Efficient discovery of multiple minimum action pathways using Gaussian process

We present a new efficient transition pathway search method based on the least action principle and the Gaussian process regression method. Most pathway search methods developed so far rely on string representations, which approximate a transition pathway by a series of slowly varying system replicas. Such string methods are computationally expensive in general because they require many replicas to obtain smooth pathways. Here, we present an approach employing the Gaussian process regression method, which infers the shape of a potential energy surface with a few observed data and Gaussian-shaped kernel functions. We demonstrate a drastic elevation of computing efficiency of the method about five orders of magnitude than existing methods. Further, to demonstrate its real-world capabilities, we apply our method to find multiple conformational transition pathways of alanine dipeptide using a quantum mechanical potential. Owing to the improved efficiency of our method, Gaussian process action optimization (GPAO), we obtain the multiple transition pathways of alanine dipeptide and calculate their transition probabilities successfully with density-functional theory (DFT) accuracy. In addition, GPAO successfully finds the isomerization pathways of small molecules and the rearrangement of atoms on a metallic surface.