不确定性扩散动力学群集模型的Monte Carlo gPC方法
Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties
摘要：
在本文中，我们介绍和讨论的动力学方程的近似数值方案的群集行为与相变，包括不确定量。这类计划在这里考虑利用蒙特卡罗方法在相空间耦合随机Galerkin展开在随机空间。所提出的方法自然地保持了解决方案的统计矩的正性，并且能够在随机空间中实现高精度。几个测试的动力学校准模型与自推进验证所提出的方法都在均匀和非均匀的设置，阴影光的影响的不确定性的相变现象驱动的噪声，如他们的平滑和置信带。
英文摘要：
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a Monte Carlo approach in the phase space coupled with a stochastic Galerkin expansion in the random space. The proposed methods naturally preserve the positivity of the statistical moments of the solution and are capable to achieve high accuracy in the random space. Several tests on a kinetic alignment model with self propulsion validate the proposed methods both in the homogeneous and inhomogeneous setting, shading light on the influence of uncertainties in phase transition phenomena driven by noise such as their smoothing and confidence band.
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