Pair potentials from diffraction data on liquids: a neural network solution

The inverse theorem of liquids states a one to one correspondence between classical mechanical pair potentials and structural functions. Molecular-dynamics and Monte Carlo simulations provide exact structural functions for known pair interactions. There is no exact or widespread method in the opposite direction, where the pair interactions are to be determined from a priori known pair-correlation functions or structure factors. The methods based on the integral equation theories of liquids are approximate and the iterative refinements of pair potentials with simulations take a long time. We applied artificial neural networks to get pair interactions from known structure factors in this study. We performed molecular-dynamics simulations on one-component systems with different pair potentials and the structure factors were calculated. To optimize (train) the weights of neural networks 2000 pair interaction-structure factor pairs were used. The performance of the method was tested on further 200 data pairs. The method provided reasonable potentials for the majority of the systems opening a "quick and dirty" method to determine pair interactions.