Composition Engineering on the Local Structure and Viscosity of the CaO-SiO 2 -Al 2 O 3 -P 2 O 5 -FeO Slag by Machine Learning Methods

: Due to the high cost and low accuracy of high-temperature tests, the viscosity data for multicomponent slag systems is difﬁcult to be obtained precisely. Therefore, it is important to fulﬁll the viscosity database of the multicomponent slag systems via reasonable methods with lower costs. In this study, a viscosity prediction method based on the machine learning method was proposed for the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 quinary slag system. To provide valid data for the machine learning model, the viscosity predicted by the molecular dynamic method and multiple semi-empirical models were compared to verify the applicability of these methods to the slag system. Different machine learning models were also developed. The results showed that the prediction results from the gradient boosting decision tree method were the most accurate for the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 quinary slag system. Based on this method, a color-map concerning the numerical effect of Al 2 O 3 and P 2 O 5 contents and slag viscosity is provided, which also provides assistance for the composition engineering to fulﬁll a certain demand on the viscosity design.


Introduction
Slag is widely applied in the ironmaking and steelmaking process for steel purification. Many scholars are studying the online modification of hot steel slag [1] to obtain slag with practical application effects by adjusting its physical phase and microstructure [2,3]. Among all the slag properties, viscosity is one of the most important properties concerning the smelting performances of the slag. The slag viscosity determines the fluidity of the slag, the speed of mass transfer in the slag, the effect of slag-steel separation, and the metal yield. Wang [4] investigated the changes in the CaO-SiO 2 -Al 2 O 3 -MgO-Fe t O-P 2 O 5 slag system caused by the composition change of P 2 O 5 and Fe t O by Raman spectroscopy, Fourier transform infrared reflection, nuclear magnetic resonance, and viscosity measurements, reporting that P 5+ copolymerizes with [SiO 4 ]. Therefore, the increase in P 2 O 5 leads to an increase in polymerization degree and viscosity. Wang [5] also claimed that the slag polymerization and the viscosity of the CaO-SiO 2 -Al 2 O 3 -MgO-FeO slag system increase with the increase in Al 2 O 3 content based on Raman and magic angle spinning nuclear magnetic resonance.
However, the experiments still have limitations. Besides the difficulties to conduct experiments at such a high temperature, the instrumentation, fluid state, and homogeneity can all contribute to errors in the experimental results. Seshadri et al. [6] suggested that the most effective way to confirm viscosity is to repeat the experiment on two devices with overlapping shear rate ranges but with different modes of operation. As components in the slag system increase and the temperature rises, less experimental data are available. To In this study, a cubic box of approximately 5000 atoms was built. The size of the box was determined by Equations (1) and (2).
(1) (2) where ω(MO)% is the mass fraction of the oxide composition in the slag, T is the actual temperature of the system, and ρslag is the density of slag melt, g/cm 3 .
The Born-Mayer-Huggins interatomic potential function and Lennard-Jones twobody potential function were adopted in the present simulations. These two potential functions have been widely used in silicate systems and showed good results [15][16][17]. The functions are shown in Equations (3) and (4), and the parameters are shown in Table 1.
where Uij(r) is the interatomic pair potential, qi,qj is the ionic charge, rij is the inter-ion distance, Evdw describes the van der Waals force interactions, Dij is the well depth, and xij is van der Waals bond length. Table 1. The potential function parameters used in this calculation [15][16][17].
where ω(MO)% is the mass fraction of the oxide composition in the slag, T is the actual temperature of the system, and ρ slag is the density of slag melt, g/cm 3 . The Born-Mayer-Huggins interatomic potential function and Lennard-Jones two-body potential function were adopted in the present simulations. These two potential functions have been widely used in silicate systems and showed good results [15][16][17]. The functions are shown in Equations (3) and (4), and the parameters are shown in Table 1.
where U ij (r) is the interatomic pair potential, q i ,q j is the ionic charge, r ij is the inter-ion distance, E vdw describes the van der Waals force interactions, D ij is the well depth, and x ij is van der Waals bond length. The simulation process was carried out with the melt quenching method. In the beginning, each sample was relaxed for 150 ps at 5000 K in a regular system synthesis (NVT), followed by a cooling rate of 10 13 K/s to 1873 K in 312.7 ps. Data were collected in a holding time of 1873 K for more than 0.3 ns. All the MD simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package [18]. The integration time step was set to 1 fs with a cut-off value of 10 Å for short-range interactions and a cut-off value of 10 Å for Coulomb interactions. Finally, the radial distribution functions, coordination numbers, atomic structure, and viscosity were analyzed with the software VMD (1.

