MonteCarloMeasurements .jl：通过方法重载实现任意多变量分布的非线性传播
MonteCarloMeasurements.jl: Nonlinear Propagation of Arbitrary Multivariate Distributions by means of Method Overloading
摘要：
这份手稿概述了一个软件包，便于工作与概率分布的蒙特卡罗方法，在某种程度上，允许传播的多元概率分布通过任意函数。我们提供了一个\emph{type}，表示概率分布的内部向量的未加权样本，\texttt{Particles}，这是一个子类型的\texttt{Real}数和行为就像一个经常的实数在计算中的方法重载。这使得软件易于使用，并为用户提供最小的摩擦。我们强调这种设计如何促进SIMD指令的最佳使用，并展示了包的不确定性传播通过现成的ODE求解器，以及强大的概率优化与自动微分。
英文摘要：
This manuscript outlines a software package that facilitates working with probability distributions by means of Monte-Carlo methods, in a way that allows for propagation of multivariate probability distributions through arbitrary functions. We provide a \emph{type} that represents probability distributions by an internal vector of unweighted samples, \texttt{Particles}, which is a subtype of a \texttt{Real} number and behaves just like a regular real number in calculations by means of method overloading. This makes the software easy to work with and presents minimal friction for the user. We highlight how this design facilitates optimal usage of SIMD instructions and showcase the package for uncertainty propagation through an off-the-shelf ODE solver, as well as for robust probabilistic optimization with automatic differentiation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
