Description

PyeCE is a Python package that implements the embedded cluster expansion (eCE) formalism. The eCE models are on-lattice models, i.e., the atomic sites are considered as fixed. These models are typically used as surrogate models to infer from properties that depends on the arrangement of species onto a lattice. A typical example is the formation energy \(E(\sigma)\), where \(\sigma\) represents a particular arrangement of atoms onto a given lattice.

The following describes the theory and the implementation of the eCE:

Contents:

• Spacegroup
  • Elements of group theory
  • Crystal structure
  • Symmetry
  • Orbits
• Cluster Expansion
  • Formalism
    • Site-basis Functions
    • Cluster Functions
    • Correlation Functions
  • Implementation
• Embedded Cluster Expansion
  • Motivation
  • Formalism
    • Chemical embedding
    • Neural Network Energy Model
    • eCE Workflow
  • Implementation
    • Input tensor