Concurrently coupling particle and continuum simulations to study block copolymer membrane fabrication

We present a concurrent multiscale simulation framework for membrane fabrication from a block copolymer solution via self-assembly and nonsolvent-induced phase separation, combining simulations of a soft, coarse-grained particle model with the continuum Uneyama-Doi model. The computationally intensive particle model provides a molecularly resolved description of micro- and macrophase separation, including thermal fluctuations, while the computationally efficient continuum model captures the process-driven self-assembly of nonequilibrium membrane morphologies on large length and time scales. Central to the approach is a machine learning-guided adaptive coupling strategy, implemented through a coordinator library, which predicts the evolving spatiotemporal subdomain where high-fidelity particle simulations are required and dynamically allocates computational resources accordingly. The two complementary models are concurrently coupled through a consistent exchange of the solvents' fluxes, enabling the treatment of spatially inhomogeneous, multicomponent systems with diffusive transport, micro- and macrophase separation, and vitrification. This adaptive strategy enables predictive simulations of membrane formation on experimentally and technologically relevant length and time scales, reaching micrometers and minutes. As an application, we examine the influence of polymer concentration in the initial casting solution. The framework is general and extensible, providing a computational tool for investigating nonequilibrium structure formation in complex multicomponent soft-matter systems.