Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

翻译：多尺度系统在科学与技术中普遍存在，但由于必须将短时空尺度与涌现的宏观物理特性恰当关联，其模拟极具挑战性。当昂贵的高维动力系统被粗粒化为低维模型时，信息熵的损失会导致动力学呈现耗散性、历史依赖性与随机性等涌现物理特性。为从粒子轨迹的时间序列观测数据中机器学习粗粒化动力学，我们提出一种基于度量泊松括号形式体系的框架，该框架通过构造保持上述特性；尤为重要的是，该框架能保证热力学第一与第二定律的离散形式、动量守恒定律，以及对捕捉非平衡统计至关重要的离散涨落-耗散平衡。我们首先抽象地介绍数学框架，再专门讨论粒子离散化情形。由于熵态变量通常缺乏标签数据，我们提出一种新颖的自监督学习策略来识别涌现的结构变量。我们在基准系统上验证了该方法，并通过两个挑战性案例展示其实用性：(1) 在极具挑战性的粗粒化层级上对星形聚合物进行粗粒化建模，同时保持非平衡统计特性；(2) 根据胶体悬浮液高速视频数据学习模型，捕捉局部重排事件与涌现随机动力学之间的耦合。我们提供了PyTorch和LAMMPS的开源实现，支持大规模推理并适用于各类粒子系统。