dataesr/scientific-paragraphs-categorization huggingface dataset:
This study aims to address this by comparing the results of a range of partial melting experiments on ultramafic and mafic compositions under P-T conditions appropriate to the subcontinental lithospheric mantle (SCLM), with the results from phase equilibrium modelling conducted with multiple software packages. Additionally, thermodynamic modelling is used to produce an envelope of uncertainty around the experimental results that considers the uncertainties in Fe, H 2 O and CO 2 content that are inherent to the experimental design. By comparing the outputs produced via modelling exercises utilising pMELTS  (Ghiorso et al. , 2002)  using the embedded thermodynamic dataset from  Berman (1988) , and Rcrust  (Mayne et al. , 2016) , which performs minimisation using Perple_X in the thermodynamic dataset of  Holland and Powell (2011) , with the results of experimental studies of selected eclogitic and peridotitic bulk compositions, extended evaluation of the performance of these modelling tools across a range of temperatures at 1.
Thermodynamic modelling under upper mantle conditionsthe available tools The ongoing expansion of phase equilibrium modelling as a tool to understand metamorphic and igneous processes has produced a range of different applications  (Lanari and Duesterhoeft, 2019). This section does not attempt a comprehensive review of all of the available options for conducting modelling at upper mantle P-T conditions (see  Riel et al. , 2022; Xiang and Connolly, 2022) , rather the work focusses on the differences in modelling strategies and/or the thermodynamic datasets used in some of the commonly utilised applications, so that the nonspecialist reader can understand why the same phase equilibria modelling exercise may produce different results when processed through different applications.
MELTS family MELTS is a thermodynamic software, solution model, and dataset package designed to facilitate thermodynamic modelling of phase relations during melting and crystallisation in magmatic systems  (Asimow and Ghiorso, 1998; Ghiorso and Sack, 1995). The original MELTS package was primarily developed for fractional crystallisation processes in systems of basic composition  (Ghiorso and Sack, 1995) , having since expanded to have the widest uptake of all the thermodynamic modelling packages in the Igneous Petrology community, particularly for mantle studies. Designed principally for forward modelling of igneous processes using a constrained energy minimisation approach  (Hirschmann et al. , 1998a) , MELTS utilises embedded thermodynamic a-x models of solid and liquid phases alongside energy optimisation techniques that are dependent on the process under investigation.
These techniques utilise iterative application of three different algorithms: estimates of stable phase identities and compositions; minimisation of applicable thermodynamic potential(s) subject to compositional constraints, whilst other variables remain constant; and metastability examinations of resultant computed phases in relation to possible miscibility gaps or additional phases excluded in initial phase assemblages  (Hirschmann et al. , 1998a). For MELTS, the standard-state properties of end-member mineral components are based on the internally-consistent dataset of  Berman (1988) , with several exceptions detailed by  Sack and Ghiorso (1994)  and references therein. The mixing properties for solid solutions are drawn from several works detailed in  Hirschmann et al. (1998a). The original MELTS bundle has been superseded by several versions with modifications to allow applicability over a range of applications.
THERMOCALC The software THERMOCALC performs thermodynamic calculations using a non-linear equation approach to solve mineral equilibria problems  (Holland and Powell, 1998; Powell et al. , 1998; Powell and Holland, 1990). The THERMOCALC application utilises an internallyconsistent thermodynamic dataset to construct and solve chemical potential calculations, supplemented by mass-balance or constraints on compositional variables where necessary, i. e. by solving for the points where the change in Gibbs free energy between two potential assemblages is zero, a reaction boundary is found. This allows the prediction of phase assemblages and phase compositions by utilising both forward and inverse calculation facilities, under user-specified conditions  (Powell et al. , 1998; Worley and Powell, 2002).
The most current sets of HPxeos families are the Metapelite set  (White et al. , 2014) , suitable for use below 1. 5 GPa; the Metabasite set  (Green et al. , 2016) , suitable for use below 2. 0 GPa; and the Igneous set  (Holland et al. , 2018; Tomlinson and Holland, 2021) , suitable for partial melting of basaltic to granitic melt compositions, allowing anhydrous (≤ 6. 0 GPa) and hydrous (≤ 3. 0 GPa) calculations. These HPx-eos families are built on the revised  Holland and Powell (2011)  dataset, which has undergone several updates from its previous versions  (Holland and Powell, 1985 , 1990 , 1998). Multiple thermodynamic modelling software have implemented the use of the HPx-eos families and the  Holland and Powell (2011)  dataset, including Perple_X  (Connolly, 2005; Connolly and Kerrick, 1987)  and Theriak/Domino  (de Capitani and Brown, 1987; de Capitani and Petrakakis, 2010).