RDF and CN Calculations
The radial distribution function (RDF) is usually determined by calculating the distance between all particle pairs and binning them into a histogram. The histogram is then normalized to the ideal gas. The expression is shown in Equation (5). In the RDF value curve, the first extreme value is the distance between the atom and its neighbors. The area under the extreme value curve is calculated as the coordination number (CN), with the expression in Equation (6).
r 2 g(r)ρdr (6) where N/V is the number density of particles within dr, n(r,∆r) is the average number of other atoms around the central atom, r0 is the rightmost position starting at r = 0 where g(r) is approximately zero, and r 1 is the first minimal value.

Viscosity Calculation Method
The viscosity of a fluid is commonly known as a measure of the internal friction that impedes the flow of the fluid. In MD studies, the calculation of viscosity is essential for the analysis of fluid transport properties and thermal properties.
Muller-Plathe [22] proposed a method to calculate shear viscosity in terms of RNEMD, which was achieved by exchanging momentum and artificially constructing the shear field; the formulas are shown in Equations (7) and (8). The velocity gradient and shear rate can be obtained from the simulation accordingly. This method has been applied to many fields, such as nanofluids, for the calculation of thermally conductive viscosity [23,24]. In this simulation, the RNEMD method was also adopted to calculate the viscosity of different slag systems. During the calculation, the two ends were fixed, and the system was sliced along the Z-axis. 50 slices were cut. The momentum components at the center and both sides were exchanged to construct the velocity gradient and form the shear field to calculate the viscosity. The schematic diagram is shown in Figure 2. During the calculation, the slag was considered as a liquid state. The solid fraction was not introduced in the model, which may cause some inaccuracies. [23,24]. In this simulation, the RNEMD method was also adopted to calculate the viscosity of different slag systems. During the calculation, the two ends were fixed, and the system was sliced along the Z-axis. 50 slices were cut. The momentum components at the center and both sides were exchanged to construct the velocity gradient and form the shear field to calculate the viscosity. The schematic diagram is shown in Figure 2. During the calculation, the slag was considered as a liquid state. The solid fraction was not introduced in the model, which may cause some inaccuracies. Moreover, the viscosities of different slag systems in a full liquid state were also predicted by several semi-empirical models, including the NPL model [25], Urbain model [26,27], and Kondratiev and Jak model [28]. The predicted results were compared with those from RNEMD methods. The relation between the structure of different slag systems and the predicted viscosities was further analyzed for the applicability assessment of these perdition methods in terms of the slag systems in this study.

Machine Learning (ML) Methods
In this paper, four ML methods, namely artificial neural network (ANN) [29], random forest (RF) [30], Support Vector Machine (SVM) [31], and gradient boosting decision tree (GBDT) [32] were used based on the MATLAB toolbox to calculate the corresponding properties of the models for prediction. ANN is an information processing system that mimics the structure and function of neural networks in the human brain by simulating neuronal activity with a mathematical model. ANN usually shows better performance for fuzzy systems [33]. RF is an integrated algorithm consisting of decision trees. RF achieves the prediction of properties by building a large number of decision trees to form a forest. SVM performs non-linear classification by a kernel method and uses a hinge loss function to calculate empirical risk. A regular term to optimize structure risk in the solution system is usually added in this method. GBDT consists of multiple decision trees and accumulates the conclusions of all trees as the final result. GBDT performs well on low-dimensional Moreover, the viscosities of different slag systems in a full liquid state were also predicted by several semi-empirical models, including the NPL model [25], Urbain model [26,27], and Kondratiev and Jak model [28]. The predicted results were compared with those from RNEMD methods. The relation between the structure of different slag systems and the predicted viscosities was further analyzed for the applicability assessment of these perdition methods in terms of the slag systems in this study.

