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Table 7

Statistical indices using the applied soft computing models for modeling the secondary flow depth of hydraulic jump (h₂) in the training and validation phases

Stage	Method	Statistical parameters
Stage	Method	RMSE (m)	R²	MAE (m)	NSE	IA
Train	ANFIS-FA	0.0038	0.988	0.0029	0.988	0.997
	ANFIS-GA	0.0042	0.984	0.0033	0.984	0.996
	ANFIS-PSO	0.005	0.978	0.0039	0.978	0.994
	ANFIS	0.0067	0.96	0.0051	0.96	0.99
	ANFIS-WOA	0.0076	0.95	0.0058	0.95	0.987
	ANFIS-MFO	0.0083	0.94	0.0061	0.94	0.984
Validation	ANFIS-FA	0.0042	0.981	0.0014	0.981	0.995
	ANFIS-GA	0.005	0.972	0.0017	0.972	0.993
	ANFIS-PSO	0.0053	0.97	0.0019	0.969	0.992
	ANFIS	0.0067	0.951	0.0024	0.951	0.987
	ANFIS-WOA	0.0076	0.936	0.0028	0.936	0.984
	ANFIS-MFO	0.0081	0.93	0.0028	0.928	0.982

Stage	Method	Statistical parameters
Stage	Method	RMSE (m)	R²	MAE (m)	NSE	IA
Train	ANFIS-FA	0.0038	0.988	0.0029	0.988	0.997
	ANFIS-GA	0.0042	0.984	0.0033	0.984	0.996
	ANFIS-PSO	0.005	0.978	0.0039	0.978	0.994
	ANFIS	0.0067	0.96	0.0051	0.96	0.99
	ANFIS-WOA	0.0076	0.95	0.0058	0.95	0.987
	ANFIS-MFO	0.0083	0.94	0.0061	0.94	0.984
Validation	ANFIS-FA	0.0042	0.981	0.0014	0.981	0.995
	ANFIS-GA	0.005	0.972	0.0017	0.972	0.993
	ANFIS-PSO	0.0053	0.97	0.0019	0.969	0.992
	ANFIS	0.0067	0.951	0.0024	0.951	0.987
	ANFIS-WOA	0.0076	0.936	0.0028	0.936	0.984
	ANFIS-MFO	0.0081	0.93	0.0028	0.928	0.982