Machine Learning-Based Prediction of Magnetocrystalline Anisotropy Constants and Energy Density in Pure Iron: An Integrated CatBoost and K₀–K₆ Texture-Factor Approach
Year: 2026
Type: preprint
Abstract: Machine Learning-Based Prediction of Magnetocrystalline Anisotropy Constants and Energy Density in Pure Iron: An Integrated CatBoost and K₀–K₆ Texture-Factor Approach This title brings together four important research elements: Prediction of magnetocrystalline anisotropy energy density in pure iron. Higher-order anisotropy constants K₀–K₆. Crystallographic orientation and ideal-fibre texture factors. CatBoost-based machine-learning regression. 2. Alternative research titles 1. CatBoost-Based Prediction of Magnetocrystalline Anisotropy Energy Density in Pure Iron Using the K₀–K₆ Framework 2. Machine Learning-Assisted Evaluation of Higher-Order Magnetocrystalline Anisotropy Constants in Pure Iron 3. Physics-Informed CatBoost Modelling of Crystallographic Orientation-Dependent Magnetic Anisotropy in Pure Iron 4. Predictive Modelling of K₀–K₆ Magnetocrystalline Anisotropy Constants Using Texture-Factor Relationships in Pure Iron 5. Integrating Crystallographic Texture and Machine Learning for Anisotropy Energy Prediction in Pure Iron 6. Data-Driven Prediction of Magnetocrystalline Anisotropy Energy Density in Pure Iron Using CatBoost Regression 7. A Hybrid Analytical and Machine Learning Framework for Higher-Order Magnetic Anisotropy Modelling in Pure Iron 8. Texture-Sensitive Prediction of Magnetocrystalline Anisotropy in Pure Iron Using Higher-Order Energy Invariants 9. Machine Learning-Assisted Estimation of Crystallographic Direction-Dependent Anisotropy Energy in Body-Centred Cubic Iron 10. A Physics-Guided Data-Driven Framework for Predicting Magnetic Anisotropy Behaviour in Pure Iron 3. Recommended subtitle Integrating Higher-Order K₀–K₆ Anisotropy Constants, Crystallographic Orientation and Sudhakar's Texture-Factor Relationships with CatBoost Regression Alternative subtitles: A Physics-Informed Machine Learning Framework for Higher-Order Anisotropy Energy Estimation. Linking Crystallographic Orientation, Texture Factor and Magnetocrystalline Energy in BCC Iron. Predictive Analysis of [100], [110] and [111] Magnetic Directions Using Higher-Order Energy Invariants. From Analytical Anisotropy Equations to Data-Driven Magnetic Property Prediction. A Computational Approach to Orientation-Dependent Magnetic Energy Modelling in Pure Iron. 4. Detailed research description Detailed Research Description Title Machine Learning-Based Prediction of Magnetocrystalline Anisotropy Constants and Energy Density in Pure Iron: An Integrated CatBoost and K₀–K₆ Texture-Factor Approach Author: Geruganti SudhakarAffiliation: Faculty, Department of Metallurgical and Materials Engineering, RGUKT IIIT Basar, Telangana, IndiaEmail: [email protected] Research Background Magnetocrystalline anisotropy is an important intrinsic magnetic property that describes the dependence of magnetic energy on the crystallographic orientation of magnetization. In body-centred cubic (BCC) iron, the preferred direction of magnetization is strongly influenced by the crystal structure and crystallographic orientation. The principal crystallographic directions [100], [110] and [111] exhibit different anisotropy-energy characteristics. The [100] direction is generally considered the easy magnetization direction, whereas [110] and [111] represent harder magnetization directions. The accurate evaluation of magnetocrystalline anisotropy energy density is essential for understanding magnetic behaviour and developing advanced magnetic materials. Conventional analytical formulations describe this behaviour through orientation-dependent energy constants. However, higher-order formulations can involve several mathematical terms and crystallographic invariants. The present research proposes a machine-learning-assisted methodology for predicting magnetocrystalline anisotropy constants and energy density in pure iron. It integrates the higher-order K₀–K₆ framework and texture-factor relationships developed by Geruganti Sudhakar with CatBoost regression. The central idea is to combine the physical interpretability of analytical anisotropy equations with the computational capability of machine learning for rapid orientation-dependent energy prediction. Scientific Foundation The study is based on the higher-order magnetocrystalline anisotropy energy representation: E* = K₀ + K₁P + K₂Q + K₃P² + K₄PQ + K₅P³ + K₆Q² where E* represents the source-defined anisotropy-energy quantity, K₀–K₆ are the corresponding energy coefficients, and P and Q are crystallographic orientation invariants. The orientation invariants are defined as: P = α₁²α₂² + α₂²α₃² + α₃²α₁² Q = α₁²α₂²α₃² Here, α₁, α₂ and α₃ represent the direction cosines of magnetization relative to the cubic crystallographic axes. The texture-factor relationship considered for pure iron is: A* = 22.5 + 52.4P − 34.74Q The