  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 optimiza tion (GPAO), we obtain the multiple transition pathways
of alaninedipeptide and calculate their transition probabilities successfully
with ab initio accuracy. In addition, GPAO successfully finds the isomerization
pathways of small molecules and the rearrangement of atoms on a metallic
surface.
