Machine learning framework for derivation and optimization of Cz-YAG crystal growth recipe

Abstract

We present a generalizable machine learning framework for rapid, dynamic optimization of Czochralski-grown undoped yttrium aluminum garnet (YAG) crystal growth recipes. This framework addresses the high cost and slow iteration cycles of conventional experimental and computational approaches. Steady-state computational fluid dynamics (CFD) simulations at only three distinct crystallization stages are combined with symbolic regression (SISSO++) and artificial neural network (ANN) surrogate models, enabling accurate, multi-objective optimization of process parameters at any crystallization stage around the CFD training window. Trained on 423 high-fidelity CFD cases, the surrogates predict key quality indicators (power, interface deflection, axial temperature gradient, and maximum von Mises stress) with high accuracy. Using an NSGA-II evolutionary optimization pipeline, we identify stage-wise Pareto-optimal settings that closely approximate fully dynamic growth while requiring only a fraction of the resources of direct CFD or experiment. The resulting dynamic process recipe prescribes stage-specific adjustments to rotation rate, pulling rate, and heater position, ensuring flat interfaces, target-aligned thermal gradients, and reduced mechanical stress across the crystallization window. Full CFD validation confirms the physical realizability and quality of the optimized recipes. This framework accelerates process development by orders of magnitude and provides an extensible platform for adaptive, data-driven oxide crystal manufacturing.