Abstract In this paper, we consider the linear Boltzmann equation subject to uncertainties in the initial conditions and matter parameters (cross-sections/opacities). In order to solve the underlying uncertain systems, we rely on moment theory and the construction of hierarchical moment models in the framework of parametric polynomial approximations. Such model is commonly called a generalized Polynomial Chaos (gPC) reduced model. In this paper, we prove the spectral convergence of the hierarchy of reduced model parametered by P (polynomial order) obtained from the uncertain linear Boltzmann equation.

中文翻译：

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从不确定线性 Boltzmann 方程得到的广义多项式混沌约简模型的谱收敛

摘要 在本文中，我们考虑了受初始条件和物质参数（横截面/不透明度）不确定性影响的线性玻尔兹曼方程。为了解决潜在的不确定系统，我们依靠矩理论和参数多项式逼近框架下的分层矩模型的构建。这种模型通常称为广义多项式混沌 (gPC) 简化模型。在本文中，我们证明了由不确定线性Boltzmann方程得到的以P（多项式阶）为参数的简化模型的层次的谱收敛性。