Machine Learning-Based Prediction of Magnetic Anisotropy Constants and Energy Density in Silicon Electrical Steels: An Integrated CatBoost and Texture-Factor Approach

Machine Learning-Based Prediction of Magnetic Anisotropy Constants and Energy Density in Silicon Electrical Steels: An Integrated CatBoost and Texture-Factor Approach This title combines the three central themes: Prediction of magnetic anisotropy constants \(K_0, K_1, K_2\). Influence of silicon concentration on magnetic anisotropy. CatBoost machine learning integrated with crystallographic texture-factor relationships. 2. Alternative research titles 1. CatBoost-Based Prediction of Magnetocrystalline Anisotropy Constants in Silicon Electrical Steels Using Composition and Texture Descriptors 2. A Data-Driven Framework for Predicting Magnetic Anisotropy Energy in Fe–Si Electrical Steels Using Texture-Factor Relationships 3. Composition-Dependent Magnetic Anisotropy Modelling of Silicon Electrical Steels Using CatBoost Regression 4. Machine Learning-Assisted Evaluation of K₀, K₁ and K₂ Anisotropy Constants in Silicon Electrical Steels 5. Integrating Crystallographic Texture and Silicon Concentration for Predictive Modelling of Magnetic Anisotropy in Electrical Steels 6. Physics-Informed CatBoost Modelling of Magnetocrystalline Anisotropy Energy Density in Fe–Si Alloys 7. Predictive Modelling of Magnetic Anisotropy and Crystallographic Orientation Effects in Non-Oriented Electrical Steels 8. Texture-Sensitive Machine Learning Prediction of Magnetic Anisotropy Constants in Silicon-Rich Iron Alloys 9. A Hybrid Analytical and Machine Learning Approach for Estimating Magnetic Anisotropy Energy in Electrical Steels 10. Data-Driven Prediction of Composition–Texture–Anisotropy Relationships in Silicon Electrical Steels 3. Recommended subtitle Integrating Silicon Content, Crystallographic Orientation and Sudhakar's Texture-Factor Relationships with CatBoost Regression Alternative subtitles: A Physics-Informed Machine Learning Framework for K₀–K₂ Constant Estimation. Linking Chemical Composition, Ideal Fibre Texture and Magnetocrystalline Energy. Predictive Analysis of Fe–Si Alloys for Advanced Soft Magnetic Applications. From Analytical Anisotropy Equations to Data-Driven Magnetic Property Prediction. 4. Detailed research description Detailed Research Description Title Machine Learning-Based Prediction of Magnetic Anisotropy Constants and Energy Density in Silicon Electrical Steels: An Integrated CatBoost and Texture-Factor Approach Research Background Silicon electrical steels are important soft magnetic materials extensively used in transformers, electric motors, generators and other electromagnetic devices. Their magnetic performance depends on chemical composition, crystallographic texture, grain structure and magnetocrystalline anisotropy. Silicon addition to iron modifies the magnetic characteristics and increases electrical resistivity, making Fe–Si alloys particularly suitable for electrical applications. Magnetocrystalline anisotropy represents the dependence of magnetic energy on the crystallographic direction of magnetization. In cubic iron-based materials, the [100], [110] and [111] directions exhibit different energy characteristics. The preferred orientation of grains, commonly described through crystallographic texture, plays an important role in determining the overall magnetic response. The present research develops a machine-learning-assisted framework for predicting magnetic anisotropy constants and anisotropy energy density in silicon electrical steels. It integrates the analytical texture-factor relationships developed by Geruganti Sudhakar with CatBoost regression to establish a composition- and orientation-sensitive predictive methodology. Scientific Foundation The study is based on the composition-dependent anisotropy relationships: K₀ = −0.5345S + 6.0895 K₁ = −1.6244S + 18.602 K₂ = 1.07676S − 12.3327 where S represents silicon concentration in weight percentage. The anisotropy energy is represented by: E* = K₀ + K₁P + K₂Q where: P = α₁²α₂² + α₂²α₃² + α₃²α₁² Q = α₁²α₂²α₃² and α₁, α₂ and α₃ are the direction cosines of magnetization relative to the crystallographic axes. The texture-factor framework considers important ideal fibre orientations, including cube or theta ([100]), Goss ([110]) and gamma ([111]). Their respective reference texture factors are 