Update DeePMD_2026_05_19.md

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@@ -52,7 +52,7 @@ The two methods can be unified within extended ensemble dynamics via the couplin
 
 Conventional ab initio molecular dynamics (AIMD) makes CPwfluc. computationally costly. This work adopted the Deep Potential (DP) approach to address this problem.
 
-All simulations were performed with neural network potentials trained by DP. The research team used the ABACUS first-principles software to generate DFT datasets and trained a DP-$$N_e$$ machine learning potential via the automatic DP-GEN workflow. This model incorporates the total electron number $$N_e$$ as well as its first and second partial derivatives. Leveraging numerical atomic orbital (NAO) basis sets, ABACUS efficiently handles large Pt/H₂O interface supercells containing hundreds of atoms. The DeePMD-kit trains deep learning force fields that precisely describe how atomic potential energy surfaces vary with electron numbers.
+All simulations were performed with neural network potentials trained by DP. The research team used the ABACUS first-principles software to generate DFT datasets and trained a DP- N<sub>e</sub> machine learning potential via the automatic DP-GEN workflow. This model incorporates the total electron number N<sub>e</sub> as well as its first and second partial derivatives. Leveraging numerical atomic orbital (NAO) basis sets, ABACUS efficiently handles large Pt/H₂O interface supercells containing hundreds of atoms. The DeePMD-kit trains deep learning force fields that precisely describe how atomic potential energy surfaces vary with electron numbers.
 
 The final DP model achieves root-mean-square errors (RMSE) of 0.6 meV/atom for energy and 54 meV/Å for force, reaching first-principles precision. Based on this potential, the team conducted long-time sampling with 300,000 steps per trajectory for systematic method comparison. The DP-N<sub>e</sub> model directly outputs ∂U/∂N<sub>e</sub> and ∂<sup>2</sup>U/∂N<sub>e</sub><sup>2</sup> via automatic differentiation, greatly accelerating electron number convergence in CPw/ofluc.