Hessian Matrix Update Scheme for Transition State Search Based on Gaussian Process Regression.

Area of Science:

• Computational chemistry
• Machine learning in scientific computing

Background:

• Optimization procedures in computational chemistry often rely on accurate Hessian matrices.
• Calculating and updating Hessians can be computationally expensive, posing significant scaling challenges.
• Existing Hessian update methods may not be optimal for all system sizes and computational contexts.

Purpose of the Study:

• To introduce a novel method for updating Hessian matrices using Gaussian process regression.
• To investigate the efficacy of Gaussian processes in incorporating gradient-based information for Hessian updates.
• To address the computational scaling issues associated with training Gaussian processes with Hessian data.

Main Methods:

• Employing Gaussian process regression to model the potential energy surface.
• Utilizing initial Hessian, energies, and gradients from electronic structure calculations to train the Gaussian process.
• Evaluating the second derivative of the trained Gaussian process to obtain updated Hessian information.
• Comparing the performance of the Gaussian process-based Hessian update method against classical updates using partitioned rational function optimization (P-RFO).

Main Results:

• Demonstrated successful application of Gaussian process regression for updating Hessian matrices.
• Showcased the ability to mitigate some of the scaling problems inherent in training Gaussian processes with Hessian information.
• Benchmark runs indicated that the proposed method outperforms classical Hessian update techniques for small molecular systems.

Conclusions:

• Gaussian process regression offers a viable and potentially superior alternative for updating Hessian matrices in optimization.
• The developed method shows particular advantages for smaller systems, providing a more efficient approach.
• This work opens avenues for integrating machine learning techniques more deeply into computational chemistry optimization workflows.