Machine Learning (ML) Methods
In this paper, four ML methods, namely artificial neural network (ANN) [29], random forest (RF) [30], Support Vector Machine (SVM) [31], and gradient boosting decision tree (GBDT) [32] were used based on the MATLAB toolbox to calculate the corresponding properties of the models for prediction. ANN is an information processing system that mimics the structure and function of neural networks in the human brain by simulating neuronal activity with a mathematical model. ANN usually shows better performance for fuzzy systems [33]. RF is an integrated algorithm consisting of decision trees. RF achieves the prediction of properties by building a large number of decision trees to form a forest. SVM performs non-linear classification by a kernel method and uses a hinge loss function to calculate empirical risk. A regular term to optimize structure risk in the solution system is usually added in this method. GBDT consists of multiple decision trees and accumulates the conclusions of all trees as the final result. GBDT performs well on low-dimensional and non-linear data. In this study, the P 2 O 5 and Al 2 O 3 contents were used as independent variables. The viscosity calculated by Urbain's method was used as the target variable. The optimal ML model is evaluated by Root Mean Squared Error (RMSE).

Slag Structure Analysis
In the basic CaO-SiO 2 -FeO converter slag system, the Si 4+ in the system acts as a network-former and has a strong adsorption capacity for surrounding oxygen atoms due to its high charge and small radius. Si atoms can combine with O and form σ-bonds. When the p-orbitals of oxygen atoms are filled, the d x -p π bonds can be formed with the d-orbitals of Si, thus enhancing the Si-O bonds. These characteristics lead that silicate structures are easy to form large irregular short-range ordered aggregates. A certain proportion of P 2 O 5 and Al 2 O 3 exhibit similar properties when brought into the system. The increase in these compositions helps increase the degree of the system polymerization. Figure Figure 3a-c, respectively, as the main body of the grid structure. While Ca 2+ and Fe 2+ in the slag exist as free states in the interstices of the structure.
In the basic CaO-SiO2-FeO converter slag system, the Si 4+ in the system acts as a network-former and has a strong adsorption capacity for surrounding oxygen atoms due to its high charge and small radius. Si atoms can combine with O and form σ-bonds. When the p-orbitals of oxygen atoms are filled, the dx-pπ bonds can be formed with the d-orbitals of Si, thus enhancing the Si-O bonds. These characteristics lead that silicate structures are easy to form large irregular short-range ordered aggregates. A certain proportion of P2O5 and Al2O3 exhibit similar properties when brought into the system. The increase in these compositions helps increase the degree of the system polymerization. Figure 3 shows the structures of CaO-SiO2-FeO-Al2O3 (A model), CaO-SiO2-FeO-P2O5 (P model), and CaO-SiO2-FeO-Al2O3-P2O5 (AP model  Figure 3a-c, respectively, as the main body of the grid structure. While Ca 2+ and Fe 2+ in the slag exist as free states in the interstices of the structure.  Table S3. The coordination plateau of P-O is also stable and constant at 4. The CNs of Al-O have a tendency to increase, indicating that with the increase in Al content, Al 3+ and O 2-have a tendency to form an octahedral structure with a coordination of 6.

Oxygen Network Structure Analysis
The variation of different oxygen types for the A model and the P model is shown in Figure 4. In the A model, with the increase in Al2O3 content, the content of bridging oxygen increases, and the content of non-bridging oxygen and free oxygen decreases. When Al2O3 content is less than 10%, OA-type non-bridging oxygen increases rapidly, and AOAtype bridging oxygen grows slowly. When Al2O3 content exceeds 10%, the growth rate of SOA-type bridging oxygen slows down, and AOA-type bridging oxygen increases rapidly. The OA-type non-bridging oxygen increases more slowly when the Al2O3 content is above 20%. In the P model, the increase in P2O5 content led to an increase in PO-type nonbridging oxygen and SOP-type bridging oxygen content in the slag. The FO in the slag system decreased under the aggregation caused by P2O5. Based on the approximate  Table S3. The coordination plateau of P-O is also stable and constant at 4. The CNs of Al-O have a tendency to increase, indicating that with the increase in Al content, Al 3+ and O 2have a tendency to form an octahedral structure with a coordination of 6.

