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Page 6 of 18 Li et al. J. Mater. Inf. 2025, 5, 29 https://dx.doi.org/10.20517/jmi.2024.103

Table 1. The characteristics of the SR4Real dataset
Type Number of equations Number of data Operation range Domain range Perfect fit Dummy variable
Base 10 1,000 (2,5) (2,12) Yes No
Ops 6 1,000 (8,15) (2,6) Yes No
Domain 6 1,000 (4,7) (30,50) Yes No
Num 10 50 (2,5) (2,12) Yes No
Noise 10 1,000 (2,5) (2,12) No No
Dummy 10 1,000 (2,5) (1,4) Yes Yes
“Operation range” represents the number of the operands in a formula, such as add, mul, pow, exp, and log operations. “Domain range”
represents the magnitude of sampling distributions; the complexity increases when sampling values from wide-range distributions. The domain
range is defined as: f (S) = |log10(max S - min S)|.
range

a total of 37 samples. The following characterizations are performed on these 37 samples:

1. Use attenuated total reflection-Fourier transform infrared spectroscopy (ATR-FTIR) to determine the
infrared spectrum of the rubber surface and cross-section to observe the changes in chemical structure
during aging.
2. Use low-field NMR (LF-NMR) to determine the changes in crosslink density (XLD) of rubber during
thermal oxidative aging.
3. Use liquid chromatography to determine the changes in the content of plasticizers and antioxidants in
rubber.
4. Use a hardness tester to measure the changes in the surface hardness of the rubber.
5. Use an electronic universal testing machine to determine the tensile properties of rubber and obtain the
variation of the fracture elongation (Fe).

Each data point in the dataset includes 11 features: four characteristic peaks on the material surface and four
on the material cross-section, identified via IR; the XLD of the polymer measured by LF-NMR; and the
content of plasticizers and antioxidants directly quantified through liquid chromatography.

Additionally, each data point contains two dependent variables, both macroscopic properties related to the
material’s mechanical performance: elongation at fracture and Shore hardness. These properties provide
insight into the material’s behavior under stress and its overall hardness. The symbolic definitions of the
variables are presented in Table 2.

In the context of this study, the materials investigated are polymer-based systems undergoing aging, which
leads to chemical changes over time. Specifically, the aging process in these materials involves crosslinking
reactions facilitated by the breaking of carbon-carbon (C=C) double bonds in the presence of oxygen, which
alters both their molecular structure and mechanical properties.

For IR, different peaks correspond to the vibrational modes of various functional groups. The peaks at 2,914
-1
and 2,840 cm correspond to the stretching vibrations of C–H bonds, which indicate the presence of carbon
atoms bonded to two hydrogen atoms. The peak at 1,736 cm is attributed to the stretching vibration of
-1
C=O bonds, characteristic of compounds such as esters, and provides indirect information about the
-1
concentration of plasticizers in the system. The peak at 964 cm is associated with the specific vibration of
C=C double bonds, including the out-of-plane bending vibration of cis-C=C, offering insight into the
remaining double-bond content, which is an important indicator of the material’s degree of crosslinking
and oxidation.