Deep Mesoscopic Dynamics
Abstract
Microscopic simulations resolve spatial patterns but are feasible only over small domains and short timescales, whereas bulk descriptions erase those patterns through spatial averaging. Mesoscopic fields preserve this spatial organisation, but their effective equations are known only for selected microscopic systems and scaling limits. We introduce Deep Mesoscopic Dynamics (DeepMesoD), which uses neural networks to learn an effective mesoscopic field equation from microscopic trajectories at a prescribed coarse-graining scale. For the nonconserved dissipative dynamics studied here, DeepMesoD learns the free-energy functional with a spatial interaction kernel and a state-dependent dissipation operator constrained by the fluctuation-dissipation relation. We first validate the construction in the Ising-Kac model, where the learned mesoscopic equation recovers the known hydrodynamic limit and rollouts remain stable far beyond the training horizon. We then treat two systems without closed-form mesoscopic descriptions. For a two-dimensional Heisenberg ferromagnet governed by atomistic spin dynamics, DeepMesoD learns a mesoscopic model whose predictions match atomistic references up to 1 ns, and a rollout with an unseen initial condition remains bounded up to 25 ns. For layered CrBr3, the learned kernel captures the suppression and sign reversal of interlayer coupling at a stacking fault whose location and strength are not supplied as inputs. Controlled changes to the learned interaction show how fault number and placement shape multistep magnetic responses, complementing our magneto-photoluminescence measurements. Across the two atomistic systems, DeepMesoD achieves a three-to-four-order-of-magnitude reduction in wall-clock time compared with atomistic spin dynamics.
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BibTeX
@misc{zhao2026deep,
title = {{Deep Mesoscopic Dynamics}},
author = {Yue Zhao and Shiqi Wu and Yihang Ouyang and Sergey Grebenchuk and Magdalena Grzeszczyk and Xiaoxu Zhao and Kostya S. Novoselov and Maciej Koperski and Qianxiao Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17885},
eprint = {2610.17885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17885},
}
RIS
TY - UNPB
TI - Deep Mesoscopic Dynamics
AU - Yue Zhao
AU - Shiqi Wu
AU - Yihang Ouyang
AU - Sergey Grebenchuk
AU - Magdalena Grzeszczyk
AU - Xiaoxu Zhao
AU - Kostya S. Novoselov
AU - Maciej Koperski
AU - Qianxiao Li
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17885
UR - https://arxiv.org/abs/2610.17885
AB - Microscopic simulations resolve spatial patterns but are feasible only over small domains and short timescales, whereas bulk descriptions erase those patterns through spatial averaging. Mesoscopic fields preserve this spatial organisation, but their effective equations are known only for selected microscopic systems and scaling limits. We introduce Deep Mesoscopic Dynamics (DeepMesoD), which uses neural networks to learn an effective mesoscopic field equation from microscopic trajectories at a prescribed coarse-graining scale. For the nonconserved dissipative dynamics studied here, DeepMesoD learns the free-energy functional with a spatial interaction kernel and a state-dependent dissipation operator constrained by the fluctuation-dissipation relation. We first validate the construction in the Ising-Kac model, where the learned mesoscopic equation recovers the known hydrodynamic limit and rollouts remain stable far beyond the training horizon. We then treat two systems without closed-form mesoscopic descriptions. For a two-dimensional Heisenberg ferromagnet governed by atomistic spin dynamics, DeepMesoD learns a mesoscopic model whose predictions match atomistic references up to 1 ns, and a rollout with an unseen initial condition remains bounded up to 25 ns. For layered CrBr_3, the learned kernel captures the suppression and sign reversal of interlayer coupling at a stacking fault whose location and strength are not supplied as inputs. Controlled changes to the learned interaction show how fault number and placement shape multistep magnetic responses, complementing our magneto-photoluminescence measurements. Across the two atomistic systems, DeepMesoD achieves a three-to-four-order-of-magnitude reduction in wall-clock time compared with atomistic spin dynamics.
ER -