- Problem Statement
- Optimization Algorithm for Crystal Structure Search
- Gradient Descent with vs.Â without Momentum
- Optimization with vs.Â without Constraint
- Initial Structure Factor vs.Â the Experimental One
- Last Structure Factor vs.Â the Experimental One
- Pictures

Prediction of the atomic crystal structure plays an important role in chemistry, planetary science, and material science.

This work aims to develop a

*new*algorithm for the crystal structure search problem.The proposed algorithm redefines the crystal structure search problem as a constrained optimization problem, which is based on two premises:

- Energy minimization: Stable crystal structure is the one that has minimum energy.
- Prior constraint: The static structure factor of the predicted crystal structure should match the experimental one, which is obtained from crystallography.