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Table 10

Statistical indices using the applied soft computing and empirical models for predicting the hydraulic jump length (L_j) in the testing phase

Method	Statistical parameters
Method	RMSE	R²	MAE	NSE	IA	RMSE changes %	RMSE improvement %
Recurrent ANFIS
RANFIS-GA	0.046	0.846	0.016	0.841	0.960	20.86	92.03
RANFIS-PSO	0.046	0.838	0.016	0.837	0.957	20	91.94
RANFIS-FA	0.047	0.835	0.015	0.834	0.955	19.14	91.86
RANFIS	0.053	0.789	0.018	0.787	0.940	8.45	90.78
RANFIS-MFO	0.065	0.685	0.022	0.678	0.906	−12.41	88.68
RANFIS-WOA	0.074	0.599	0.026	0.588	0.880	−27.24	87.19
Conventional ANFIS
ANFIS-GA	0.052	0.799	0.017	0.796	0.944	10.34	90.97
ANFIS-PSO	0.047	0.834	0.016	0.831	0.956	18.96	91.84
ANFIS-FA	0.048	0.827	0.016	0.824	0.953	16.72	91.61
ANFIS	0.058	0.751	0.020	0.746	0.929	Base	89.93
ANFIS-MFO	0.064	0.692	0.022	0.687	0.909	−10.86	88.84
ANFIS-WOA	0.074	0.598	0.026	0.587	0.879	−27.24	87.19
Empirical relation
Silvester (1964)	0.576	0.296	0.229	−24.09	0.270	−893.10	Base

Method	Statistical parameters
Method	RMSE	R²	MAE	NSE	IA	RMSE changes %	RMSE improvement %
Recurrent ANFIS
RANFIS-GA	0.046	0.846	0.016	0.841	0.960	20.86	92.03
RANFIS-PSO	0.046	0.838	0.016	0.837	0.957	20	91.94
RANFIS-FA	0.047	0.835	0.015	0.834	0.955	19.14	91.86
RANFIS	0.053	0.789	0.018	0.787	0.940	8.45	90.78
RANFIS-MFO	0.065	0.685	0.022	0.678	0.906	−12.41	88.68
RANFIS-WOA	0.074	0.599	0.026	0.588	0.880	−27.24	87.19
Conventional ANFIS
ANFIS-GA	0.052	0.799	0.017	0.796	0.944	10.34	90.97
ANFIS-PSO	0.047	0.834	0.016	0.831	0.956	18.96	91.84
ANFIS-FA	0.048	0.827	0.016	0.824	0.953	16.72	91.61
ANFIS	0.058	0.751	0.020	0.746	0.929	Base	89.93
ANFIS-MFO	0.064	0.692	0.022	0.687	0.909	−10.86	88.84
ANFIS-WOA	0.074	0.598	0.026	0.587	0.879	−27.24	87.19
Empirical relation
Silvester (1964)	0.576	0.296	0.229	−24.09	0.270	−893.10	Base