We note that the Hubbard U correction is applied to Co ions. We set the U value as 5.14 eV, which was obtained from previous work. Both the Co 3+ and Co 4+ ions are in the low spin state, that is, the magnetic moments of the Co 3+ and Co 4+ ions are 0 μB and 1 μB respectively. Then, the PES of the LixCoO2 material (including the O3/O1/spinel phases) is constructed by a concurrent learning process (see Figure ). We investigate the performance of the DP model by comparing energies, forces, formation energies and voltage plateaus predicted by the DFT+U calculations and the DP model, respectively. The root mean square errors (RMSEs) for energies and forces are 3.89 meV/atom and 148 meV/Å, respectively (Figure and). The convex hull results and voltage plateaus (computational details can be seen in SI) match well (Figure and 1d) between the first-principles and the machine-learning models. The above comparison demonstrates that the DP model can be used to construct the atomic interaction potential of the LixCoO2 cathode material, only with a requirement that the electronic structures of all the training systems' configurations are in the ground states (with respect to the degree of freedom of the TM ions' spin states) in the DFT+U calculations for this complicated TM oxide material. Recently, Zhang et al. constructed a global neural network potential of the LixCoO2 with the SCAN functional level. This work further demonstrates that the deep neural network can be used to fit the PES for the complicated TM oxide materials. We then return to the core scientific question of this work: the dynamic correlations between the TM cation migrations and the associated oxygen dimer formation, and the Ti dopant's effect on the above processes. The TM cation migrations from an octahedral site in the TM layer to an octahedral site in the Li layer goes through a tetrahedral site in the Li layer. In fact, the TM cation hopping within the Li layer (all of the Li ions are extracted in the CoO2 model) are relatively easy, we thus only focus on the migration process from the octahedral site in the TM layer to the tetrahedral site in the Li layer, in which the Co ion needs to overcome a high-barrier transition state and convectional unbiased MD simulations cannot capture this process within an affordable time scale. Thus, an enhanced sampling technique -the moving restraint method -is used to drive the Co ion migration. To accurately capture the dynamic correlation between the TM cation migrations and associated oxygen lattice instability, we use a relatively large supercell containing 324 atoms (17.00×17.00×13.01 Å 3 ) to avoid periodic images' interaction. In addition, descriptions of the complete dynamic process of the TM migrations and the oxygen dimer formations need long simulation time even if the enhanced sampling technique is applied. The large spatial and temporal scales make traditional spin-polarized abinitio molecular dynamics (AIMD) impractical. We thus use enhanced sampling DeePMD simulations to investigate the above dynamic processes.