As a result, THERMOCALC and such other programs should produce identical outputs for calculations involving the same thermodynamic dataset and a-x models, as has been shown to be the case (e. g. Connolly, 2007 Connolly, , 2021;; Horváth, 2007). This application of the HPx-eos and  Holland and Powell (2011)  dataset requires regular updates across platforms, and routine benchmark comparisons provide quick insights into the correct implementation of such input data to other programs.
Theriak/Domino Theriak/Domino is a software program collection that uses a linear programming strategy combined with a Gibbs free energy minimisation calculation method to conduct and produce a wide range of thermodynamic equilibrium calculations and illustrations, including thermodynamic functions of phases, phase diagrams, equilibrium assemblages, and pseudosections  (de Capitani and Brown, 1987; de Capitani and Petrakakis, 2010). The equilibrium phase compositions and stable mineral assemblage for a bulk rock composition along a specified P-T path or set of P-T conditions is calculated using the Theriak program, and Domino is used for plotting a range of equilibrium assemblage diagrams  (de Capitani and Petrakakis, 2010). Theriak/Domino has compatibility with the currently available thermodynamic datasets, and the capability of porting most THERMOCALC HPx-eos families, as mentioned above.
Perple_X and derivatives of the program The software package Perple_X is a modular collection of subprograms created for the rapid computation of all types of phase diagrams, as well as performing general thermodynamic calculations  (Connolly, 2005; Connolly and Kerrick, 1987). By utilising a calculation method based on minimisation of total Gibbs free energy of multiple phase configurations and pseudocompounds, Perple_X programs are able to calculate the most stable set of phase equilibria for an arbitrary chosen system  (Connolly, 2005; Connolly and Petrini, 2002). The thermodynamic datasets and a-x models implemented in Perple_X can be selected from several compiled databases, as the software accepts thermodynamic data that has been suitably formatted for Perple_X from any source; as mentioned, the THERMOCALC HPx-eos families and  Holland and Powell (2011)  dataset are readily incorporated into Perple_X.
Rcrust Rcrust is a phase equilibria modelling tool that utilises the Meemum function of Perple_X  (Connolly, 2009)  to calculate phase stabilities for a series of points, inheriting databases and a-x models from Perple_X  (Mayne et al. , 2016). The Rcrust calculation strategy applies path dependencies to allow bulk compositional change via processes of mass transfer. Importantly, Rcrust strategies allow the investigation of processes dependent on assemblages evolving throughout a given P-T-X space, as changes in bulk compositions are transferred across points. Prior to passing the information along, phases can be extracted or added depending on a broad range of flexible trigger signals (e. g. mode of melt, melt viscosity, phase proportion, phase to melt ratio, etc), allowing open or closed systems.
Mayne et al. (2019)  describe the division of the full system (bulk rock composition) into a reactive subsystem and an extract subsystem, the former being the system on which phase equilibrium modelling is conducted and the latter representing the phases that have been removed from the residual system by phase extraction events. The development of Rcrust was primarily as a tool for the forward modelling of partial melting and magma generation in the crust, but the use of Perple_X formatted input data allows Rcrust to perform modelling across any P-T-X range that is compatible with the available thermodynamic datasets and a-x models  (Mayne et al. , 2019). Thus, if the P-T resolution in Rcrust is set to match the highest resolution attained by Perple_X gridded-minimisation, Rcrust and Perple_X modelled outputs will be identical if the same a-x models are utilised.
