Accelerating multi-species field-theoretic simulations using Bayesian optimization

Abstract

Field-based simulations can be challenging in multi-component polymer systems and are highly sensitive to the choice of relaxation coefficients ($\bm\lambda$) used in the field update algorithms. Judiciously chosen relaxation coefficients are critical for both the stability and convergence of field-based simulations, yet their selection is challenging when the number of unique chemical species in the system is large. In this work, we develop a new method to automatically and efficiently locate optimal relaxation coefficients in systems with large numbers of species. We begin by analyzing the effects of relaxation coefficients in two- and three-species systems and demonstrate that regions of high-performance are both narrow and system-specific. Based on these findings, we next develop a method based on Bayesian optimization that automatically locates relaxation coefficients that are stable and exhibit good performance. We demonstrate that our method is considerably faster than naive search methods and becomes particularly efficient as the system complexity increases. This work demonstrates that Bayesian optimization can be used to stabilize and accelerate field-based simulations that contain many different chemical species.