Multi-objective optimization design of process parameters for rare earth hard magnetic materials based on machine learning

Haozhen Hu; Mengxian Zhao; Cun Chen; Haozhen Hu; Mengxian Zhao; Cun Chen

doi:10.3934/bdia.2025013

Big Data and Information Analytics

2025, Volume 9, 285-301. doi: 10.3934/bdia.2025013

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Research article

Multi-objective optimization design of process parameters for rare earth hard magnetic materials based on machine learning

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

Received: 12 November 2025 Revised: 20 November 2025 Accepted: 23 November 2025 Published: 01 December 2025

In the present work, combining machine learning and optimization theory, a novel framework is designed to optimize the process parameters of rare earth hard magnetic materials Nd₇Fe_67.5B₂₁Nb_2.5Zr₂ with multi-objective performance. Considering the small dataset problem, the interpolation and extrapolation technique was introduced for data augmentation. Based on the expanded dataset, predictive models for coercivity (H_cj) and maximum magnetic energy product ((BH)_max) concerning heat treatment parameters (annealing temperature and magnetic field strength) are established. Based on the enhanced data, the prediction accuracy of the model for H_cj and (BH)_max reaches 0.980 and 0.997, respectively. After that, the NSGA-II algorithm is utilized for multi-objective optimization; the top 12 optimal process parameter combinations are recommended with higher coercivity and maximum magnetic energy product. This study provides a new way for the performance prediction and process optimization of rare earth hard magnetic materials, which can accelerate the design of materials with multi-objective performance.
- machine learning,
- rare-earth hard magnetic materials,
- coercivity,
- maximum magnetic energy product,
- multi-objective optimization,
- data augmentation
Citation: Haozhen Hu, Mengxian Zhao, Cun Chen. Multi-objective optimization design of process parameters for rare earth hard magnetic materials based on machine learning[J]. Big Data and Information Analytics, 2025, 9: 285-301. doi: 10.3934/bdia.2025013

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Abstract

In the present work, combining machine learning and optimization theory, a novel framework is designed to optimize the process parameters of rare earth hard magnetic materials Nd₇Fe_67.5B₂₁Nb_2.5Zr₂ with multi-objective performance. Considering the small dataset problem, the interpolation and extrapolation technique was introduced for data augmentation. Based on the expanded dataset, predictive models for coercivity (H_cj) and maximum magnetic energy product ((BH)_max) concerning heat treatment parameters (annealing temperature and magnetic field strength) are established. Based on the enhanced data, the prediction accuracy of the model for H_cj and (BH)_max reaches 0.980 and 0.997, respectively. After that, the NSGA-II algorithm is utilized for multi-objective optimization; the top 12 optimal process parameter combinations are recommended with higher coercivity and maximum magnetic energy product. This study provides a new way for the performance prediction and process optimization of rare earth hard magnetic materials, which can accelerate the design of materials with multi-objective performance.

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