Development of Strain Functionals for Physics Informed Machine Learning of Grain Boundary Structures

The analysis of molecular dynamics simulations of the deformation of metals and the validation of potential functions used in these simulations compared require a robust set of descriptors that can identify a wide variety of crystal and defect structures. The use of strain functionals descriptors for characterizing such arbitrarily ordered atomistic structures is demonstrated here for use in conjunction with machine learning applications. This approach is derived using using a Taylor series expansion of the geometry of the local atomic neighborhood, ensuring both numerical convergence and a direct relationship to physical properties. They are reduced to a minimal non-redundant set using closure relationships from angular momentum / spherical tensor properties. The resulting functionals naturally describe the deformations in terms of simple physical concepts: measuring how tetrahedral or cubic a geometry is, how much shear or trigonal deformation is present. This formulation cleanly maps onto other entities that are described by tensor formulations: strain, stress, elasticity, and other physical properties. Using these as a basis facilitates the development of physically-informed models from machine-learning applications. Here, the method is extended out to sixth order, which is necessary to fully distinguish all possible crystallographic symmetries. The approach has been extended to the analysis of vector (velocities, forces) and tensor (stress, strain) fields as well. Applications of the method to the characterization of grain boundaries will be shown.