COPEX

Official Resources

• Homepage: https://www.nature.com/articles/s41524-021-00668-5
• Source Repository: https://github.com/Dustglaxy/Co-evolutionary-crystal-structure-prediction-algorithm-for-complex-systems
• Documentation: Available in publication and USPEX documentation
• License: As specified by USPEX (upon which COPEX is based)

Overview

COPEX (Co-USPEXs) is a co-evolutionary crystal structure prediction algorithm for complex systems, based on the well-known evolutionary algorithm USPEX. Published in npj Computational Materials in 2021, COPEX addresses the challenge of predicting stable stoichiometries and structures of ternary or more complex systems, where the chemical and configurational space grows explosively.

Inspired by co-evolution in biology, COPEX runs multiple USPEX calculations in parallel: a few for ternary systems and multiple for energetically-favored pseudobinary or fixed-composition systems. Co-evolution is achieved by sharing structural information on the fittest individuals among different USPEX sub-processes during joint evolution. Each USPEX process is viewed as the evolution of one biological species, and the co-evolution between different USPEX processes is the key feature. The algorithm was validated on W-Cr-B, Mg-Si-O, and Hf-Ta-C systems, identifying many stable ternary compounds.

Scientific domain: Crystal structure prediction, materials discovery
Target user community: Computational materials scientists predicting complex ternary compounds

Theoretical Methods

• Co-evolutionary algorithm inspired by biological co-evolution
• Based on USPEX evolutionary structure prediction
• Parallel USPEX sub-processes for ternary and pseudobinary systems
• Sharing of fittest structural information between sub-processes
• Evolutionary operators (mutation, crossover, selection)
• Variable-composition and fixed-composition searches
• Energy-based fitness evaluation (DFT or ML potentials)

Capabilities (CRITICAL)

• Crystal structure prediction for ternary and complex systems
• Parallel co-evolution of multiple USPEX processes
• Simultaneous exploration of chemical and configurational space
• Sharing fittest individuals among sub-processes
• Stable stoichiometry and structure identification
• Validated on W-Cr-B, Mg-Si-O, and Hf-Ta-C systems
• Combines efficiency and reliability for complex systems
• Accelerates exploration of chemical space

Inputs & Outputs

Input formats:

• Chemical composition space specification (elements, stoichiometry ranges)
• USPEX input parameters for each sub-process
• DFT or ML potential calculation settings
• Number of parallel sub-processes

Output data types:

• Predicted stable crystal structures
• Convex hull diagrams (stability)
• Stoichiometry-composition phase diagrams
• Energetically favorable ternary compounds
• Structure-property relationships

Interfaces & Ecosystem

• Based on USPEX: Uses USPEX as the underlying evolutionary engine
• DFT backends: VASP, Quantum ESPRESSO, and other USPEX-compatible codes
• ML potentials: Can use machine learning potentials for acceleration
• Programming language: MATLAB/Python (USPEX-based)
• GitHub: Code available on GitHub

Limitations & Known Constraints

• Requires multiple parallel USPEX calculations (computational cost)
• Depends on USPEX license and installation
• Chemical space exploration still limited for very complex systems
• Human factor in setting up sub-process configurations
• Requires significant computational resources

Performance Characteristics

• Parallel sub-processes run simultaneously
• Co-evolution accelerates convergence by sharing information
• More efficient than independent USPEX runs for ternary systems
• Computational cost scales with number of sub-processes and system complexity
• Can leverage ML potentials for faster energy evaluation

Comparison with Other Codes

• vs USPEX: COPEX extends USPEX with co-evolutionary parallelism for complex systems
• vs CALYPSO: CALYPSO uses particle swarm optimization; COPEX uses co-evolutionary GA
• vs AIRSS: AIRSS uses random structure searching; COPEX uses evolutionary approach
• vs XTALOPT: XTALOPT is a single evolutionary process; COPEX runs co-evolutionary parallel processes

Best Practices

• Run sufficient number of parallel sub-processes for adequate chemical space coverage
• Include pseudobinary and fixed-composition sub-processes for energetically-favored regions
• Share structural information frequently between sub-processes
• Use DFT for final energy evaluation; ML potentials for initial screening
• Analyze convex hull for thermodynamic stability assessment

Verification & Sources

Primary sources:

1. Nature article: https://www.nature.com/articles/s41524-021-00668-5
2. GitHub: https://github.com/Dustglaxy/Co-evolutionary-crystal-structure-prediction-algorithm-for-complex-systems
3. S. Liu et al., npj Comput. Mater. 7, 199 (2021), DOI: 10.1038/s41524-021-00668-5

Confidence: VERIFIED - Published in npj Computational Materials with GitHub repository