Crystal Structure Search using Constrained Optimization

Outlines

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

Problem Statement

• 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.

Optimization Algorithm

Optimization with vs. without Momentum

Optimization with vs. without Constraint

Initial Structure Factor vs. the Target

Last Structure Factor vs. the Target

Thesis Defense

Graduation day

Receiving the Diploma from Research Advisor Prof. Sandro Scandolo

Accepting Merit Certificate from ICTP’s Director Prof. Katepalli Sreenivasan for Securing the Highest Grade

Miramare Castle, Trieste, Italy

Leaning Tower of Pisa, Pisa, Italy

Thank you!