A statistical framework for domain shape estimation in Stokes flows
A statistical framework for domain shape estimation in Stokes flows
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DOI：
10.1088/1361-6420/acdd8e
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发表时间：
2022-12
期刊：
影响因子：
2.1
通讯作者：
J. Borggaard;N. Glatt-Holtz;J. Krometis
中科院分区：
文献类型：
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作者：
J. Borggaard;N. Glatt-Holtz;J. Krometis
我们开发并实现了贝叶斯方法的形状估计的二维环形域封闭的斯托克斯流从稀疏和嘈杂的观测封闭的流体。我们的设置包括直接观测流场的情况下，以及被动平流和扩散内流的溶质浓度的测量。采用统计方法提供了由于前向图的不可逆性和测量误差引起的形状不确定性的估计。当形状表示试图匹配期望目标结果的设计问题时，这种“不确定性”可以被解释为识别设计者可用的剩余自由度。我们证明了我们的框架上的三个具体的测试问题的可行性。这些问题说明了我们的应用框架的承诺，同时提供了一个测试用例的集合，最近开发的马尔可夫链蒙特卡罗算法，旨在解决无限维的统计量。
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 algorithms designed to resolve infinite-dimensional statistical quantities.