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Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian
Qingfei Song1,2, Xingyu Zhang1, Daniel Peláez2
1Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072Xi'an, China.
Abstract:
A Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of a multidimensional potential energy surface (PES) by discrete training energies is proposed and denoted by CPD-GPR. The present CPD-GPR method requires the kernel function in a product of a series of one-dimensional functions. To test CPD-GPR, the reactive probabilities of H + H2 as a function of kinetics energy are performed. Comparing the dynamics results computed by the CPD-GPR PES with those by the original PES, a good agreement between these results can be clearly found. Discussions on the previous algorithms for building the decomposed form are also given. We further show that the CPD-GPR method might be the general algorithm for building the decomposed form. However, further development is needed to reduce the CPD rank. Therefore, the present CPD-GPR method might be helpful to inspire ideas for developing new tools in building decomposed potential functions.
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