Both methods will likely result in some C-bearing gas species in the charge prior to melting. In thermodynamic modelling, bulk compositions and fluid states are set, and analytical errors sensu stricto are non-existent. Nevertheless, the internal consistency of thermodynamic datasets are important in their perceived accuracy; internal consistency is dependent on the thermodynamic properties of pure phases and end-members in thermodynamic datasets, and their interactions with a-x models  (Lanari and Duesterhoeft, 2019). These thermodynamic properties, together with the formulation of a-x models, can be a great source of systematic uncertainties  (Berman, 1988; García-Arias, 2020; Holland and Powell, 2011; Powell, 1985; White et al. , 2014). For example, the complexity of certain chemical components, such MnO, NiO, and P 2 O 5 , currently inhibit the development of complete a-x models to describe the activity relations of mineral phases that incorporate these components  (Gervais and Trapy, 2021).
The omission of these components from thermodynamic datasets is likely to be an important source of error when modelling rock compositions where these components are important to the stability of one or more phases (e. g. Forshaw et al. , 2019; García-Arias, 2020). Consequently, an important consideration of thermodynamic modelling is that these calculations are wholly dependent on the input thermodynamic data, and the outcomes remain a simplification of natureeven with extended chemical systemsonly reporting approximations of phase behaviours that also do not consider any kinetics, such as crystal sizes, crystal growth and nucleation, and diffusion, amongst others (García-Arias, 2020;  White et al. , 2011).
Pertermann and Hirschmann (2003a, 2003b ) also report packing capsules in a layer of Fe 2 O 3 powder to reduce the influx of hydrogen to the experiments, a potential source of H 2 O in the capsules. In all of the studies, capsules were loaded and welded in an air environment, and therefore the development of CO 2 and CO from the reaction of air with the graphite liner is inevitable. Both H 2 O and CO 2 lower the mafic and ultramafic rock solidi at upper mantle pressures. As Similarly, the effects of the loss of Fe to the capsule were also investigated, the details of which are described below. The thermodynamic modelling software utilised in the comparative study investigating closed system evolution includes pMELTS (mafic and ultramafic compositions) and Rcrust (ultramafic to intermediate compositions).
The outcomes for all comparisons have been recorded in Appendix A. Firstly, runs were performed for each P-T point listed in the relevant experiments using the latest pMELTS (version 5. 6. 1. ) bundle in the NKCFMASTOCr (Na 2 O-K 2 O-CaO-FeO-MgO-Al 2 O 3 -SiO 2 -TiO 2 -Fe 2 O 3 -Cr 2 O 3 ) chemical system, embedded with the thermodynamic dataset from  Berman (1988)  with modifications detailed in  Ghiorso et al. (2002) , and a-x models included in the pMELTS calibration. The system was considered H 2 O and CO 2 free, and the fO 2 was set along the C-COH buffer for the three source compositions. Phase assemblages, phase proportions, and phase compositions were recorded at the specific P-T conditions of each experiment performed in the experimental set within the range of 1. 0 to 3. 0 GPa. As pMELTS outputs FeO and Fe 2 O 3 , direct comparison to experimental results required recalculation to FeO t.
Secondly, runs were performed for each P-T point listed in the relevant experiments in the NKCFMASTOCr chemical system using Rcrust version 2022-09-03, the 2022 revised hp634ver. dat thermodynamic data file from Perple_X, and the internally consistent dataset of  Holland and Powell (2011). The following a-x models were used: Cpx (TH) for clinopyroxene, Gt(TH) for garnet, Opx(TH) for orthopyroxene, Sp(TH) for spinel, and melt(TH) for melt  (Tomlinson and Holland, 2021) , O(HGP) for olivine  (Holland et al. , 2018) , Fsp(C1) for plagioclase and potassium-feldspar  (Holland and Powell, 2003) , and Ilm(WPH) for ilmenite  (White et al. , 2000). Adjustments made to a-x model parameters are listed in Appendix A. Similar volatile content and fO 2 constraints were applied as is described for the pMELTS bundle; data was also recorded similarly.
Thirdly, the effects of Fe loss, and H 2 O or CO 2 addition was modelled similarly to that described above, with changes made to the reported bulk compositions of KLB-1 and MM3 assuming either a 10% decrease in the FeO t content, or the inclusion of 0. 05 wt% H 2 O, or 0. 08 wt% CO 2 in the capsule. These are upper realistic boundaries for water adsorbed to the charge and liner and CO 2 production by air included the capsule. Runs were performed using Rcrust in a similar manner as above, but using the 2020 revised hp633ver. dat thermodynamic data file from Perple_X, and the following a-x models: Cpx(HGP) for clinopyroxene, Gt (HGP) for garnet, O(HGP) for olivine, Opx(HGP) for orthopyroxene, and Sp(HGP) for spinel  (Holland et al. , 2018) , melt(HGPH) for melt  (Heinrich and Connolly, 2022; Holland et al.
