## 3 Results
### Elastic Modulus
Notably, the DP model's predictions consistently fall within 10% tolerance of reported values, further supporting its reliability and accuracy in capturing SOC-dependent mechanical behavior. The relatively lower experimental moduli in Figure 6 may result from the indirect nature of nanoindentation measurements and the influence of defects and grain boundaries, whereas our simulations are based on a defect-free perfect crystal structure. Interestingly, the Buckingham model predicts higher modulus values than both the DP model and reference data. This overestimation is likely due to the Buckingham model's reliance on full formal charges, which are known to exaggerate Coulombic interactions [11; 51]. While the calculated values are elevated, the overall trend remains consistent with both the DP model and experimental references. Adjusting the formal charges to reduced values could improve the Buckingham model's quantitative accuracy. When comparing the two models, the DP model demonstrates notable advantages in several aspects. First, it exhibits improved consistency, with minimal fluctuations across SOC states, resulting in smoother and more predictable trends. Second, the DP model shows closer agreement with reference data, as its predictions align well with experimental values and fall within an acceptable tolerance limit. Lastly, the DP model offers enhanced physical  
Figure 8: Shear strain distribution at a strain of 0.09 for (**a**) SOC = 0.25, (**b**) SOC = 0.5, and (**c**) SOC = 0.83. Figure 9: Stress–strain curves in the x direction for various SOC obtained by DP model. realism by effectively capturing the evolving contributions of Co\({}^{3+}\) and Co\({}^{4+}\) interactions, thereby providing a more accurate representation of the material's true behavior. The results also reveal important implications for mechanical stability. As SOC decreases, the increasing dominance of Co\({}^{4+}\) interactions introduces localized stress concentrations, which may promote crack initiation and accelerate electrode degradation. Furthermore, the variation in oxygen's contribution suggests evolving Co-O bonding environments that may contribute to structural instability at low SOC levels. These findings highlight the need to account for SOC-driven mechanical changes when designing cycling protocols or developing electrode coatings to mitigate fracture risks. Overall, these findings underscore the superior accuracy and reliability of the machine learning-based DP model. Its improved predictive capabilities make it a promising tool for future studies, particularly for investigating the mechanical behavior of cathode materials under various electrochemical conditions. Recent work by [PERSON] et al. has highlighted the importance of mechanical degradation mechanisms, such as modulus softening, particle cracking, and interface delamination, in dictating the long-term electrochemical performance and safety of lithium-ion batteries [52]. In this context, mechanical properties such as elastic modulus and fracture energy evolve with cycling and can be directly linked to state-of-health (SOH) indicators. As damage accumulates, the material's ability to maintain structural integrity under electrochemical and thermal stresses degrades, reducing its remaining useful life (RUL). Our findings on strain localization and mechanical response at different states of charge suggest that such mechanical descriptors could be integrated into future battery prognostics models, providing a more comprehensive understanding of degradation and lifetime estimation.