Optimization Algorithms in Optimal Predictions of Atomistic Properties by Kriging.

Area of Science:

• Computational Chemistry and Materials Science
• Machine Learning Applications in Physics

Background:

• Kriging is a machine learning technique valuable for developing next-generation force fields.
• Optimizing the kriging fitness function is crucial for accurate atomistic property prediction.
• Optimization complexity increases significantly with system dimensionality and training set size.

Purpose of the Study:

• To compare Particle Swarm Optimization (PSO) and Differential Evolution (DE) for optimizing kriging fitness functions.
• To assess the efficiency of PSO and DE in handling high-dimensional optimization problems.
• To evaluate the performance of these algorithms against traditional Newton and quasi-Newton methods.

Main Methods:

• Implementation and comparison of PSO and DE algorithms for maximizing the kriging fitness function.
• Utilizing the first derivative of the fitness function to assess the algorithms' ability to find stationary points.
• Refinement of converged solutions using the limited-memory Broyden-Fletcher-Goldfarb-Shanno bounded (L-BFGS-B) algorithm.

Main Results:

• Both PSO and DE effectively locate stationary points of the kriging fitness function, even in high-dimensional scenarios.
• These algorithms achieve convergence in a computationally reasonable time compared to Newton and quasi-Newton methods.
• The choice of starting position in the hyperparameter search space does not significantly hinder PSO and DE performance.

Conclusions:

• PSO and DE are robust and efficient search algorithms for optimizing kriging hyperparameters in force field development.
• The L-BFGS-B algorithm provides precise refinement of the identified maximum, achieving desired accuracy.
• These findings facilitate the construction of more accurate and efficient atomistic simulations through advanced machine learning.