Optimal design of acoustic metamaterial cloaks under uncertainty

TL;DR

This paper develops scalable approximation and optimization methods for the optimal design of acoustic cloaks that are robust under material uncertainty, enabling efficient solutions for high-dimensional problems with complex geometries.

Contribution

It introduces a novel computational approach using Taylor approximation and an approximate Newton method for high-dimensional, uncertain acoustic cloak design problems.

Findings

Method is scalable with respect to design and uncertainty dimensions.

Achieves robust optimal design under material variability.

Applicable to large-scale, complex geometries.

Abstract

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. We demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method's Hessian computation is viable for large, complex problems.