Table 8 Statistical metrics achieved by ML models for MAR-M case.

From: Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition

Model

Metric

R

RMSE

MAPE

IA

MaxAE

VSD

U95%

OMVMD-GRKR

Train

0.981

1.442

3.444

0.990

5.023

21.873

4.000

Test

0.964

2.293

5.331

0.982

7.896

22.821

6.366

GRKR

Train

0.565

6.144

16.548

0.671

25.414

562.533

17.041

Test

0.388

8.016

19.044

0.534

26.002

313.627

22.256

OMVMD-Ridge

Train

0.966

1.953

4.833

0.981

6.695

44.606

5.418

Test

0.947

2.893

6.751

0.970

11.081

36.825

7.866

Ridge

Train

0.591

6.014

16.086

0.698

24.431

541.240

16.682

Test

0.112

9.626

23.625

0.426

36.006

508.858

26.368

OMVMD-LSSVM

Train

0.981

1.490

3.702

0.989

5.439

26.301

4.132

Test

0.948

2.765

6.528

0.972

9.643

33.866

7.669

LSSVM

Train

0.438

7.221

19.869

0.148

28.550

813.038

20.030

Test

0.176

8.874

20.710

0.288

31.773

385.385

24.251

OMVMD-DELM

Train

0.974

2.001

5.462

0.979

9.740

64.911

5.429

Test

0.877

5.204

11.220

0.858

18.030

117.530

13.888

DELM

Train

0.459

7.254

20.325

0.192

29.518

840.909

20.067

Test

0.158

8.802

20.664

0.257

31.281

382.005

24.167

OMVMD-DRVFL

Train

0.969

1.847

4.520

0.983

6.570

38.723

5.123

Test

0.950

2.775

6.433

0.973

9.497

33.432

7.613

DRVFL

Train

0.565

6.149

16.374

0.695

25.266

558.116

17.056

Test

0.170

9.354

22.987

0.451

35.876

477.016

25.686

OMVMD-stacking

Train

0.988

1.141

2.835

0.994

3.484

13.778

3.165

Test

0.777

6.211

13.427

0.846

16.322

173.539

16.268

Stacking

Train

0.489

6.492

17.479

0.604

24.865

651.163

18.008

Test

0.198

8.682

19.942

0.395

30.661

384.000

23.990

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