## 4 Conclusions  
This study provides a thorough analysis of the mechanical properties of cathode materials under different SOCs using both an empirical Buckingham potential model and machine learning-based Deep Potential models. The Buckingham potential model showed a significant reduction in Young's modulus as the SOC decreased, indicating that the mechanical behavior of the material is highly sensitive to changes in structure and ionic state. Analyzing the stress factors revealed that pairwise interactions, particularly involving Co\({}^{3+}\) and Co\({}^{4+}\), play a dominant role in driving these changes. The transition from Co\({}^{3+}\) to Co\({}^{4+}\) and the resulting alterations in bonding characteristics were identified as key mechanisms influencing the observed trends.  
In contrast, the Deep Potential model, which uses advanced machine learning techniques, demonstrated significant advantages over the analytical model. It provided more consistent and reliable predictions with minimal fluctuations, closely aligning with reference data within an acceptable tolerance range. The model's ability to capture a clear linear trend, along with its robustness and adaptability, highlights its potential for more accurate simulations of mechanical properties in energy storage materials.  
Moreover, the analysis revealed that the Buckingham model's sharp fluctuations at lower SOCs could be linked to structural instability or phase transition effects. The increased dominance of Co\({}^{4+}\) interactions at lower SOCs introduces localized stress concentrations, which may enhance crack initiation and accelerate electrode degradation. This observation underscores the importance of considering SOC-dependent mechanical changes when designing battery cycling protocols or developing protective coatings to mitigate fracture risks.  
Importantly, the calculated mechanical properties provide valuable input for continuum-scale models that are widely used in studying the chemo-mechanical behavior and mechanical degradation of LCO materials due to aging. By incorporating SOC-dependentmaterial properties, continuum models can improve the prediction of stress evolution, crack formation, and degradation processes in LCO-based battery systems, enabling the design of more durable and stable electrodes.  
Overall, the findings validate the superiority of the Deep Potential model for studying complex cathode materials. Its predictive accuracy and capacity to unveil intricate material behaviors make it a valuable tool for future research and development. This approach shows promise for optimizing the design of advanced materials with tailored mechanical properties, ultimately facilitating the development of more efficient and reliable energy storage systems.  
Conceptualization, S.L. and I.U.H.; methodology, I.U.H.; software, I.U.H.; validation, I.U.H.; formal analysis, I.U.H.; investigation, I.U.H.; resources, S.L.; data curation, I.U.H.; writing--original draft preparation, I.U.H.; writing--review and editing, S.L.; visualization, I.U.H.; supervision, S.L.; project administration, S.L.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Research Foundation of Korea, along with a research grant funded by the Ministry of Science and ICT (No. 2022R1A2C1003003).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.