随机建模界面识别问题的计算方法
Computational Aspects for Interface Identification Problems with Stochastic Modelling
摘要：
本文提出了一个带纯Neumann边界的随机椭圆型偏微分方程约束的形状最优化问题。该模型的动机是在接口识别中的应用，我们假设系数和输入受到不确定性。该问题是作为一个随机目标函数的期望依赖于不确定参数的最小化。提出了一种迭代求解该问题的数值方法，它是经典随机梯度法在形状空间中的推广。此外，我们进行了数值实验，证明了算法的有效性。
英文摘要：
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume coefficients and inputs are subject to uncertainty. The problem is posed as a minimization of the expectation of a random objective functional depending on the uncertain parameters. A numerical method for iteratively solving the problem is presented, which is a generalization of the classical stochastic gradient method in shape spaces. Moreover, we perform numerical experiments, which demonstrate the effectiveness of the algorithm.
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