Oxygen Network Structure Analysis
The variation of different oxygen types for the A model and the P model is shown in Figure 4. In the A model, with the increase in Al 2 O 3 content, the content of bridging oxygen increases, and the content of non-bridging oxygen and free oxygen decreases. When Al 2 O 3 content is less than 10%, OA-type non-bridging oxygen increases rapidly, and AOA-type bridging oxygen grows slowly. When Al 2 O 3 content exceeds 10%, the growth rate of SOA-type bridging oxygen slows down, and AOA-type bridging oxygen increases rapidly. The OA-type non-bridging oxygen increases more slowly when the Al 2 O 3 content is above 20%. In the P model, the increase in P 2 O 5 content led to an increase in PO-type non-bridging oxygen and SOP-type bridging oxygen content in the slag. The FO in the slag system decreased under the aggregation caused by P 2 O 5 . Based on the approximate relationship between the content of bridging oxygen proposed by Diao [15] and the local structure changes in this simulation, which are shown in Equations (9)-(11), the Si-O-P connection is more stable than SOS and POP at higher P 2 O 5 content. The growth rate of AOA is greater than the growth rate of SOA with the increase in Al 2 O 3 content when the Al 2 O 3 content is greater than 10% due to the influence of Si in the slag.   Figure 5 shows the changing trends of BO, FO, and NBO in the A BO content, when the Al2O3 content is fixed, the BO content barely incr crease in P2O5 content. When the P2O5 content is fixed, the BO content cantly with the increase in Al2O3 content. For the NBO content, when the increase in P2O5 content impels the NBO content to increase slightly content is fixed, the content of NBO decreases as the content of Al2O3 i the NBOs transfer to BO with the assistance of Al 3+ . For the FO conte both Al2O3 and P2O5 content decreases the FO content in the slag. The cov the different oxygen types and the content of Al2O3 and P2O5 were ana are shown in Table 2. There is a strong positive correlation of Al2O3 wit negative correlation with NBO. The Al2O3 and P2O5 contents also show tive correlation for FO.     Table 2. There is a strong positive correlation of Al 2 O 3 with BO but a strong negative correlation with NBO. The Al 2 O 3 and P 2 O 5 contents also showed the same negative correlation for FO.
AOA is greater than the growth rate of SOA with the increase in Al2O3 content when the Al2O3 content is greater than 10% due to the influence of Si in the slag.  Figure 5 shows the changing trends of BO, FO, and NBO in the AP model. For the BO content, when the Al2O3 content is fixed, the BO content barely increases with the increase in P2O5 content. When the P2O5 content is fixed, the BO content increases significantly with the increase in Al2O3 content. For the NBO content, when the Al2O3 content, the increase in P2O5 content impels the NBO content to increase slightly. When the Al2O3 content is fixed, the content of NBO decreases as the content of Al2O3 increases. Some of the NBOs transfer to BO with the assistance of Al 3+ . For the FO content, the increase in both Al2O3 and P2O5 content decreases the FO content in the slag. The covariances between the different oxygen types and the content of Al2O3 and P2O5 were analyzed. The results are shown in Table 2. There is a strong positive correlation of Al2O3 with BO but a strong negative correlation with NBO. The Al2O3 and P2O5 contents also showed the same negative correlation for FO.     Figure 6 shows the effects of Al 2 O 3 and P 2 O 5 on different types of NBO and BO in the slag. For the NBO, the content of OP increases with the increase in P 2 O 5 content. The increase in Al 2 O 3 content hardly affects the content of OP. The increase in Al 2 O 3 content leads to the increase in OA content, but the increase in P 2 O 5 content slightly decreases the content of OA. Combined with the changing trend of BO, it can be obtained that when the P 2 O 5 content increases, the P atom combines with OA to form POA-type bridging oxygen. The depolymerization effect of Ca 2+ and Fe 2+ on the structure of AOA [34] also results in a higher OA content at low P content and high Al content in the slag. The increases in Al and P content also have the same reducing effect on the OS content. These OS structures will polymerize into structures such as SOA and SOP accordingly. As for BO, POP hardly appears. The AOA content increases with the increase in Al content. The AOA structure can be influenced by the depolymerization effect of Ca 2+ and Fe 2+ , while the P 2 O 5 content barely affects the AOA structure. In the slag system with low Al and high P contents, the SOS-type BO is easier to be formed. While high Al and low P content reduce the SOS content on the other hand. The POS-type bridging oxygen is only observed in the slag system with higher P 2 O 5 content. When the Al content increases, Al content promotes the production of POS-type BO. The POA-type BO exists in the slag system with high Al and P contents. The SOA-type BO increases with the increase in Al content. Figure 7 shows the reaction mechanism of the oxygen network structures under the effects of P and Al atoms.

Viscosity Prediction with MD Models and Semi-Empirical Models
The Viscosity prediction results with the NPL model [25], Urbain model [26,27], Kondratiev, and Jak model [28] were used and analyzed along with RNEMD simulation results, which are shown in Figure 10.

