Scaling field-theoretic simulation for multi-component mixtures with neural operators

TL;DR

This paper introduces a neural operator-based method to efficiently simulate multi-component polymer mixtures, overcoming computational challenges of traditional molecular dynamics and field theories, especially for long polymers.

Contribution

The authors develop a scalable neural operator approach for field-theoretic simulations, enabling efficient analysis of complex multi-component mixtures beyond mean-field approximations.

Findings

Outperforms existing pseudospectral integrators in speed and accuracy

Successfully simulates six-component mixtures with diverse compositions

Significantly improves scalability for long polymer chains

Abstract

Multi-component polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, *neural operators*, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.