Table 5 Comparative performance of hybrid ML–PINN framework versus classical RSM on external test set.

From: Predictive optimization of curcumin nanocomposites using hybrid machine learning and physics informed modeling

Model

Target

R2

RMSE

MAE

Gradient Boosting Regressor (GBR)

LE%

0.89

6.24

4.87

Physics-Informed Neural Network (PINN)

LE%

0.85

8.10

6.25

Response Surface Methodology (CCD)

LE%

0.74

10.80

8.50

Gradient Boosting Regressor (GBR)

EE%

0.87

7.15

5.42

Physics-Informed Neural Network (PINN)

EE%

0.83

8.10

6.25

Response Surface Methodology (CCD)

EE%

0.71

12.30

9.80