论文标题
riemannian随机表示，用于量化分子动力学模拟中的模型不确定性
A Riemannian Stochastic Representation for Quantifying Model Uncertainties in Molecular Dynamics Simulations
论文作者
论文摘要
提出了分子动力学中模型不确定性的riemannian随机表示。该方法依赖于降低的模型，该模型的投影基础是随机分配在Stiefel歧管的子集中，其特征是一组线性约束，例如定义的，例如物理空间中的Dirichlet边界条件。我们首先表明，这些约束确实是通过Riemannian的推动力和回调动作保存的，并从任何可接受的点到歧管的切线空间。随后利用这种基本属性来得出一个利用原子环境的多模型性质的概率模型。所提出的配方提供了几个优点，包括简单且可解释的低维参数化，限制了对歧管上的Fréchet平均值的能力以及易于实施和传播的能力。最终在各种应用程序上证明了所提出的建模框架的相关性，包括基于石墨烯的系统的多尺度模拟。
A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by a set of linear constraints defining, e.g., Dirichlet boundary conditions in the physical space. We first show that these constraints are, indeed, preserved through Riemannian pushforward and pullback actions to, and from, the tangent space to the manifold at any admissible point. This fundamental property is subsequently exploited to derive a probabilistic model that leverages the multimodel nature of the atomistic setting. The proposed formulation offers several advantages, including a simple and interpretable low-dimensional parameterization, the ability to constraint the Fréchet mean on the manifold, and ease of implementation and propagation. The relevance of the proposed modeling framework is finally demonstrated on various applications including multiscale simulations on graphene-based systems.
