Table 8. Engine Torque Prediction with Different Fitting Methods.

			fitting result (validationa)
	fitting methods	hyperparameters	RMSE	R2	MSE	MAE
	GPR introduced in this study	combined kernel defined in this study	1.7381	1.00	3.0211	1.0077
linear regression	linear	preset: linear robust option: off	11.34	1.00	128.59	8.1743
	interaction linear	preset: interactions linear robust option: off	7.7276	1.00	59.715	4.2302
	robust linear	preset: robust linear robust option: on	11.786	0.99	138.91	7.9663
decision tree	fine tree	minimum leaf size: 4 surrogate decision splits: off	6.1395	1.00	37.694	1.6206
	medium tree	minimum leaf size: 12 surrogate decision splits: off	6.0582	1.00	36.702	1.672
	coarse tree	minimum leaf size: 36 surrogate decision splits: off	6.6141	1.00	43.747	1.8936
	boosted trees	minimum leaf size: 8preset: boosted trees	14.932	0.99	222.96	11.591
	bagged tree	minimum leaf size: 8preset: bagged trees	5.149	1.00	26.512	1.341
SVM	linear SVM	kernel function: linear kernel scale: automatic	12.409	0.99	153.99	9.7683
	quadratic SVM	kernel function: quadratic kernel scale: automatic	10.492	1.00	110.08	8.0499
	fine Gaussian SVM	kernel function: Gaussian kernel scale: 0.97	12.908	0.99	166.62	9.952
	medium Gaussian SVM	kernel function: Gaussian kernel scale: 3.9	10.949	1.00	119.88	8.7303
	coarse Gaussian SVM	kernel function: Gaussian kernel scale: 15	10.394	1.00	108.03	7.6224
neural network	narrow neural network	number of fully connected layers: 1; first layer size: 10;activation: ReLu	7.1358	1.00	50.92	3.8654
	medium neural network	number of fully connected layers: 1; first layer size: 25;activation: ReLu	6.1125	1.00	37.362	2.8717
	bilayered neural network	number of fully connected layers: 2; first layer size: 10; second layer size: 10;activation: ReLu	6.69	1.00	44.756	3.326
	trilayered neural network	number of fully connected layers: 3; first layer size: 10; second layer size: 10; third layer size: 10;activation: ReLu	12.728	0.99	162	6.4575

^aValidation data are 5% randomly selected from the training dataset.