Physics- and data-driven Active Learning of neural network representations for free energy functions of materials from statistical mechanics

As is now well understood, well trained ML model can provide insight to unlabeled or out of network data, without having to do time intensive experiments or use computationally expensive forward models. Our work is motivated by the continuum-scale modeling of materials physics, specifically using phase field methods to understand the phase dynamics and degradation effects of battery materials. Predictive phase field modeling of these processes relies on an accurate representation of the free energy density function. Historically, these free energies have been phenomenologically based which often can miss detailed physics such as high order interactions and complex phase dynamics needed to match with and explain experiments. With this background, we aimed to develop a framework enabling the creation of an atomistically informed free energy representation. The free energy densities can have compositions, order parameters, strains and temperature as arguments, attaining complex forms in the associated high-dimensional spaces. Therefore, we have employed ML models-specifically neural networks-in workflows that bridge first principles statistical mechanics and continuum scale models to represent the free energy density [4]. As an overview, our workflow uses density functional theory (DFT)-informed Monte Carlo (MC) to yield training data on generalized order parameter ηand chemical potentials µpairs.