Machine learning surrogate models for burst velocity analysis of functionally graded carbon nanotube-reinforced composite rotating disks

The burst velocity of a rotating disk, the speed at which its elastic response grows without bound, is a primary design constraint for flywheels and turbine rotors. For functionally graded carbon nanotube reinforced composite (FG-CNTRC) disks it follows from the repeated solution of a variable-coefficient boundary value problem. The aim of this study is to establish which family of surrogate models reproduces such solutions most faithfully, how far their validity extends beyond the sampled parameter combinations, and whether the burst velocity admits a compact closed form. An artificial neural network, a physics-regularized Kolmogorov-Arnold inspired network (PIKAN) and LightGBM are trained on 99 Complementary Functions Method solutions spanning 3 distribution patterns, 3 volume fractions, and 11 thickness profiles, with random forest, XGBoost, and Gaussian process baselines. On the fixed 20-case test partition every trained model exceeds an R ² of 0.995. PIKAN is the closest of the three primary models, at R ²  = 0.9999 and a mean absolute percentage error of 0.23%, while the Gaussian process surpasses all of them at 0.031% with calibrated 95% prediction intervals. A symbolic expression is reported separately as a descriptive fit to the complete grid, at 0.56% mean and 2.75% largest deviation. Thirty repeated splits, a leave-one-group-out study that delimits the retrained models as interpolators, and a penalty ablation showing that the soft constraints give no consistent accuracy gain support these findings. The reference solutions are also read mechanically, the burst velocity following a separable scaling in the nanotube stiffness contribution and the thickness profile. Within their calibrated ranges the surrogates provide efficient design-stage screening.