Hybrid machine-learning model improves TiN thickness prediction with limited calibration data

A computational modeling study reported in the Journal of Materials Science found that a hybrid model-agnostic meta-learning and Gaussian process regression framework, termed MAML-GPR, produced more accurate predictions of titanium nitride coating thickness than several comparison models when calibration data were limited. The abstract indicates that the study focused on reactive magnetron sputtering, where substrate bias and the N2/Ar gas-flow ratio can interact nonlinearly and produce non-monotonic thickness responses.

The researchers developed MAML-GPR to combine information from historical deposition records with local model refinement and predictive-uncertainty estimates. They compared the hybrid framework with conventional Gaussian process regression, standalone model-agnostic meta-learning, XGBoost and neural-network models. Under the same fivefold cross-validation protocol on the source-domain dataset, MAML-GPR achieved lower mean absolute error and root-mean-square error than the reference models, while its coefficient of determination remained close to that of standard Gaussian process regression.

Additional few-shot evaluations examined how quickly the model could adapt under low-data conditions. Six deposition experiments were held out for external validation. These experiments used fixed power and fixed pressure, and the average measured thickness values for the tested combinations of substrate bias and N2/Ar flow rate were consistent with the ranges predicted by the framework. This validation was limited to six runs and the specific process conditions tested, rather than establishing performance across every possible deposition setting.

The available source is an abstract rather than the full article, so it does not provide the size and composition of the historical dataset, numerical error values, individual experimental measurements or uncertainty estimates. It also does not report comparative performance for the six validation runs. Within those boundaries, the reported evidence supports MAML-GPR as a promising thickness-prediction approach for data-constrained TiN deposition records, with external agreement reported for a limited set of experimental conditions.

Subject of Research: Machine-learning prediction of TiN coating thickness under varied substrate bias and N2/Ar gas-flow conditions.

Article Title: Predictive modeling of TiN coating thickness under varying substrate bias and N2/Ar flow ratio

Article References: Zhou, Q., Wei, W., Zhang, E.-G., Chen, Q., Liang, D.-D., Huang, B., & Hou, H. (2026). Predictive modeling of TiN coating thickness under varying substrate bias and N2/Ar flow ratio. Journal of Materials Science, 61(43), 33914-33935. https://doi.org/10.1007/s10853-026-13678-9

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13678-9

Keywords: TiN coatings, reactive magnetron sputtering, machine learning, Gaussian process regression, meta-learning, few-shot learning, thickness prediction, experimental validation, Predictive, modeling, coating, thickness