Bridging Atomistic and Mesoscale Lithium Transport via Machine-Learned Force Fields and Markov State Models

Lithium diffusion in silicon battery anodes is governed by thermally activated jumps between (meta)stable sites separated by significant energy barriers, making such events rare on ab initio molecular dynamics (AIMD) time scales. To overcome this limitation, we establish a multiscale workflow that links AIMD, machine-learned force fields (MLFFs), and Markov state models (MSMs) to bridge atomistic mechanisms to mesoscale diffusion. Focusing on crystalline Li-Si phases, our MLFFs trained on AIMD data, achieve near-DFT accuracy while enabling large-scale molecular dynamics simulations extending to tens of nanoseconds. From these trajectories, we extract converged lithium-jump statistics to construct MSMs that quantitatively reproduce diffusivities with uncertainties an order of magnitude smaller than those obtained from 100 ps AIMD simulations. Demonstrated here for crystalline Li_xSi_y phases, the AIMD → MLFF → MSM workflow provides a transferable route for quantitative transport modeling in amorphous structures, defect-mediated diffusion, and alternative solid-state anodes.