论文标题
在物理上受到约束的问题中，无数据驱动的推断的收敛率
Convergence rates for ansatz-free data-driven inference in physically constrained problems
论文作者
论文摘要
我们研究了一种数据驱动的方法，用于在衡量理论框架中进行物理系统的推论。所考虑的系统的特征是在相空间中定义的两个措施：i）在满足所有管理物理定律的意义上，表达系统状态是可以接受的，表达了系统状态的可能性； ii）一种表达在实验室中观察到材料的局部状态的可能性措施。我们假设确定性加载，这意味着第一个度量是在线性子空间上支持的。另外，我们假设第二个度量仅通过一系列经验（离散）度量大致知道。我们开发了一种基于平面度量的收敛性分析的方法，并获得退火和离散化或采样程序的误差界限，从而确定了适当的定量退火速率。最后，我们提供了一个示例，说明该理论在运输网络中的应用。
We study a Data-Driven approach to inference in physical systems in a measure-theoretic framework. The systems under consideration are characterized by two measures defined over the phase space: i) A physical likelihood measure expressing the likelihood that a state of the system be admissible, in the sense of satisfying all governing physical laws; ii) A material likelihood measure expressing the likelihood that a local state of the material be observed in the laboratory. We assume deterministic loading, which means that the first measure is supported on a linear subspace. We additionally assume that the second measure is only known approximately through a sequence of empirical (discrete) measures. We develop a method for the quantitative analysis of convergence based on the flat metric and obtain error bounds both for annealing and the discretization or sampling procedure, leading to the determination of appropriate quantitative annealing rates. Finally, we provide an example illustrating the application of the theory to transportation networks.
