A Riemannian stochastic representation for quantifying model uncertainties in molecular dynamics simulations
A Riemannian stochastic representation for quantifying model uncertainties in molecular dynamics simulations
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DOI：
10.1016/j.cma.2022.115702
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发表时间：
2022-07
影响因子：
7.2
通讯作者：
Hao Zhang;J. Guilleminot
中科院分区：
文献类型：
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作者：
Hao Zhang;J. Guilleminot
提出了分子动力学模型不确定性的一种黎曼随机表示。该方法依赖于降阶模型，其投影基础在Stiefel流形的子集上随机化，该Stiefel流形的子集由一组线性约束来表征，例如，物理空间中的狄利克雷边界条件。我们首先表明，这些限制，的确，通过黎曼的向前推和向后拉行动，并从切空间的流形在任何允许的点保存。随后利用这一基本属性来推导出一个概率模型，该模型利用了原子设置的多模型性质。所提出的配方提供了几个优点，包括一个简单的和可解释的低维参数化，能够约束的Fréchet平均流形上，易于实施和传播。最后证明了所提出的建模框架的相关性的各种应用程序，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.