corresponding pure-iron energy relationship is: E* = 0.355A* − 1.898 These relationships provide an analytical reference for constructing and checking the proposed machine-learning dataset. Principal Crystallographic Orientations The three important crystallographic directions are: Crystallographic direction P Q Texture factor A* [100] 0 0 22.5 [110] 0.25 0 35.6 [111] 1/3 1/27 38.68 The corresponding analytical reference energies under the stated source convention are approximately: Direction Reference energy E* [100] 6.0895 [110] 10.7400 [111] 11.8334 These values are used as reference calculations and should not be described as newly measured experimental results. Research Objectives To develop a CatBoost-based prediction framework for magnetocrystalline anisotropy energy density in pure iron. To investigate the relationship between crystallographic orientation and magnetic anisotropy energy. To incorporate the higher-order K₀–K₆ energy representation into a physics-informed machine-learning methodology. To examine the influence of texture-factor descriptors on predicted anisotropy energy. To compare CatBoost predictions with analytical reference calculations. To identify the most influential crystallographic descriptors governing the predicted magnetic anisotropy response. To establish a computational methodology that can subsequently be validated using experimental magnetic and crystallographic texture data. Proposed Computational Methodology 1. Dataset preparation A physics-informed dataset will be developed using the cubic direction-cosine constraint: α₁² + α₂² + α₃² = 1 The dataset will include different crystallographic orientation combinations, with the principal [100], [110] and [111] directions serving as reference cases. The input parameters will include: Direction cosines α₁, α₂ and α₃. Orientation invariants P and Q. Texture factor A*. Crystallographic direction. Analytical reference anisotropy energy E*. Verified K₀–K₆ coefficients, where available. Intermediate orientation combinations will be generated systematically to cover the orientation space. 2. CatBoost regression model CatBoost regression will be used to learn the relationship between crystallographic orientation descriptors and magnetocrystalline anisotropy energy. The proposed prediction model is: Epred = fCatBoost(α₁, α₂, α₃, P, Q, A, direction) The model will be trained using the analytical reference energies generated from the selected source-consistent equations. Hyperparameter optimization will consider tree depth, learning rate, number of iterations, regularization and loss function. 3. Model validation The predictive performance will be assessed using: Coefficient of determination (R²). Root mean square error (RMSE). Mean absolute error (MAE). Five-fold cross-validation. Independent test-set evaluation. The dataset should be divided by orientation groups to reduce information leakage between closely related orientations. 4. Analytical and machine-learning comparison The predicted anisotropy energies will be compared with the analytical reference values. Predicted-versus-reference plots, residual-error distributions and feature-importance analysis will be used to evaluate the model. Expected Scientific Contributions The proposed research is expected to provide: A higher-order, texture-sensitive machine-learning framework for predicting magnetocrystalline anisotropy energy in pure iron. Integration of the K₀–K₆ energy representation with CatBoost regression. A systematic analysis of the influence of crystallographic orientation on anisotropy energy. A comparison between analytical texture-factor calculations and machine-learning predictions. A computational methodology that can be extended to other cubic magnetic materials. A foundation for incorporating measured crystallographic texture and magnetic characterization data. Potential Applications The proposed framework may contribute to research and development in: Pure iron and iron-based magnetic materials. Soft magnetic materials. Electrical and magnetic steels. Magnetic core materials. Crystallographic texture engineering. Computational materials science and magnetic-property prediction. Overall Research Significance The principal significance of this research lies in integrating an established analytical framework for magnetocrystalline anisotropy with modern machine-learning techniques. The K₀–K₆ formulation provides a higher-order mathematical representation of crystallographic orientation dependence, while the texture-factor relationship provides a physically meaningful descriptor of preferred orientations. CatBoost is introduced as a computational prediction tool to learn the relationship between orientation variables and anisotropy energy. The proposed approach is intended to reduce repetitive analytical calculations and
Author: geruganti, sudhakar
Language: English
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225659558
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