Page 51 - Read Online

Page 10 of 18 Li et al. J. Mater. Inf. 2025, 5, 29 https://dx.doi.org/10.20517/jmi.2024.103

2
Table 3. The R score of each SR method on SR4Real dataset
SR algorithm E2E DSO uDSR
Base 0.880 1.000 1.000
Ops 0.129 0.617 0.901
Dummy 0.944 0.880 0.999
Noise -0.115 0.647 0.643
Num 0.833 1.000 1.000
Domain 0.476 0.732 0.398
Average 0.525 0.813 0.824

2
R : Coefficient of determination; SR: symbolic regression; E2E: end-to-end symbolic regression; DSO: deep symbolic optimization; uDSR: unified
deep symbolic regression.

Table 4. The NED of each SR method on SR4Real dataset
SR algorithm E2E DSO uDSR
Base 65.500 3.300 10.500
Ops 205.500 15.833 132.333
Dummy 269.400 17.000 26.700
Noise 74.600 16.400 70.700
Num 48.400 4.600 12.000
Domain 132.667 10.167 17.667
Average 132.678 11.217 44.983

NED: Normalized edit distance; SR: symbolic regression; E2E: end-to-end symbolic regression; DSO: deep symbolic optimization; uDSR: unified
deep symbolic regression.

2
Figure 2. The performance of three SR methods, namely E2E, DSO, and uDSR, on six datasets. (A) R , (B) 1+exp(-Z score (NED)). For both of
the indicators, a larger value indicates a superior performance. SR: Symbolic regression; E2E: end-to-end symbolic regression; DSO: deep
2
symbolic optimization; uDSR: unified deep symbolic regression; R : coefficient of determination; NED: normalized edit distance.
data (noise), E2E suffers a significant performance decline, whereas DSO and uDSR, though affected,
maintain a certain degree of efficacy. In the scenario with an irrelevant variable (Dummy), uDSR excels, and
E2E and DSO remain relatively stable. For the scenario involving a large number of formula operands (ops),