论文标题
部分可观测时空混沌系统的无模型预测
A Statistical Framework for Domain Shape Estimation in Stokes Flows
论文作者
论文摘要
我们开发并实施了一种贝叶斯方法，以估计二维环形结构域的形状，从而封闭了封闭流体的稀疏和嘈杂观察结果。我们的设置包括直接观察流场的情况，以及测量溶质的溶质的浓度，被流动中的溶质被动趋势和扩散。采用统计方法提供了由于前向映射的不可逆性和测量误差而导致的形状不确定性的估计值。当形状代表试图匹配所需目标结果的设计问题时，这种“不确定性”可以解释为确定剩余的自由度。我们证明了框架在三个具体测试问题上的生存能力。这些问题说明了我们对应用程序框架的希望，同时为最近开发的马尔可夫链蒙特卡洛（MCMC）算法提供了一系列测试用例，旨在解决无限的维度统计量。
We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this "uncertainty" can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov Chain Monte Carlo (MCMC) algorithms designed to resolve infinite dimensional statistical quantities.
