Research Article
Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression
Table 7
Prediction errors of the GPR model with different kernel functions.
| Physical quantities | Statistical metrics | GPR training phase | GPR checking phase | Kernel functions | Exponential | Squared exponential | Rational quadratic | Matérn | Exponential | Squared exponential | Rational quadratic | Matérn |
| | MSE | 2.04E − 10 | 1.37E − 08 | 1.43E − 08 | 1.72E − 08 | 1.67E − 09 | 1.42E − 05 | 1.36E − 05 | 1.98E − 07 | MAE | 8.34E − 06 | 5.78E − 05 | 5.06E − 05 | 5.73E − 05 | 3.09E − 05 | 2.94E − 03 | 2.82E − 03 | 0.000321 | MAPE | 2.54E − 03 | 1.48E − 02 | 1.47E − 02 | 1.55E − 02 | 7.25E − 03 | 6.13E − 01 | 5.84E − 01 | 0.069743 | MAPE | 1.43E − 05 | 0.000117 | 0.000119 | 0.000131 | 4.09E − 05 | 0.003764 | 0.003689 | 0.000445 | | 0.999999982 | 0.999998799 | 0.999998718 | 0.99999451 | 0.999999973 | 0.999774302 | 0.999783212 | 0.999996841 | R | 0.99999991 | 0.00000383 | 0.999999359 | 0.999999226 | 0.999999987 | 0.999887145 | 0.9998916 | 0.999998421 |
| | MSE | 2.72E − 09 | 9.27E − 06 | 6.56E − 08 | 7.55E − 08 | 2.28E − 10 | 1.40E − 08 | 1.22E − 08 | 7.72E − 09 | MAE | 2.95E − 05 | 1.96E − 03 | 1.36E − 04 | 1.55E − 04 | 8.87E − 06 | 7.09E − 05 | 6.97E − 05 | 5.09E − 05 | MAPE | 1.02E − 02 | 6.59E − 01 | 4.49E − 02 | 5.12E − 02 | 2.65E − 03 | 2.31E − 02 | 2.23E − 02 | 0.0152 | RMSE | 5.22E − 05 | 0.003045 | 0.000256 | 0.000275 | 1.51E − 05 | 0.000118 | 0.000111 | 8.79E − 05 | | 0.999997263 | 0.9906798 | 0.999934081 | 0.999924121 | 0.999999974 | 0.999998392 | 0.999998589 | 0.999999111 | R | 0.999998632 | 0.995328991 | 0.99996704 | 0.99996206 | 0.999999987 | 0.999999196 | 0.999999295 | 0.999999555 |
| | MSE | 1.51E − 08 | 2.76E − 07 | 2.76E − 07 | 2.27E − 07 | 5.60E − 10 | 6.67E − 05 | 1.14E − 07 | 7.26E − 08 | MAE | 6.45E − 05 | 3.36E − 04 | 3.36E − 04 | 2.99E − 04 | 1.31E − 05 | 5.24E − 03 | 1.64E − 04 | 0.00012481 | MAPE | 1.46E − 02 | 7.52E − 02 | 7.52E − 02 | 6.69E − 02 | 4.91E − 03 | 1.64E + 00 | 4.76E − 02 | 0.039045 | RMSE | 1.23E − 04 | 0.000526 | 0.000526 | 0.000476 | 2.37E − 05 | 0.008165 | 0.000337 | 0.000269 | | 0.999822566 | 0.996755364 | 0.996755366 | 0.997335641 | 0.99999998 | 0.997567793 | 0.999995848 | 0.999997353 | R | 0.999911279 | 0.998376364 | 0.998376365 | 0.998666932 | 0.99999999 | 0.998783156 | 0.999997924 | 0.999998677 |
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