Recurrent Neural Network Model to Retrieve the Long Range Spherical Potential Energy Function from Second Virial Coefficient

Abstract

Simulated second virial coefficient data were used to recover the long range dispersion potential function for the Ar - Ar system using a Hopfield neural network. A Fredholm integral equation of first order makes the connection between the second virial data and the potential energy function and is used to invert data. For noiseless data the computed potential from the stationary points gives errors from 0.4 to 3.2%, when compared with the exact potential. The effect of noise in the neural network inversion procedure is also investigated. The agreement with exact results is excelent if error are less than 0.2% of the simulated data. For larger values, up to 1.0%, an acceptable potential can still be recovered.