Learning to interpolate molecular potential energy surfaces with confidence: A Bayesian approach

A modified form of Shepard interpolation of ab initio molecular potential e nergy surfaces is presented. This approach yields significant improvement i n accuracy over previous related schemes. Here each Taylor expansion used i n the interpolation formula is assigned a confidence volume which controls the relative weight assigned to that expansion. The parameters determining this confidence volume are derived automatically from a simple Bayesian ana lysis of the interpolation data. As the iterative scheme expands the data s et, the confidence volumes are also iteratively refined. The potential ener gy surfaces for nine reactions are used to illustrate the accuracy obtained . (C) 1999 American Institute of Physics. [S0021-9606(99)00727-8].