Viscosity Prediction with MD Models and Semi-Empirical Models
The Viscosity prediction results with the NPL model [25], Urbain model [26,27], Kondratiev, and Jak model [28] were used and analyzed along with RNEMD simulation results, which are shown in Figure 10. It can be found that the viscosity of the slag increases with the increase in P content and Al content. Based on the NBO/T theory proposed by Mills [10], the amount of nonbridging oxygen possessed by a single polymer particle contributes significantly to the variation of viscosity. The increase in the Al and P content leads to a decrease in NBO/T, which also increases the slag polymerization and the viscosity.
Due to the absence of experimental data in the slag system in this study, it is difficult to measure the applicability of these semi-empirical models and the RNEMD method on It can be found that the viscosity of the slag increases with the increase in P content and Al content. Based on the NBO/T theory proposed by Mills [10], the amount of non-bridging oxygen possessed by a single polymer particle contributes significantly to the variation of viscosity. The increase in the Al and P content leads to a decrease in NBO/T, which also increases the slag polymerization and the viscosity.
Due to the absence of experimental data in the slag system in this study, it is difficult to measure the applicability of these semi-empirical models and the RNEMD method on the CaO-SiO 2 -FeO-(P 2 O 5 )-(Al 2 O 3 ) slag systems. Considering that the positive relationship between the BO number and the contents of Al 2 O 3 and P 2 O 5 has been confirmed by existing studies [4,5], the Pearson correlation coefficient between BO number and the contents of Al 2 O 3 and P 2 O 5 was introduced for the applicability assessment of these models of the viscosity prediction, which is shown in Figure 11. Based on Table 2, the covariances between BO and the contents of Al 2 O 3 and P 2 O 5 have provided proof that the positive relationship between BO and Al 2 O 3 is stronger than that between BO and P 2 O 5 . Hence, the positive value of Pearson correlation coefficients of Al 2 O 3 should be larger than that of P 2 O 5 . Only the viscosities predicted by Urbain's model are in accord with these inferences. Other viscosity prediction models and RNEMD methods are not suitable for the viscosity prediction of the slag system in this study. Therefore, Urbain's model is determined to be the most applicable for the viscosity prediction of the slag system in this study. The predicted viscosity data of Urbain's model was also adopted in the ML models developed in the following section.

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P2O5. Only the viscosities predicted by Urbain's model are in acco Other viscosity prediction models and RNEMD methods are not prediction of the slag system in this study. Therefore, Urbain's m the most applicable for the viscosity prediction of the slag syste dicted viscosity data of Urbain's model was also adopted in the the following section.

ML Model Development for Viscosity Prediction
To improve the accuracy of viscosity prediction by the M models were developed in this section, including ANN, RF, SVM forming the prediction, the different model parameters were op tion. ANN used two hidden layers with a maximum of 100 iter 0.01. RF used 20 decision trees with several bins of 32. GBDT u squared error and 20 decision trees with a convergence toleranc the data with a regularization parameter is 0.01, and a polynomi with a kernel parameter p of 1. The prediction results of differen in Figure 12. The values of RMSE between Urbain model data a for each ML model were calculated accordingly, which is shown