22.5, 35.6 and 38.68. Research Objectives To investigate the influence of silicon concentration on magnetic anisotropy constants in Fe–Si electrical steels. To establish composition-dependent relationships for K₀, K₁ and K₂. To investigate the role of crystallographic orientation and texture factor in determining anisotropy energy density. To develop CatBoost regression models for predicting magnetic anisotropy constants and energy density. To compare machine-learning predictions with the analytical texture-factor framework. To identify the most influential descriptors governing the predicted magnetic anisotropy response. To establish a predictive methodology that can subsequently be validated using experimental magnetic and crystallographic texture measurements. Proposed Methodology The initial dataset will include Fe–Si compositions containing 0.51, 1.38, 2.8 and 3.2 wt.% silicon, corresponding to the compositions considered in the analytical reference study. The input parameters will include silicon concentration, texture factor, direction cosines, crystallographic orientation, and orientation invariants P and Q. The analytical equations will be used to generate reference values of K₀, K₁, K₂ and E*. CatBoost regression will then be developed to learn the relationships between composition, texture, crystallographic orientation and magnetic anisotropy. Model performance will be evaluated using R², RMSE and MAE, together with cross-validation and independent testing. Predicted values will be compared against analytical reference values using correlation plots, residual-error plots and feature-importance analysis. The equation-derived dataset will be clearly distinguished from experimental measurements. Independent validation using measured silicon composition, EBSD or XRD texture data and magnetic characterization will be necessary to establish the model's experimental predictive capability. Expected Scientific Contributions The proposed study is expected to provide: A unified composition- and texture-sensitive prediction framework for magnetic anisotropy in Fe–Si electrical steels. A computational approach for estimating K₀, K₁ and K₂ from material and orientation descriptors. A systematic analysis of silicon concentration effects on orientation-dependent anisotropy energy. A comparison between analytical calculations and CatBoost predictions. A foundation for extending the approach to higher-order anisotropy formulations and experimentally measured texture distributions. Potential Applications The research may contribute to the development and screening of soft magnetic materials used in: Transformer cores. Electric motors and generators. Non-oriented electrical steels. High-efficiency electromagnetic devices. Advanced Fe–Si magnetic alloys. Overall Research Significance The principal significance of this work is the integration of established analytical anisotropy relationships with modern machine-learning techniques. Rather than replacing the physical basis of magnetocrystalline anisotropy, CatBoost is used as a computational prediction tool to explore nonlinear relationships between silicon concentration, crystallographic texture and anisotropy energy. This integrated approach provides a pathway towards faster composition-sensitive magnetic-property estimation and can be extended to experimental datasets for the development of validated predictive models for advanced electrical-steel applications. 5. Suggested graphical abstract concept DRAGen in Application—An Approach for Microstructural Fatigue Predictions of Non-Oriented Electrical Steel Sheets | MDPI mdpi.com The graphical abstract can follow this scientific sequence: Fe–Si Electrical Steel 0.51, 1.38, 2.8 and 3.2 wt.% Si Composition and Texture Descriptors Silicon content · A* · P · Q · Orientation CatBoost Regression Prediction of K₀, K₁, K₂ and E* Prediction and Validation Analytical comparison · Error analysis · Experimental validation 6. My final recommendation Recommended title Machine Learning-Based Prediction of Magnetic Anisotropy Constants and Energy Density in Silicon Electrical Steels: An Integrated CatBoost and Texture-Factor Approach This is the strongest choice because it communicates the material system, scientific property, machine-learning technique and original texture-factor contribution without making an unsupported claim of experimental discovery.