Get started
Work

Comparative analysis of machine learning approaches for predicting and interpreting Cz-sapphire growth

Year: 2025
Type: article
Abstract: This study evaluates four machine learning (ML) "white-box" methods - Decision Trees, Linear Regression, Python Symbolic Regression (PySR), and SISSO - and five "gray-box" methods - Gradient Boosting, XGBoost, Support Vector Machines (SVM), Gaussian Processes, and Random Forests - for analyzing data from the Cz-sapphire crystal growth process. The objective is to develop a model that achieves a balance between high predictive accuracy and interpretability in this small-data domain.Twelve input variables - including process parameters, sapphire optical properties, and furnace geometry parameters - were analyzed in relation to five output variables: heating power, interface deflection, temperature gradients averaged at the solid/liquid interface and symmetry axis, and v/G. Using 500 data tuples from CFD simulations, the results highlighted significant performance differences across the models. SVM demonstrated superior performance in predicting temperature gradients, XGBoost excelled in interface deflection predictions, and Gradient Boosting was most effective for v/G. SISSO, known for its high interpretability, performed best in predicting heating power, particularly in cases where nonlinear noise was less pronounced.The best model for each output produced 3D plots illustrating the relationship between the outputs and their two most strongly correlated inputs - for example, interface deflection as a function of crystal rotation rate and crucible radius. These plots provide theoretical insights to optimize the Cz-sapphire crystal growth process and design.
DOI: 10.1016/j.jcrysgro.2025.128185
Language: English
Open Access status: hybrid
Estimated APC paid: $3,110
OpenAlex ID: W4409302078
FWCI: 1.662
Cites: 68
Cited by: 8
Related to: 10