Machine-Learned Adaptive Multiscale Coupling for Efficient Simulation of Membrane Fabrication

  • Busch, Matthias (Technical University of Hamburg)
  • Häfner, Gregor (University of Göttingen)
  • Xi, Jiayu (University of Göttingen)
  • Tacke, Marius (Helmholtzzentrum Hereon)
  • Müller, Marcus (University of Göttingen)
  • Cyron, Christian (Helmholtzzentrum Hereon)
  • Aydin, Roland (Helmholtzzentrum Hereon)

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Molecular-level particle simulations face fundamental limits in computational scalability when applied to large spatiotemporal domains [1]. Hybrid multiscale methods address this by combining simulations of different resolution, activating expensive high-fidelity methods only where necessary [2]. Traditional coupling schemes rely on heuristic triggers that may overlook subtle error dependencies. We present a machine learning-based decision model that dynamically selects between simulation methods at runtime [3]. This approach is applied to diblock copolymer membrane fabrication via the SNIPS process, where particle-based and continuum-based simulations are coupled. The decision model uses a multilayer perceptron (MLP) to predict the expected discrepancy between both simulation methods, enabling localized use of particle simulations only where they add value. The architecture consists of three stages: (1) pre-processing extracts information-dense descriptors from the concentration field, (2) the trained MLP predicts layer-resolved divergence for multiple future time steps, and (3) post-processing interprets the divergence as local error to determine domain partitioning. A key design choice is the layer-wise prediction formulation, which enforces generalization across layers and provides domain-size independence. Results demonstrate good qualitative agreement between predicted and reference errors. The model accurately captures structure-formation front movement, reproduces error peak locations, and remains robust under varying simulation parameters. This machine learning approach provides a data-driven alternative to heuristic coupling triggers, offering a framework for efficient multiscale simulations applicable to a range of multi-fidelity problems. Referrences: [1] Müller M., Abetz V., Nonequilibrium Processes in Polymer Membrane Formation, Chem. Rev., 121, pp. 14189--14231, 2021. [2] W. E, Engquist B., The heterogeneous multiscale methods, Commun. Math. Sci., 1, pp. 87--132, 2003. [3] Busch M. et al., Machine-learned domain partitioning for coupling of continuum and particle simulations, arXiv:2510.19051, 2025.