Table 1 Adjust the control parameter quantities for simple-ML and MVMD-ML models to forecast the future behavior of Brook.

From: A hybrid framework: singular value decomposition and kernel ridge regression optimized using mathematical-based fine-tuning for enhancing river water level forecasting

Time

 

Methods

Values of parameters

t + 1

Simple-ML

L-SKRR

\(\alpha = 1.98E + 02\), \(\delta = 2.04E + 01\), \(\rho = 2.98E - 01\), \(\mu = 1.71E - 03\), \(\mu_{0} = 1.96E - 6\),\(\theta = 0.71\)

KRidge

\(\alpha = 3.59E + 09\), \(\delta = 2.00E + 12\), \(\rho = 5.17E + 08\),\(\mu = 1.00E - 12\)

dRVFL

NoLs* = 10, NoNs = 20, Scf* = 200, Acf = sign, C = 1.00E+10

LASSO

Alpha = 0.001

CFNN

Structure = [5 3 1]

MVMD-ML

L-SKRR

\(\alpha = 1.62E + 10\), \(\delta = 7.75E + 09\), \(\rho = 2.14E + 09\), \(\mu = 1.00E - 12\), \(\mu_{0} = 1.00E - 3\),\(\theta = 0.62\)

KRidge

\(\alpha = 4.69E + 09\), \(\delta = 2.00E + 12\), \(\rho = 2.56E + 08\),\(\mu = 4.63E - 14\)

dRVFL

NoLs = 20, NoNs = 300, Scf = 800, Acf = sign, C = 1.00E + 08

LASSO

Alpha = 1.00E-08

CFNN

Structure = [4 3 3 1]

t + 3

Simple-ML

L-SKRR

\(\alpha = 5.30E + 00\), \(\delta = 8.37E + 00\), \(\rho = 1.29E - 02\), \(\mu = 3.47E + 00\), \(\mu_{0} = 9.73\),\(\theta = 0.74\)

KRidge

\(\alpha = 5.12E + 08\), \(\delta = 3.49E + 11\), \(\rho = 1.16E + 11\),\(\mu = 1.00E - 12\)

dRVFL

NoLs = 5, NoNs = 50, Scf = 10, Acf = sign, C = 1.00E+10

LASSO

Alpha = 1.00E−04

CFNN

Structure = [5 5 1]

MVMD-ML

L-SKRR

\(\alpha = 1.04E + 04\), \(\delta = 1.92E + 04\), \(\rho = 1.91E + 03\), \(\mu = 1.00E - 10\), \(\mu_{0} = 0.78\),\(\theta = 0.54\)

KRidge

\(\alpha = 1.00E - 12\), \(\delta = 1.49E + 10\), \(\rho = 9.49E + 09\), \(\mu = 1.00E - 10\),

dRVFL

NoLs = 10, NoNs = 150, Scf = 100, Acf = sign, C = 1.00E+10

LASSO

Alpha = 1.00E−10

CFNN

Structure = [3 3 1]

  1. NoNs* = Number of neurons, NoLs* = Number of layers, Acf * = activation function Scf* = scaling factor.