Adjoint computation of Berry phase gradients

IF 4.9 2区 工程技术 Q1 ACOUSTICS
Cyrill Bösch , Marc Serra-Garcia , Christian Böhm , Andreas Fichtner
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引用次数: 0

Abstract

Berry phases offer a geometric perspective on wave propagation and are key to designing materials with topological wave transport. However, controlling Berry phases is challenging due to their dependence on global integrals over the Brillouin zone, making differentiation difficult. We present an adjoint-based method for efficiently computing the gradient of the Berry phase with respect to system parameters. We introduce an adjoint-based algorithm that computes Berry-phase gradients via only one forward and one adjoint solve. Under reasonable assumptions the algorithm’s time complexity is O(N1+1/D), where N is number of grid points in a numerical discretization scheme and D is the space dimension. Thereby it outperforms numerical differentiation and perturbation theory for problems with a large number of design variables. This approach enables the use of advanced, gradient-based optimization techniques to design new continuously parameterized materials with tailored topological wave properties. Furthermore, via multi-objective optimizations this method allows to co-design the topological characteristics in tandem with other objectives. We apply the method to an elastic metamaterial rod.
Berry相位梯度的伴随计算
Berry相提供了波传播的几何视角,是设计具有拓扑波输运的材料的关键。然而,控制Berry相位是具有挑战性的,因为它们依赖于布里渊区上的全局积分,使得微分变得困难。我们提出了一种基于伴随的方法来有效地计算Berry相位相对于系统参数的梯度。我们介绍了一种基于伴随的算法,该算法仅通过一个正解和一个伴随解来计算berry相位梯度。在合理的假设下,算法的时间复杂度为O(N1+1/D),其中N为数值离散化方案中的网格点数,D为空间维数。因此,对于具有大量设计变量的问题,它优于数值微分和微扰理论。这种方法可以使用先进的、基于梯度的优化技术来设计具有定制拓扑波特性的新型连续参数化材料。此外,通过多目标优化,该方法允许与其他目标协同设计拓扑特征。我们将该方法应用于弹性超材料棒。
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来源期刊
Journal of Sound and Vibration
Journal of Sound and Vibration 工程技术-工程:机械
CiteScore
9.10
自引率
10.60%
发文量
551
审稿时长
69 days
期刊介绍: The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.
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