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Li et al. J. Mater. Inf. 2025, 5, 29 https://dx.doi.org/10.20517/jmi.2024.103 Page 3 of 18

property changes. These data are then analyzed using machine learning methods to assess how microscopic
structural changes influence the overall system’s performance [25,26] .

The aging of rubber materials is largely reflected in changes in mechanical properties. Predicting
macroscopic mechanical properties based on microscopic changes in material composition and structure
plays a crucial role in understanding aging and predicting service life. However, there is still limited research
exploring the relationship between microscopic and macroscopic properties of aging materials [27-30] ,
particularly in terms of identifying quantitative correlations. In the current research paradigm, expert
knowledge and theoretical models have their limitations and may not fully capture the complex
relationships in real-world systems, leading to inaccurate predictions. Simulation calculations are highly
complex and require substantial computational resources. Data-driven methods often lack interpretability,
as they do not adequately explain the underlying mechanisms behind the predicted results.

Consequently, symbolic regression (SR) algorithms are introduced for material aging research. SR, a distinct
machine learning approach, constructs mathematical models from input data without prior assumptions
about the model form. It explores a mathematical expression space comprising operators, variables,
constants, and functions. The core strength of SR is its intelligent search within the symbolic combination
space to identify the optimal model for a dataset, providing highly interpretable analytical solutions. Unlike
traditional machine learning, SR autonomously discovers hidden patterns and relationships.

Traditional SR methods, such as polynomial interpolation and curve fitting, have limitations. The sparse
[31]
identification of nonlinear dynamics (SINDy) method uses sparse regression with a predefined term
[32]
library, restricting its scope. Hopcroft proposed an expression tree generation method . Genetic
programming (GP) is sensitive to parameters and unstable. With the advent of deep learning, models such
[33]
[34]
as End-to-end SR (E2E) , SymbolicGPT and AIFeynman use neural networks for variable analysis and
[35]
expression search. Deep reinforcement learning methods, e.g., deep symbolic regression (DSR) , employ
[36]
recursive neural networks to generate expressions and a quantile-based reward strategy to avoid training
instability. The unified DSR (uDSR) model combines multiple SR-solving strategies, achieving better
[37]
[38]
performance in SRBench tasks.
[39]
SR algorithms have found extensive applications in the materials field . He et al. compared the SR
algorithm with common machine learning techniques and demonstrated that the SR algorithm can be used
[40]
to classify materials and describe material stability . Abdusalamov et al. developed a new procedure based
on the SR algorithm to automatically generate interpretable hyperelastic material models, which are highly
[41]
consistent with experimental data . In materials science, the selection of descriptors is essential for
material characterization. SR plays a significant role in choosing and defining material descriptors, thereby
facilitating the prediction of material properties. For instance, it has been employed to predict perovskite
Landau free energy expressions , obtaining function forms consistent with real values. It can also be
[39]
[42]
applied to infrared spectral data to forecast properties such as bond energy .
However, when it comes to polymer materials, especially in the context of rubber material aging, the
application of SR remains unexplored. The potential of SR in understanding the aging mechanisms of
rubber materials has not been tapped. Rubber materials, as polymer materials, inherently possess an
amorphous characteristic, and the materials themselves have a certain degree of uncertainty, such as the
molecular weight being a distribution. Therefore, the measurement of polymer materials has a certain
amount of noise. In addition to the problem of noise, there are also the impacts of data scarcity and
irrelevant variables. Due to the above conditions, it is difficult to obtain interpretable quantitative