Machine-learned domain partitioning for computationally efficient coupling of continuum and particle simulations of membrane fabrication

TL;DR

The paper tackles the computational cost of simulating membrane fabrication across large spatiotemporal scales by proposing a machine-learning–driven decision model that predicts local discrepancies between particle-based and continuum solvers to guide adaptive multiscale coupling. It implements an MLP that forecasts the fidelity error at runtime, enabling a localized high-fidelity particle subdomain within an otherwise continuum-based simulation of the SNIPS process. The approach is validated on EISA/NIPS morphologies, with SHAP-based interpretability showing which descriptors drive predictions, and demonstrates generalization to unseen parameters and longer time horizons. This error-aware partitioning framework advances scalable multiscale simulations and provides a blueprint for applying data-driven adaptive coupling to other complex, heterogeneous systems.

Abstract

All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal resolution leads to rapidly increasing computational demands. To overcome these limitations, hybrid methods that combine simulations with different levels of resolution offer a promising solution. In this context, we present a machine learning-based decision model that dynamically selects between simulation methods at runtime. The model is built around a Multilayer perceptron (MLP) that predicts the expected discrepancy between particle and continuum simulation results, enabling the localized use of high-fidelity particle simulations only where they are expected to add value. This concurrent approach is applied to the simulation of membrane fabrication processes, where a particle simulation is coupled with a continuum model. This article describes the architecture of the decision model and its integration into the simulation workflow, enabling efficient, scalable, and adaptive multiscale simulations.

Figures (13)

• Figure 1: Schematic representation of the EISA and NIPS process. During EISA the volatile solvent evaporates from the casting solution -- diblock copolymers dissolved in a two-solvents mixture -- by diffusion. The evaporation is captured in simulation by conversion of solvent into the gas phase at the top. During NIPS nonsolvent-solvent exchange is initiated by exchanging the gas phase for nonsolvent. Inside the solution film, a combination of macrophase separation and simultaneous polymer vitrification results in the final nonequilibrium structure.
• Figure 2: Time evolution of the B-block concentration fields, $\phi_B(\mathbf{r})$, during the EISA and NIPS process in a) the particle simulations and b) the continuum simulation. Indicated times are measured from the start of each process. The far right panel additionally shows the nonsolvent concentration field, $\phi_N(\mathbf{r})$, after the full SNIPS process.
• Figure 3: Panel a) shows spinodal curves of membrane casting solutions at different nonsolvent concentrations on the Gibbs triangle. Dashed and solid lines indicate instabilities of the spatially homogeneous state against composition fluctuations with finite and infinite length scales, respectively. Panels b) and c) show the 1D laterally-averaged concentration profiles, $\bar{\phi}_\alpha^{xy}(z)$ (lines) and 2D cross-sections of the block concentration difference, $\phi_A(\mathbf{r})-\phi_B(\mathbf{r})$ (background) for a) the particle simulations and b) the continuum simulations of the base parameter pair (top) and the weakened solvent attraction, $\chi_{SC}N_P=-28$ (bottom). Time increases from left to right as indicated. For the 2D cross sections, the $y$-axis is scaled the same as the $z$-axis. The approximated front positions are indicated as dashed gray lines -- vitrification front left of the structure-formation front.
• Figure 4: Final $B$-block concentration field, $\phi_B(\mathbf{r})$ after the NIPS process in the continuum simulation (left) and in the particle simulation (right) for the reduced solvent attraction, $\chi_{SC}N_P=-28$, compared to the base parameter combination.
• Figure 5: Overview diagram for the decision model. The different steps of data processing with intermediate results are shown. For details on each step, refer to the following sections \ref{['preprocessing']}, \ref{['prediction']} and \ref{['postprocessing']}. In the pre-processing step descriptors are extracted from the density field (5 for each $z$-layer, abbreviations: CV -- coefficient of variation; IQR -- interquartile range of finite differences; max$\nabla$ -- maximum gradient magnitude; Mean -- layer mean; EC -- Euler characteristic) , with the IQR being computed from the finite difference of two consecutive (in time) density fields. The prediction is done by a MLP, which takes descriptors of multiple $z$-layers as input and outputs predicted errors for a single $z$-layer at multiple future time steps. The post-processing aggregates the errors for the requested time range and finds the largest error region above a threshold.