Fixed-configuration inversion of interaction potentials from equilibrium configurations at fixed state points
Year: 2026
Type: other
Abstract: Recovering interaction potentials from structural information is a fundamental inverse problem in statistical physics and soft-matter research. We investigate a force-sampling implementation of fixed-configuration inversion for particle-resolved equilibrium configurations. A distance-histogram estimate from 10,000 configurations provides a fixed, potential-independent target, whereas forces recalculated from the current trial potential on fixed coordinate subsets generate smooth, potential-dependent responses. Disjoint training and validation subsets of 200 configurations each enable validation-controlled checkpoint selection and termination without generating new equilibrium trajectories. We test the method for a three-dimensional Lennard-Jones system at reduced inverse temperature and reduced number densities of 0.01, 0.70, 0.75, 0.80, 0.85, and 0.90, where is the number density and and are the energy and length scales. Over the reliable radial interval, the inversion recovers the principal features of the reference potential and reproduces the target structure within statistical resolution. A trajectory block bootstrap that repeats the complete inversion quantifies uncertainty in the target radial distribution function, validation response, and recovered potential, identifying sparse low-density pair statistics and limited pair occupancy near the repulsive core as important sources. Independent forward molecular dynamics simulations at and 0.90 confirm reproduction under renewed sampling. At , a matched comparison showed an approximately 204-fold reduction in wall-clock cost relative to conventional iterative Boltzmann inversion under the present implementations and validation-controlled stopping protocol. These results establish force sampling as an efficient, statistically controlled response estimator for fixed-configuration pair-potential inversion.
Source: AIP Publishing
Authors: XuRui Li, Jianxiang Tian, Qiuju Chen, Yuan Liu
Language: English
Subfield: Physical and Theoretical Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213347258