Data-driven approximations to the bridge function yield improved closures for the Ornstein-Zernike equation.

Rhys E A Goodall,Alpha A Lee

doi:10.1039/d1sm00402f

Rhys E A Goodall, Alpha A Lee

Open Access

https://doi.org/10.1039/d1sm00402f

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Abstract

A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an elegant framework for solving this inverse problem. Pioneering work in liquid state theory derived analytical closures for the framework. However, these analytical closures are approximations, valid only for specific classes of interaction potentials. In this work, we combine the physics of liquid state theory with machine learning to infer a closure directly from simulation data. The resulting closure is more accurate than commonly used closures across a broad range of interaction potentials.

Highlights

A central question in soft matter pertains to the inverse problem of determining the interaction potentials between building blocks, e.g. colloids or molecules, that give rise to desired structures through self-assembly.[1,2] Applications of this inverse problem abound in disparate fields
To compare these learnt closures to Hyper-netted Chain approximation (HNC), VM, and Percus–Yevick approximation (PY) we look at how they perform on a randomly sampled test set comprising 90/450 (20%) of the simulation systems that were withheld when training the closures
As the feature set is extended to include additional physically motivated features (Fig. 3A), the learnt closures offer rapidly improving performance compared to HNC, PY, and VM

Summary

Introduction

A central question in soft matter pertains to the inverse problem of determining the interaction potentials between building blocks, e.g. colloids or molecules, that give rise to desired structures through self-assembly.[1,2] Applications of this inverse problem abound in disparate fields. Molecular interactions can be optimised to yield porous structures in liquids[3] which in turn are crucial for chemical processes such as gas separation and storage.[4,5] Studying the inverse problem for these porous structures, both on computationally designed systems[6] and by back-tracking potentials from experimental data, allows for greater understanding of their physics. This knowledge can be leveraged to further optimise these systems and improve their properties. A related but important class of inverse problems looks at how external fields can be applied to induce desired changes in the structures of fluids for example controlling the density profile at wall-fluid interfaces.[10]

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