论文标题
随机近似以优化形状空间
Stochastic approximation for optimization in shape spaces
论文作者
论文摘要
在这项工作中，我们提出了一种解决随机形状优化问题的新方法。我们的方法是将经典随机梯度方法扩展到无限尺寸形状歧管。我们证明了该方法在Riemannian歧管上的收敛性，然后将连接到形状空间。该方法在接口标识的模型形状优化问题上进行了证明。不确定性以随机偏微分方程的形式出现，其中假定随机系数和输入的潜在概率分布已知。我们验证了模型问题收敛的某些条件，并以数值证明该方法。
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the method on Riemannian manifolds and then make the connection to shape spaces. The method is demonstrated on a model shape optimization problem from interface identification. Uncertainty arises in the form of a random partial differential equation, where underlying probability distributions of the random coefficients and inputs are assumed to be known. We verify some conditions for convergence for the model problem and demonstrate the method numerically.
