BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion pressure. The NNs trained with data molecular dynamics simulations monoatomic gases and liquids, sampled in NVT ensemble at various densities. We find that provide much more accurate results compared analytic low-density limit estimate second coefficient Carnahan–Starling equation for hard sphere liquids. Furthermore, we design train computing (effective) potentials radial distribution functions, g(r), task is often performed inverse coarse-graining. Providing additional information on forces greatly improves accuracy predictions since correlations taken into account; predicted become smoother, significantly closer target potentials, transferable as result.