Roadmap to spline-fitting potentials in high dimensions

The use of the theory of splines to approximate the potential energy surface in molecular dynamics is examined. It is envisaged that such an approximation should be able to accurately capture the potentials’ behavior and be computationally cost effective, both for one-dimensional and $n$ -dimensional problems with $n$ arbitrary. In this regard, the problem of dimensionality is pinpointed, with shape-preserving splines emerging as a viable alternative for fitting surfaces in multidimensional spaces. An algorithm is also presented to allow the use of non-uniform meshes with high accuracy fitting and less interpolation points.