Prediction of Li-Dendrite Growth with Physics-Informed Neural Network and Transformer Model

The growth of lithium-dendrite at anodes has long been a well-known hindrance limiting the development of lithium-ion batteries. Gaining a deeper understanding of the mechanism behind dendrite growth is a challenging yet pivotal task. Although phase-field models (PFM) have proven to be an effective numerical approach for modeling Li dendrite growth behaviors compatible with experiments in time and length scales, seeking for a computationally efficient surrogate model still remains imperative due to the computationally demanding fine meshes required for PFM. Recently, deep learning (DL) has demonstrated promising potential in learning dynamical systems. Herein, we introduce two DL models to capture the spatial and temporal evolution of Li dendrite growth, ion concentrations, and electrostatic potential of Li metal anode upon charging. The first model integrates the physics-informed neural networks (PINNs) with PFM. In the learning phase, we train our PINNs model to learn PFM with imposed governing equations and boundary conditions so as to retain consistency with physics laws. In the second model, we develop a transformer, originated from Natural Language Processing (NLP), for the prediction of dynamic evolution of lithium dendrite growth. We utilize embedded dynamical systems as input sequences and predict Li deposition based on past time steps with stochastic initial conditions. The results obtained from both models yield notable consistency with those from numerical models. While further efforts are required to delve deeper into the application of deep learning in PFM, our findings propose an alternative platform for exploring phase-field of Li-dendritic morphology.