ML Model Development for Viscosity Prediction
To improve the accuracy of viscosity prediction by the ML models, different ML models were developed in this section, including ANN, RF, SVM, and GBDT. Before performing the prediction, the different model parameters were optimized for implementation. ANN used two hidden layers with a maximum of 100 iterations and a tolerance of 0.01. RF used 20 decision trees with several bins of 32. GBDT used a loss function with squared error and 20 decision trees with a convergence tolerance of 0.1. SVM normalized the data with a regularization parameter is 0.01, and a polynomial kernel function is used with a kernel parameter p of 1. The prediction results of different ML models are shown in Figure 12. The values of RMSE between Urbain model data and the prediction results for each ML model were calculated accordingly, which is shown in Table 3. the data with a regularization parameter is 0.01, and a polynomial kernel function is used with a kernel parameter p of 1. The prediction results of different ML models are shown in Figure 12. The values of RMSE between Urbain model data and the prediction results for each ML model were calculated accordingly, which is shown in Table 3.   According to the values of RMSE in Table 3, GBDT and ANN have the best and worst predictive power for the viscosity prediction of the slag system in this study, respectively. To further prove this conclusion, the Pearson correlation coefficients of viscosity perdition results from the four ML models were also calculated, which is shown in Figure 12b. Both Al 2 O 3 and P 2 O 5 contents appear positively correlated with viscosity when we adopted the GBDT predictor. While in the prediction results of the ANN model, the Al 2 O 3 content appears to have a negative correlation with viscosity, which is contrary to the rules provided by the semi-empirical models.
Based on the ML model with GBDT methods, a color-map concerning the numerical effect of Al 2 O 3 and P 2 O 5 contents and slag viscosity is provided in Figure 13a. The blue color represents the smaller value of viscosity. The red color represents the larger value of viscosity. The iso-viscosity lines with a viscosity of 0.15Pa·s, 0.175Pa·s, 0.2Pa·s, 0.225Pa·s, and 0.25 Pa·s were also extracted in Figure 13b. According to this figure, the slag viscosity of the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 slag system in terms of different Al 2 O 3 and P 2 O 5 contents can be predicted and it could also be used for composition engineering to fulfill a certain demand on the viscosity design.
Crystals 2022, 12, x FOR PEER REVIEW 13 According to the values of RMSE in Table 3, GBDT and ANN have the best and w predictive power for the viscosity prediction of the slag system in this study, respect To further prove this conclusion, the Pearson correlation coefficients of viscosity perd results from the four ML models were also calculated, which is shown in Figure 12b. Al2O3 and P2O5 contents appear positively correlated with viscosity when we adopte GBDT predictor. While in the prediction results of the ANN model, the Al2O3 conten pears to have a negative correlation with viscosity, which is contrary to the rules prov by the semi-empirical models.
Based on the ML model with GBDT methods, a color-map concerning the num effect of Al2O3 and P2O5 contents and slag viscosity is provided in Figure 13a. The color represents the smaller value of viscosity. The red color represents the larger va viscosity. The iso-viscosity lines with a viscosity of 0.15Pa·s, 0.175Pa·s, 0.2Pa·s, 0.225 and 0.25 Pa·s were also extracted in Figure 13b. According to this figure, the slag visc of the CaO-SiO2-FeO-Al2O3-P2O5 slag system in terms of different Al2O3 and P2O5 con can be predicted and it could also be used for composition engineering to fulfill a ce demand on the viscosity design.

Conclusions
(1) With the increase in the mass fraction of Al2O3 and P2O5, the concentration o increases, and the concentration of FO decreases, which complicates the melt s ture of the slag system and increases the polymerization degree. (2) In the CaO-SiO2-FeO-Al2O3-P2O5 slag system, the content of BO was positively c lated with the content of Al2O3 and P2O5. The positive correlation was strong the content of Al2O3. (3) Different semi-empirical models and RNEMD methods were used to predict th cosity of the three slag systems. The reliability of the Urbain model in predictin viscosity of the CaO-SiO2-FeO-Al2O3-P2O5 slag system has been proved accordi the Pearson correlation coefficient analysis. (4) Among all the ML methods in this study, GBDT has the best predictive power fo

Conclusions
(1) With the increase in the mass fraction of Al 2 O 3 and P 2 O 5 , the concentration of BO increases, and the concentration of FO decreases, which complicates the melt structure of the slag system and increases the polymerization degree. (3) Different semi-empirical models and RNEMD methods were used to predict the viscosity of the three slag systems. The reliability of the Urbain model in predicting the viscosity of the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 slag system has been proved according to the Pearson correlation coefficient analysis. (4) Among all the ML methods in this study, GBDT has the best predictive power for the viscosity prediction of the slag system in this study, building a credible correlation between the structure of the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 slag system and viscosity prediction. Iso-viscosity lines of the CaO-SiO 2 -FeO-Al 2 O 3 -P 2 O 5 slag system were provided accordingly.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/cryst12101338/s1, Figure S1: Radial distribution function and coordination numbers of the major atomic pairs in the P models; Figure S2: Radial distribution function and coordination numbers of the major atomic pairs in the A models; Figure S3: Radial distribution function and coordination numbers of the main atomic pairs in the AP models; Table S1: Component content of different CaO-SiO 2 -FeO-(P 2 O 5 )-(Al 2 O 3 ) slag systems; Table S2: Bond lengths of major atom pairs for different models; Table S3: The coordination number of each major atomic pair for different models. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to further studies are on-going.