONS furnace, the diversity of the thermochemical conditions are more pronounced than those generated by the canonical problem reported above. One of the major issue lies in the huge variability in the amount of burnt gases locally mixed with the reactants, mainly because the recirculation rate of burnt products is far from being uniform in space. The fuel may for instance be mixed only with burnt gases without air within coherent flow structures, which are then convected quite far downstream before meeting air. (See Figs. 11  and 12 ). A successful attempt was made to extend the above database by considering additional levels of burnt gases recirculation, i. e. , varying the amount of stochastic particles within the third inlet of the model problem (Eqs. (  4 )-(  5 )).
However, these additional levels coupled together with the different heat-loss levels lead to a computing effort for training which rapidly became prohibitive. Following previous works in which the control of database augmentation combined with improvement in training efficiency was achieved from a systematic blurring  [19, 21, 25] , 5% of Gaussian noise is added to all variables in all cases of the above dataset, still conserving mass thanks to Eqs. (  6 )-  (7). The final database contains 25. 238. 581 rows. The training is performed following the very same procedure reported above but in parallel using 8 GPUs (NVIDIA Tesla K80) and it is completed in about 7 h runtime. Fig. 10  shows the temperature and CO 2 responses in mixture fraction space for the noised database. Following the same procedure as above, the ANNs obtained with this noised database are verified by solving Eqs.
Acknowledgments The Ph. D. of the first author is funded by  ANRT (Agence Nationale de la Recherche et de la Technology), France and ArcelorMittal, France  under the CIFRE No. 2019/0056. This work is also supported by  ADEME (Agence de l'Environnement et de la Maîtrise de l'Energie), France  under the project  IGAR  ( Injection de Gaz de Recycle)  Grant  Nb 1882C001. Computing resources were provided by CRIANN (http: //www. criann. fr).
In our experiment, the temporal luminous waveform was optically detected by a remote sensing device consisting in a small telescope and a photodiode. By aiming the telescope at the selected lamp, its luminous temporal waveform was detected and sent to the reference input of optical lock-in spectrometer. The results showed that the spectral power distribution of each LED lamp was accurately retrieved and the background (up to 30 times greater than the weakest signal) was rejected. The lock-in modulation amplitude spectra were used to determine color parameters with excellent agreement with data measured individually in the conventional unlocked manner without background light. The ratio between the Fourier amplitude of the temporal waveform and its dc value provided a scaling factor allowing the absolute irradiance and illuminance of each LED lamp to be measured in the presence of the background lights.
Characterizations X-ray powder diffraction (XRD) patterns were recorded at room temperature in the 10-90 • 2θ range with a step size of 0. 0261 • and an effective scan time per step of 40 s using a PANalytical X'Pert Pro diffractometer (Cu-L2,L3 radiation, λ = 1. 5418 Å, 40 kV,40 mA, PIXcel 1D detector). Data collector and HighScore Plus programs were used, respectively, for recording and analysis of the patterns. The XRD patterns for Rietveld refinements were collected at room temperature in the 5-120 • 2θ range with a step size of 0. 0131 • and an effective scan time per step of 200 s. All calculations were carried out with Fullprof and WinPLOTR programs  [42, 43]. Nitrogen and oxygen contents were determined with a LECO TC-600 Analyzer using the inert gas fusion method in which nitrogen and oxygen contents were measured as N 2 by thermal conductivity and as CO 2 by infrared detection, respectively.
Powders morphology was examined by scanning electron microscopy (SEM) with a JEOL JSM 7100 F equipment operating at a 6 mm working distance, with an accelerating voltage of 20 kV. Energy dispersive X-ray spectroscopy (EDS) characterizations were performed using a JEOL IT300 microscope operating at a 10 mm working distance, with an accelerating voltage of 20 kV and a probe current of 7. 45 nA. Sample preparation consisted in powder deposition on a carbon tape then metallization with gold. Diffuse reflectance spectra were collected using a Varian Cary 100 Scan spectrometer equipped with a Varian WinUV software and a Labsphere DRA-CA-30I 70 mm integrating sphere. Experimental data were collected within the 200-800 nm range with a 1 nm step. Band gaps of the materials (E g ) were estimated using the Kubelka-Munk formalism  [44].
Acknowledgments The instrumental development and the quantification algorithm were funded via a collaboration between the  GSMA laboratory  of the  Université de Reims Champagne-Ardenne (URCA)  and the  R&D LQA laboratory of TotalEnergies , within the frame of the  AUSEA  project and the common  laboratory LabCom LYNNA  (hosted by  545 CNRS ,  URCA  and  TotalEnergies). Observations around offshore platforms were conducted from a supply boat chartered by TEPNL from  Den Helder  harbor. We thank the crew for their assistance and all the affiliated people that helped us to manage those experiments. Participations to the TADI campaign were possible thanks to the facilities and assistance of the  TotalEnergies 550 TADI  teams from the  PERL (Pôle d'Etude et de Recherches de Lacq) , who organised the controlled releases.