## 1 Introduction  
Lithium-ion batteries (LIBs) are indispensable in modern technology, powering applications from portable electronics to electric vehicles due to their high energy density, long lifespan, and efficiency [1, 2]. A critical component influencing LIB performance and durability is the cathode material. Among the various candidates, lithium cobalt oxide (LiCoO\({}_{2}\), LCO) was the first widely commercialized cathode and continues to be used in high-energy-density applications, especially in thin-film [3] and solid-state battery research [4]. Its layered structure, well-defined electrochemical profile, and stable cycling performance make it a model system for fundamental studies. Despite LCO's well-characterized electrochemical behavior, its mechanical integrity across varying states of charge (SOCs) remains underexplored. Mechanical degradation, such as particle cracking and interfacial delamination, is a major contributor to capacity fade and safety risks in LIBs [5, 6, 7]. While prior studies have investigated mechanical properties at either fully lithiated or delithiated states, a systematic understanding of how elastic properties evolve with lithium content is lacking. Given that [PERSON]'s modulus and stress evolution are key inputs for continuum models that predict electrode-level degradation, understanding these SOC-dependent mechanical behaviors is both timely and essential. Experimental characterization of SOC-dependent elasticity is inherently difficult due to lithium's low atomic number, complex charge compensation mechanisms, and structural heterogeneity. As a result, atomistic simulations have become essential tools to investigate mechanical properties of battery materials. Molecular dynamics (MD) simulations using empirical force fields have been extensively employed to assess elastic constants, fracture mechanisms, and diffusion-induced stresses in oxide cathodes [8; 9; 10]. For instance, studies on LiNi\({}_{1/3}\)Mn\({}_{1/3}\)Co\({}_{1/3}\)O\({}_{2}\) and LiMn\({}_{2}\)O\({}_{4}\) have successfully captured trends in SOC-dependent stiffness and anisotropic deformation using classical potentials with core-shell models [11]. Several MD simulation studies have investigated LiCoO\({}_{2}\) to better understand its structural, transport, and mechanical behavior. [PERSON] and [PERSON] performed MD simulations using a Lennard-Jones-based force field to analyze lithium-ion diffusion in LCO under varying voltage and lithium content [12]. They reported diffusion coefficients and anisotropic transport trends consistent with experimental data. [PERSON] et al. developed a charge-transfer modified embedded-atom method (CT-MEAM) to model the Li-Co-O system, demonstrating its ability to capture dynamic charge transfer, phase stability, and cathode voltages across Li-rich and Li-deficient compounds [13]. More recently, [PERSON] et al., proposed a second nearest-neighbor modified embedded-atom method (2 NNMEAM) combined with a charge equilibration scheme (Qeq) and applied it to simulate lithium diffusion and mechanical properties in Li\({}_{1-x}\)CoO\({}_{2}\)[14]. Their model reproduced key properties such as elastic constants, migration barriers, and redox potentials in good agreement with DFT and experimental results. However, empirical force fields often rely on parameters fitting to specific chemistries, limiting their transferability across phases or charge states. This is particularly problematic for complex charge compensation phenomena in LCO, where the Co\({}^{3+}\)/Co\({}^{4+}\) ratio evolves with lithiation. First-principles methods like density functional theory (DFT) offer quantum-level accuracy but are computationally prohibitive for the system sizes required to model microstructural effects. To address this trade-off, machine learning-based potentials such as the Deep Potential (DP) model have recently gained traction [15; 16]. By training on DFT data, DP models preserve quantum mechanical fidelity while enabling simulations of large and realistic supercells.