Nonlinear Modeling of Luminescence‐Pressure Behavior: A Case Study Using (Y,Gd)(Al,Ga) ₃ (BO ₃ ) ₄ :Cr ³⁺ Phosphors for Optical Pressure Sensing Applications

Luminescence pressure sensors, valued for their remote sensing capability and high resolution, have been developed recently. However, most current sensors rely on a linear relationship between an optical property and pressure. We propose a nonlinear machine learning (ML) method to model the luminescence intensity ratio (LIR) as a function of pressure. The versatility and performance of this method are demonstrated using (Y,Gd)(Al,Ga) 3 (BO 3 ) 4 :Cr 3+ phosphors as luminescent pressure sensors. The relative sensitivities of the 2 E → 4 A 2 / 4 T 2 → 4 A 2 LIRs in (Y,Gd)(Al,Ga) 3 (BO 3 ) 4 :Cr 3+ range from 1.58%/GPa to 25.27%/GPa. The ML fitting demonstrates a superior performance compared to linear fitting, with lower mean absolute errors (0.0355–0.1499 GPa vs. 0.1209–0.6955 GPa) and higher R 2 values (99.70–99.98% vs. 93.69–99.79%). The ML fitting method is more suitable for modeling the nonlinear relationships between LIR and pressure than traditional linear fitting. The nonlinear ML fitting approach offers a powerful new way to model the relationships between luminescence features and various physical parameters.