An adaptive interpolation scheme for molecular potential energy surfaces

TL;DR

This paper introduces an adaptive interpolation method using polyharmonic splines and partition of unity to efficiently and accurately construct potential energy surfaces, reducing computational effort in quantum dynamics simulations.

Contribution

The paper presents a novel adaptive interpolation algorithm that significantly improves the efficiency and reliability of potential energy surface construction over non-adaptive methods.

Findings

Reduces number of sample points needed for accurate interpolation

Demonstrates scalability in 2, 3, and 4 dimensions

Provides faster and more reliable potential energy surface interpolation

Abstract

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.