Algorithms for Finding Saddle Points and Minimum Energy Paths Using Gaussian Process Regression

• Published in: Nanosystems: Physics, Chemistry, Mathematics
• Main Author: Koistinen, Olli-Pekka
• Other Authors: Perustieteiden korkeakoulu, School of Science, Tietotekniikan laitos, Department of Computer Science, Vehtari, Aki, Prof., Aalto University, Department of Computer Science, Finland, Jónsson, Hannes, Prof., University of Iceland, Iceland, University of Iceland, Aalto-yliopisto, Aalto University
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: Aalto University 2019
• Subjects: Computer science; saddle point; minimum energy path; Gaussian process; machine learning; satulapiste; minimienergiapolku; gaussinen prosessi; koneoppiminen; Saddle Point; Iceland
• Online Access: https://aaltodoc.aalto.fi/handle/123456789/41794

This doctoral dissertation has been conducted under a convention for the joint supervision at Aalto University (Finland) and University of Iceland (Iceland). Chemical reactions and other transitions involving rearrangements of atoms can be studied theoretically by analyzing a potential energy surface defined in a high-dimensional space of atom coordinates. Local minimum points of the energy surface correspond to stable states of the system, and minimum energy paths connecting these states characterize mechanisms of possible transitions. Of particular interest is often the maximum point of the minimum energy path, which is located at a first-order saddle point of the energy surface and can be used to estimate the activation energy and rate of the particular transition. Minimum energy paths and saddle points between two known states have been traditionally searched with iterative methods where a chain of discrete points of the coordinate space is moved and stretched towards a minimum energy path according to imaginary forces based on gradient vectors of the potential energy surface. The actual saddle point can be found by reversing the component of the gradient vector parallel to the path at one of the points of the chain and letting this point climb along the path towards the saddle point. If the end state of the transition is unknown, the saddle point can be searched correspondingly by rotating a pair of closely spaced points towards the orientation of the lowest curvature, reversing the gradient component corresponding to this direction, and moving the pair towards the saddle point. These methods may, however, require hundreds of iterations, and since accurate evaluation of the gradient vector is often computationally expensive, the information obtained from previous iterations should be utilized as efficiently as possible to decrease the number of iterations. Using statistical models, an approximation to the energy surface can be constructed, and a minimum energy path or a saddle point can be searched on the ...