Table 7 Comparison of our supervised model against previous echo state network approaches, showing consistent performance improvements over published methods across multiple datasets and time series prediction tasks.
From: Input driven optimization of echo state network parameters for prediction on chaotic time series
Title paper | Data set | Reservoir number | Base ESN NRMSE | Suggested model | All data | Train and valid data | test | Percentage of improvement (+ means get better) | Our Simple | Our model | Percentage of improvement |
|---|---|---|---|---|---|---|---|---|---|---|---|
Chaotic time series prediction using echo state network based on selective opposition grey wolf optimizer | MG Tua = 17 | 100 | 3.69e−4 | 5.34e−4 | 5000 | 4200 | 800 | −44.72% | 0.2804 | 0.1652 | + 41.08% |
3.18e−4 | + 13.82% | ||||||||||
2.98e−4 | + 19.24% | ||||||||||
2.83e−4 | + 23.31% | ||||||||||
200 | 3.66e−4 | 4.75e−4 | −29.78% | 0.2236 | 0.1088 | + 51.34% | |||||
2.57e−4 | + 29.78% | ||||||||||
1.95e−4 | + 46.72% | ||||||||||
1.85e−4 | + 49.45% | ||||||||||
500 | 3.74e−4 | 4.94e−4 | −32.09% | 0.1097 | 0.059 | + 46.22% | |||||
2.34e−4 | + 37.43% | ||||||||||
1.54e−4 | + 58.82% | ||||||||||
1.46e−4 | + 60.96% | ||||||||||
Collective behavior of a small-world recurrent neural system with scale-free distribution | Laser times series(18) | 500 | 0.1422 | 0.1148 | 2400 | 2200 | 200 | + 19.27% | 0.28 | 0.25 | + 10.71% |
Laser times series(19) | 500 | 0.0804 | 0.0558 | 2700 | 2500 | 200 | + 30.60% | 0.26 | 0.23 | + 11.54% | |
SCESN, SPESN, SWESN: Three recurrent neural echo state networks with clustered reservoirs for prediction of nonlinear and chaotic time series | Laser times series(18) | 500 | 0.1422 | 0.1141 | 2400 | 2200 | 200 | + 19.76% | 0.28 | 0.25 | + 10.71% |
0.1118 | + 21.38% | ||||||||||
0.1135 | + 20.18% | ||||||||||
Laser times series(19) | 500 | 0.0804 | 0.0512 | 2700 | 2500 | 200 | + 36.32% | 0.26 | 0.23 | + 11.54% | |
0.0491 | + 38.93% | ||||||||||
0.0531 | + 33.96% | ||||||||||
Design of a reservoir for cloud-enabled echo state network with high clustering coefficient | Laser times series(18) | 500 | 0.1422 | 0.1140 | 2400 | 2200 | 200 | + 19.83% | 0.28 | 0.25 | + 10.71% |
0.1138 | + 19.97% | ||||||||||
0.1132 | + 20.39% | ||||||||||
0.1107 | + 22.15% | ||||||||||
Laser times series(19) | 500 | 0.0804 | 0.0510 | 2700 | 2500 | 200 | + 36.57% | 0.26 | 0.23 | + 11.54% | |
0.0497 | + 38.18% | ||||||||||
0.0501 | + 37.69% | ||||||||||
0.0442 | + 45.02% | ||||||||||
Parameterizing echo state networks for multi-step time series prediction | MG Tua = 17 | 2024 | 15.710 | 0.025 | 2368 | 2082 | 286 | + 99.84% | 0.32 | 0.31 | + 3.13% |
