Table 4 Statistical metrics of the B-MVMD-WKELM-R-GBO model and four other hybrid ML models.

From: Development of a novel modeling framework based on weighted kernel extreme learning machine and ridge regression for streamflow forecasting

 

Hybrid model

 

R

RMSE

MAPE

NSE

IA

U95%

Q(t + 3)

K = 5

B-MVMD-WKELM-R-GBO

Train

0.996

0.291

13.003

0.993

0.998

0.805

Test

0.992

0.426

22.548

0.983

0.996

1.181

B-MVMD-Ridge-GBO

Train

0.943

1.168

46.780

0.880

0.964

3.238

Test

0.954

1.031

62.880

0.901

0.971

2.857

B-MVMD-GRNN-GBO

Train

0.957

1.035

49.480

0.906

0.973

2.852

Test

0.920

1.360

98.449

0.827

0.943

3.769

B-MVMD-ENET-GBO

Train

0.977

0.720

37.757

0.954

0.988

1.997

Test

0.987

0.534

43.882

0.973

0.993

1.480

B-MVMD-LGBM-GBO

Train

0.984

0.604

11.361

0.968

0.992

1.674

Test

0.968

0.826

33.167

0.936

0.983

2.289

Q(t + 7)

K = 10

B-MVMD-WKELM-R-GBO

Train

0.991

0.459

16.993

0.982

0.995

1.270

Test

0.997

0.249

21.267

0.994

0.999

0.690

B-MVMD-Ridge-GBO

Train

0.977

0.717

41.200

0.955

0.988

1.987

Test

0.988

0.509

46.479

0.976

0.994

1.410

B-MVMD-GRNN-GBO

Train

0.958

1.024

47.767

0.908

0.973

2.830

Test

0.866

1.674

109.882

0.738

0.909

4.640

B-MVMD-ENET-GBO

Train

0.962

0.926

46.902

0.925

0.980

2.567

Test

0.978

0.687

56.400

0.956

0.988

1.904

B-MVMD-LGBM-GBO

Train

0.987

0.553

9.874

0.973

0.993

1.532

Test

0.948

1.083

46.010

0.890

0.967

3.000

Q(t + 14)

K = 12

B-MVMD-WKELM-R-GBO

Train

0.985

0.589

14.543

0.970

0.992

1.634

Test

0.996

0.304

16.694

0.991

0.998

0.842

B-MVMD-Ridge-GBO

Train

0.938

1.176

63.791

0.879

0.966

3.260

Test

0.957

1.001

73.758

0.907

0.973

2.774

B-MVMD-GRNN-GBO

Train

0.959

1.000

43.152

0.913

0.975

2.765

Test

0.820

1.875

97.717

0.672

0.891

5.198

B-MVMD-ENET-GBO

Train

0.939

1.166

67.669

0.881

0.967

3.234

Test

0.956

1.004

78.862

0.906

0.973

2.783

B-MVMD-LGBM-GBO

Train

0.977

0.729

40.543

0.953

0.988

2.022

Test

0.902

1.422

83.286

0.811

0.943

3.942

  1. Significant values are given in bold.
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