Table 4 Result of supervised model.

From: Input driven optimization of echo state network parameters for prediction on chaotic time series

Data set

Model name

Metric

N = 5

N = 50

N = 500

N = 1000

A

Supervised model

NRMSE

0.26 ± 0.06

2.6550 ± 9.8

0.0268 ± 0.03

0.0253 ± 0.02

MSE

0.0912 ± 0.03

9.5 ± 60

(9.6 ± 1)e-4

(8.6 ± 1)e-4

Simple ESN

NRMSE

2.24 ± 9.7

2.3 ± 9.7

0.078 ± 0.053

0.097 ± 0.12

MSE

6.76 ± 50.4

7.13 ± 51

(8.2 ± 0.9)e-3

0.0126 ± 0.02

B

Supervised model

NRMSE

0.179 ± 0.11

0.0229 ± 0.01

(6.47 ± 0.1)e-04

(4.415 ± 0.2)e-04

MSE

0.026 ± 0.03

(4.3 ± 4)e-4

(3.4 ± 0.1)e-5

(1.6 ± 1)e-5

Simple ESN

NRMSE

4.157 ± 9.7

0.061 ± 0.13

0.0043 ± 0.004

0.049 ± 0.04

MSE

14.23 ± 73

0.307 ± 0.14

(1.5 ± 0.3)e-4

(1.9 ± 0.3)e-3

C

Supervised model

NRMSE

0.005 ± 5e-04

(5.09 ± 0.3)e-05

(6.84 ± 0.2)e-04

(6.33 ± 0.1)e-04

MSE

(7.1 ± 0.3)e-5

(7.62 ± 0.2)e-6

(1.37 ± 0.1)e-5

(1.17 ± 0.6)e-5

Simple ESN

NRMSE

6.01 ± 9.9

0.0013 ± 0.002

0.0006 ± 0.0006

0.0004 ± 0.0002

MSE

6.01 ± 5

(5 ± 0.2)e-4

(1.05 ± 3)e-5

(4.7 ± 8)e-5

D

Supervised model

NRMSE

0.2206 ± 0.001

0.2198 ± 0.002

0.2252 ± 0.001

0.2234 ± 0.001

MSE

0.0445 ± 0.0004

0.04418 ± 0.0008

0.0463 ± 0.0004

0.0456 ± 0.0004

Simple ESN

NRMSE

0.25 ± 0.003

0.26 ± 0.002

6.11 ± 9.7

10 ± 0.0

MSE

0.0571 ± 0.001

0.0618 ± 0.0009

34.1 ± 10

91 ± 0.0

E

Supervised model

NRMSE

0.2454 ± 0.016

0.2364 ± 0.08

0.159 ± 0.07

0.13008 ± 0.01

MSE

0.03432 ± 0.004

0.03276 ± 0.02

0.0118 ± 0.003

0.01002 ± 0.002

Simple ESN

NRMSE

0.2583 ± 0.01

0.3363 ± 0.006

0.2106 ± 0.02

0.1614 ± 0.01

MSE

0.0884 ± 0.09

0.0579 ± 0.002

0.02485 ± 0.01

0.0204 ± 0.002

F

Supervised model

NRMSE

0.217 ± 0.005

0.2089 ± 0.046

0.1116 ± 0.064

0.15103 ± 0.01

MSE

0.0352 ± 0.002

0.0442 ± 0.01

0.0104 ± 0.01

0.01110 ± 0.02

Simple ESN

NRMSE

0.2699 ± 0.01

0.2553 ± 0.07

0.1449 ± 0.02

0.2607 ± 0.04

MSE

0.06171 ± 0.006

0.0599 ± 0.02

0.0209 ± 0.006

0.0594 ± 0.02

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