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