Table 3 Robustness evaluation of SR models under different noise types and levels (1%–5%) for the expression- tree score.
Experiment | SR Model | Feature noise | Target noise | Both noise | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1% | 2% | 3% | 4% | 5% | 1% | 2% | 3% | 4% | 5% | 1% | 2% | 3% | 4% | 5% | ||
Dropping ball | DEAP | 0.17 | 0.22 | 0.26 | 0.29 | 0.30 | 0.29 | 0.37 | 0.40 | 0.42 | 0.44 | 0.46 | 0.52 | 0.55 | 0.56 | 0.57 |
PySR | 0.11 | 0.15 | 0.20 | 0.22 | 0.25 | 0.15 | 0.20 | 0.25 | 0.27 | 0.30 | 0.25 | 0.30 | 0.35 | 0.37 | 0.40 | |
gplearn | 0.20 | 0.25 | 0.30 | 0.32 | 0.35 | 0.31 | 0.40 | 0.42 | 0.43 | 0.45 | 0.48 | 0.54 | 0.57 | 0.58 | 0.60 | |
Simple harmonic motion | DEAP | 0.12 | 0.17 | 0.22 | 0.24 | 0.25 | 0.22 | 0.27 | 0.30 | 0.33 | 0.35 | 0.29 | 0.34 | 0.37 | 0.39 | 0.40 |
PySR | 0.07 | 0.10 | 0.12 | 0.14 | 0.15 | 0.10 | 0.14 | 0.17 | 0.20 | 0.22 | 0.20 | 0.24 | 0.27 | 0.28 | 0.30 | |
gplearn | 0.10 | 0.15 | 0.17 | 0.19 | 0.20 | 0.20 | 0.24 | 0.27 | 0.30 | 0.33 | 0.28 | 0.32 | 0.35 | 0.37 | 0.40 | |
Electromagnetic wave | DEAP | 0.10 | 0.15 | 0.19 | 0.20 | 0.22 | 0.25 | 0.30 | 0.32 | 0.34 | 0.35 | 0.35 | 0.40 | 0.42 | 0.44 | 0.45 |
PySR | 0.05 | 0.08 | 0.10 | 0.11 | 0.12 | 0.12 | 0.17 | 0.20 | 0.22 | 0.25 | 0.22 | 0.27 | 0.29 | 0.30 | 0.30 | |
gplearn | 0.08 | 0.12 | 0.15 | 0.17 | 0.18 | 0.22 | 0.27 | 0.29 | 0.30 | 0.32 | 0.32 | 0.37 | 0.39 | 0.40 | 0.40 | |
