Direct Boltzmann inversion method from particle configurations at arbitrary state points

TL;DR

This paper presents a direct, non-iterative Boltzmann inversion method for inferring interaction potentials from particle configurations at any state point, avoiding costly simulations and applicable to complex systems.

Contribution

The authors introduce a novel direct inversion approach that enforces consistency between two estimates of the pair correlation function, eliminating the need for iterative simulations.

Findings

Method is computationally inexpensive and easy to implement.

Performs well across diverse test potentials in simulations.

Applicable to high-density and non-equilibrium systems.

Abstract

We introduce a direct Boltzmann inversion method to infer the interaction potential in particle systems using as input particle configurations generated at an arbitrary state point of the system. Unlike iterative Boltzmann inversion, the proposed method does not require performing a new Monte Carlo simulation at each step of the iteration process. It relies instead on enforcing consistency between two independent estimates of the pair correlation function, respectively obtained from interparticle distances and from pairwise forces. As a result, the approach is computationally inexpensive and straightforward to implement. Because it relies on the sole expression of interparticle forces, our method naturally applies to any state point, including when the density is large and alternative methods may fail. Here we present the basic principles of the method and benchmark its performance on a diverse set of test potentials studied using computer simulations. Practical aspects and detailed implementation of the method are also discussed. Owing to its simplicity and generality, the method should be broadly applicable, from the construction of coarse-grained interaction potentials to the inference of effective interactions in non-equilibrium systems.