# Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order disorder transitions in LixCoO2

arXiv: https://arxiv.org/abs/2302.08991 · HTML: https://mlsanity.com/paper/2302.08991/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2023.

## Built on by (most cited first, 3 of 3)

- [Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models](https://mlsanity.com/paper/2407.00761/) (2024)
- [Differentiable neural network representation of multi-well, locally-convex potentials](https://mlsanity.com/paper/2506.17242/) (2025)
- [Physics- and data-driven Active Learning of neural network representations for free energy functions of materials from statistical mechanics](https://mlsanity.com/paper/2503.07619/) (2025)

## Abstract (arXiv)

LixTMO2 (TM=Ni, Co, Mn) forms an important family of cathode materials for Li-ion batteries, whose performance is strongly governed by Li composition-dependent crystal structure and phase stability. Here, we use LixCoO2 (LCO) as a model system to benchmark a machine learning-enabled framework for bridging scales in materials physics. We focus on two scales: (a) assemblies of thousands of atoms described by density functional theory-informed statistical mechanics, and (b) continuum phase field models to study the dynamics of order-disorder transitions in LCO. Central to the scale bridging is the rigorous, quantitatively accurate, representation of the free energy density and chemical potentials of this material system by coarsegraining formation energies for specific atomic configurations. We develop active learning workflows to train recently developed integrable deep neural networks for such high-dimensional free energy density and chemical potential functions. The resulting, first principles-informed, machine learning-enabled, phase-field computations allow us to study LCO cathodes' phase evolution in terms of temperature, morphology, charge cycling and particle size.