解决大量的微尺度相互作用，建立随机偏微分方程模型
Resolve the multitude of microscale interactions to model stochastic partial differential equations
摘要：
构造有噪声的偏微分方程的数值模型是非常精细的。我们的长期目标是利用现代动力系统理论导出耗散随机偏微分方程的离散化。作为第二步，我们在这里考虑一个小的域，代表一个有限元，并应用随机中心流形理论推导出一个自由度模型的动态元素。该方法自动参数化的空间变化的随机噪声引起的元素内的微尺度结构。这项工作的关键方面是，我们探讨有多少噪声过程可能会相互作用的非线性动力学。我们看到，噪声过程与粗结构的有限元的建模是显着的噪声。此外，非线性动力学有效地抽象新的噪声源的宏观时间尺度解决了模型。
英文摘要：
Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a second step we here consider a small domain, representing a finite element, and apply stochastic centre manifold theory to derive a one degree of freedom model for the dynamics in the element. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within the element. The crucial aspect of this work is that we explore how many noise processes may interact in nonlinear dynamics. We see that noise processes with coarse structure across a finite element are the significant noises for the modelling. Further, the nonlinear dynamics abstracts effectively new noise sources over the macroscopic time scales resolved by the model.
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