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

## TL;DR

This paper employs neural networks to accurately predict equations of state from pair potentials and to derive effective pair potentials from radial distribution functions, improving inverse design and coarse-graining in molecular simulations.

## Contribution

It introduces neural network models that outperform traditional methods in predicting equations of state and effective pair potentials, incorporating force information for enhanced accuracy and transferability.

## Key findings

- Neural networks outperform low-density analytic estimates for virial coefficients.
- Including force data improves potential predictions, making them smoother and more accurate.
- The models are effective for inverse design and coarse-graining applications.

## Abstract

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