MM3: partial melting of peridotite under upper mantle conditions Comparison of the MM3 experiments with the results from pMELTS have previously been conducted by  Ghiorso et al. (2002) , however, the comparison has been repeated here to analyse predicted peridotite partial melting behaviour in Rcrust at 1. 0 GPa using a more detailed experimental dataset. In this study, both the experiments and modelling agree in the presence of olivine, orthopyroxene, clinopyroxene, spinel and melt, with Rcrust predicting 100% and pMELTS almost 95% of the assemblage, as is reported in Table  4. Comparisons between abundances of melt, clinopyroxene, orthopyroxene, olivine and spinel as a function of temperature at 1. 0 GPa are illustrated in Fig. 3. Fig. 4  displays components from the experimental and modelled melt compositions as a function of increasing melt fraction (in wt%) and increasing temperature.
G2: partial melting of eclogite under upper mantle conditions Both the experiments and modelling agree in the presence of clinopyroxene, garnet, rutile, quartz, plagioclase and melt, with a higher Qasm for Rcrust as is reported in Table  5. Due to the limited phase proportion data reported in the experimental study at 2. 0 GPa and only a Fig. 2. Modelled melt fractions at 1. 5 GPa and 3. 0 GPa from pMELTS and Rcrust as determined in this study, compared with melt fractions from the experimental study on KLB-1 of  Takahashi et al. (1993)  at 1. 5 GPa (the only pressure that phase proportion information was reported in the experimental study within the pressure range of 1. 0 to 3. 0 GPa). At 1. 5 GPa, pMELTS predicts the liquidus to be at much lower temperatures than the experiments, whereas there is excellent agreement between melt fraction (and consequently, olivine consumption) predicted by Rcrust and the experiments.
For the eclogite, Rcrust predicts increased garnet and decreased clinopyroxene proportions as compared to the experiments (Fig. 5 ). Clinopyroxene is consumed more rapidly, and due to its lower proportions, is exhausted at the same temperature as garnet. Conversely, because clinopyroxene has higher proportions in the experimental results, it is exhausted at a higher temperature due to its rate of consumption. Although this difference influences the melt proportion at lower temperatures, the curve of the melt fraction mostly follows that of the experiments and thus produce mostly similar melt compositions, apart from FeO content (Fig. 6 ). Similar behaviour can be noted in Fig. 3 , although melt components show notable variation from experimental results for peridotite partial melting. It is clear that the discrepancies displayed by pMELTS and Rcrust compared to experimental results are likely as a result of differences in the thermodynamic datasets and formulation of the a-x models (particularly the melt a-x model), because the calculation strategy of the software are reported as similar (Table  1 ).
The interactions of a-x models with the thermodynamic dataset should also be taken into consideration. The input data clearly result in notable variance across P-T-X space, but unfortunately, due to the embedded nature of these input components in the pMELTS software, this cannot be investigated in more Fig. 5. A comparison of melt (glass), clinopyroxene, garnet, quartz and rutile abundances at 3. 0 GPa from the experimental study on G2 of  Pertermann and Hirschmann (2003a) , with the calculated values from pMELTS and Rcrust as determined by this study. pMELTS predicts the liquidus to be at much higher temperatures than the experiments, whilst there is good agreement between the curve of the melt fraction predicted by Rcrust and the experiments. This is similarly observed for rutile and quartz (although greater phase abundances are predicted by Rcrust), which was not predicted by pMELTS.
As discussed in-text, pMELTS indicates significantly lower values for several of the melt phase components, showing bad agreement with experimental melts in terms of melt fraction and temperature. detail. Similar discrepancies have been noted where software utilise the same thermodynamic dataset and related a-x models, which may be a result of two important factors: The requirement of HPx-eos families to be formatted for use in Perple_X (and subsequently, Rcrust and others) mean that small oversights or mistakes, or even a delay in the formatting process can easily result in a mismatch in the predicted outcomes. The second factor is the calculation method of the software, where different strategies can cause mismatches due to user-specified parameters inherent to the strategy. For example, failing to identify assemblage tielines in THERMOCALC could exclude an entire assemblage field from the pseudosection, or not implementing the appropriate resolution in Perple_X (and Rcrust) would cause a failure to identify phases or even small assemblage fields.
