[Analysis Example] Analysis of Li ion diffusion in solid-state battery by MD-GAN

Molecular Dynamics (MD) are effective in providing insights at the atomic level, However, the computational costs are notably high, particularly ab initio MD (AIMD). Even as parallelization techniques have expanded the spatial scale of MD, the extension of the temporal scale remains a persisting challenge. MD-GAN[1,2,3] is a machine learning model using Generative Adversarial Network (GAN) capable of generating long-time data from multiple short-time data segments. In other words, it enables parallelization of temporal calculation.
In this study, MD-GAN is trained on Li ion diffusion in solids calculated by AIMD to generate long-term time series MD data.

Figure 1. visualization of ion paths (1ps)

Figure 2 shows an overview of MD-GAN.
In input data preparation, particles of interest (Li ions) are extracted from the MD data.
MD-GAN learns the rules for 128 records in the input data. The time interval between records is determined by step skip, and the length of a time series to be trained at a time is 128×step skip; the smaller the step skip, the more samples that can be taken from the same input data.(Figure 3)

Figure 2. Overview of MD-GAN

Figure 3. Relationship between step skip and the number of samples

In this case, we performed 3 MD simulations for LiZr2(PO4)3, which is a material used in solid-state electrolytes. Step skip was set to 2, and the total steps was set 25000 in MD-GAN.
Table shows the details of the calculation conditions.

The number of Li ions in the input data was 12 × 3, whereas the number of Li ions in the generated data was 8192.

We calculated and compared the mean square displacement (MSD) and coordinate 　displacement for MD and MD-GAN, respectively.
Figure 4 shows the displacement of the z-coordinate of each particle in both MD and MD-GAN. MD-GAN successfully replicated the random walk observed in MD.
Figure 5 illustrates MSD of MD data and MD-GAN. The gray area represents the duration of the training data. The time-series data are generated with high accuracy, matching nonlinear regions with small time scales to regions larger than the learned time-series data.

Table Calculation conditions for MD and MD-GAN

MD simulation conditions

Solver	AIMD with SIESTA[4]
Total steps	10000
Delta t	4fs
Temperature	1773K
Number of trajectories	3

MD-GAN conditions

SStep skip	2
Feature extraction	Li ion
Extracted particles	12
Input particles	12×3
Generated particles	8192

	Machine	Computation time
MD	CPU (Intel(R) Xeon(R) Gold 6226R CPU @ 2.90GHz)	30 days
MD-GAN	GPU (NVIDIA Quadro T1000)	28 hours