Conclusions This comparative study supports two primary conclusions. Firstly, when compared with experimental results, the use of phase equilibrium modelling routines is a viable method for analysing the phase assemblages, proportions, and compositions in ultramafic and mafic rock compositions under SCLM P-T conditions. This approach should be seen as complementary to experimental work, with several advantages such as being an extremely rapid form of investigation when compared to experimental studies, allowing greater P-T-X resolution and control over the incorporation of volatiles, as well as their fugacities. Secondly, Rcrust using Gibbs free energy minimisation from Perple_X, the internally consistent dataset of  Holland and Powell (2011) , and the a-x models of clinopyroxene, garnet, orthopyroxene, spinel, and melt  (Tomlinson and Holland, 2021) , olivine  (Holland et al.
, 2018) , feldspar  (Holland and Powell, 2003) , and ilmenite  (White et al. , 2000) , generally mapped out melt production and compositions reliably at SCLM P-Ts, when compared with the experimental results. The software, a-x models and thermodynamic dataset are a good combination for studying petrogenic processes where the melt fraction changes significantly within the P-T-X range of this study, and for compositions that range from ultramafic to mafic. This, in combination with the capability of Rcrust to allow phase extraction and accommodate the resultant bulk compositional change, makes the Rcrust methodology presented here well-suited for the study of partial melting reactions in the upper mantle, including the effects of magma segregation.
Acknowledgements The authors thank  M. Garçia-Arias  and an anonymous reviewer for their comments and suggestions that aided in the improvement of this manuscript. This work was supported by the  South African National Research Foundation (NRF)  through the  South African Research Chairs Initiative (SARChI)  awarded to  G. Stevens , and the  BuCoMO International Research Project (IRP)  by the  French Centre for Scientific Research (CNRS)  and the  NRF.
14, 18  The development of tools capable of predicting the properties of polymers, both via molecular dynamics (MD) and machine learning (ML), without resorting to the complete and heavy experimental procedure of synthesis and characterization, has the potential to dramatically accelerate the identification of promising candidates for targeted applications. Such approaches already appear as a cornerstone of the transition towards a greener and more circular economy, as they allow to study more chemicals in less time, provide deep atomistic insights, reduce laboratory-generated waste, and decrease the risk of R&D. Thanks to the important on-going effort undertaken in many fields of material sciences to collect, curate and provide access to both empirical and computational databases of materials and to the development of publicly accessible ML resources and tools, the design of new materials has already started to integrate data-driven approaches.
19, 20  This is particularly attractive in polymer science, because, as soon as one starts combining monomers in copolymers, with different ratios and synthesis conditions, one is facing a combinatorial wall of possibilities. The Polymer Genome platform  21, 22  is a bright example of a commercial endeavor that harnesses data spanning from the general polymer literature to density functional theory (DFT) calculations, in order to predict a series of polymer properties from the SMILES code 23 of the polymer. Some examples of these polymer properties are the glass transition temperature, polymer compatibility with 24 solvents, or polymer gas permeability. In order to extend their work to copolymers,  24, 25  the same group collected more than 7,500 data points (which corresponds to about 40% of their final dataset) from the PoLyInfo database.
26  While others also report having collected large amount of data for more than 12,000 homopolymers from PoLyInfo,  27, 28  MatNavi, the database service hosting PoLyInfo, now explicitly forbids the "acquisition of large amounts of data, whether by manual or mechanical means". 29  Therefore, as pointed out by Gormley et al. ,  30  even though several polymer databases have been assembled, their data are not freely accessible in a downloadable and programmatic manner. 26, [31] [32] [33]  Consequently, a series of works have assembled disparate datasets for the prediction of a variety of properties, from the ionic conductivity of solid polymer electrolytes  34  to the Young modulus of polyurethane elastomers  35  or the performance as organic photovoltaic material. 36  More detail on the exciting progresses of the polymer informatics community can be found in several recent review articles.