Sound Localization through Multi-Scattering and Gradient-Based Optimization

A gradient-based optimization (GBO) method is presented for acoustic lens design and sound localization. GBO uses a semi-analytical optimization combined with the principle of acoustic reciprocity. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. We first derive a formula for the gradients of the pressure at the focal point with respect to positions of a set of cylindrical scatterers. The analytic form of the gradients enhances modeling capability when combined with optimization algorithms and parallel computing. The GBO algorithm maximizes the sound amplification at the focal point and enhances the sound localization by evaluating pressure derivatives with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while incorporating multiple scattering between the cylindrical scatterers. The results of the GBO of the uni- and multi-directional broadband acoustic lens designs are presented including several performance measures for the frequency dependence and the incidence angle. A multi-directional broadband acoustic lens is designed to localize the sound and to focus acoustic incident waves received from multiple directions onto a predetermined localization region or focal point. The method is illustrated for configurations of sound hard and sound soft cylinders as well as clusters of elastic thin shells in water.

Inverse Design Framework with Invertible Neural Networks for Passive Vibration Suppression in Phononic Structures

Automated inverse design methods are critical to the development of metamaterial systems that exhibit special user-demanded properties. While machine learning approaches represent an emerging paradigm in the design of metamaterial structures, the ability to retrieve inverse designs on-demand remains lacking. Such an ability can be useful in accelerating optimization-based inverse design processes. This paper develops an inverse design framework that provides this capability through the novel usage of invertible neural networks (INN). We exploit an INN architecture that can be trained to perform forward prediction over a set of high-fidelity samples, and automatically learns the reverse mapping with guaranteed invertibility. We apply this INN for modeling the frequency response of periodic and aperiodic phononic structures, with the performance demonstrated on vibration suppression of drill pipes. Training and testing samples are generated by employing a Transfer Matrix Method. The INN models provide competitive forward and inverse prediction performance compared to typical deep neural networks (DNN). These INN models are used to retrieve approximate inverse designs for a queried non-resonant frequency range; these inverse designs are then used to initialize a constrained gradient-based optimization process to find a more accurate inverse design that also minimizes mass. The INN initialized optimizations are found to be generally superior in terms of the queried property and mass compared to randomly-initialized and inverse DNN-initialized optimizations. Particle Swarm Optimization with INN-derived initial points is then found to provide even better solutions, especially for the higher-dimensional aperiodic structures.

End-to-end nanophotonic inverse design for imaging and polarimetry

By codesigning a metaoptical front end in conjunction with an image-processing back end, we demonstrate noise sensitivity and compactness substantially superior to either an optics-only or a computation-only approach, illustrated by two examples: subwavelength imaging and reconstruction of the full polarization coherence matrices of multiple light sources. Our end-to-end inverse designs couple the solution of the full Maxwell equations—exploiting all aspects of wave physics arising in subwavelength scatterers—with inverse-scattering algorithms in a single large-scale optimization involving ≳ 10 4 $\gtrsim {10}^{4}$ degrees of freedom. The resulting structures scatter light in a way that is radically different from either a conventional lens or a random microstructure, and suppress the noise sensitivity of the inverse-scattering computation by several orders of magnitude. Incorporating the full wave physics is especially crucial for detecting spectral and polarization information that is discarded by geometric optics and scalar diffraction theory.

Metamodel Based Forward and Inverse Design for Passive Vibration Suppression

Aperiodic metamaterials represent a class of structural systems that are composed of different building blocks (cells), instead of a self-repeating chain of the same unit cells. Optimizing aperiodic cellular structural systems thus presents high-dimensional design problems, that become intractable to solve using purely high-fidelity structural analysis coupled with optimization. Specialized analytical modeling along with metamodel based optimization can provide a more tractable alternative to designing such aperiodic metamaterials. To explore this concept, this paper presents an initial design automation framework applied to a case study representative of a simple 1D metamaterial system. The case under consideration is a drill string, where vibration suppression is of utmost importance. The drill string comprises a set of nonuniform rings attached to the outer surface of a longitudinal rod. As such, the resultant system can now be perceived as an aperiodic 1D metamaterial with each ring/gap representing a cell. Despite being a 1D system, the simultaneous consideration of multiple degrees of freedom (associated with torsional, axial, and lateral motions) poses significant computational challenges. To deal with these challenges, a transfer matrix method (TMM) is employed to analytically determine the frequency response of the drill string. However, due to the minute scale cost of the TMM method, the optimization remains computationally burdensome. This latter challenge is addressed by training a suite of neural networks on a set of TMM samples, with each network providing the response w.r.t. a specific frequency. Optimization is then performed to minimize mass subject to constraints on the gap between consecutive resonance peaks in one case, and minimizing this gap in the second case. Crucial improvements are accomplished over the initial baselines in both cases. Further novel contributions occur through the development of an inverse modeling approach that can learn optimal inverse designs with minimum mass and a desirable non-resonant frequency range, which partially mimics band gap behavior in perfectly periodic dispersive structures. To this end, we introduce the use of an emerging modeling formalism called in-vertible neural nets. Our study indicates that the inverse model is able to generate constraint satisfying designs with slightly higher mass.

Study and Verification of Continuous Adjoint System for Aerodynamic Optimization in Turbomachinery Cascades

This paper is a further study of the authors’ previous work on the continuous adjoint method based on the variation in grid node coordinates and Jacobi Matrices of the flow fluxes. This method simplifies the derivation and expression of the adjoint system, and reduces the computation cost. In this paper, the differences between the presented and the traditional methods are analyzed in details by comparing the derivation processes and the adjoint systems. In order to demonstrate the reliability and accuracy of the adjoint system deduced by the authors, the presented method is applied to different optimal problems, which include two inverse designs and two shape optimizations in both 2D and 3D cascades. The inverse designs are implemented by giving the isentropic Mach number distributions along the blade wall for 2D inviscid flow and 3D laminar flow. The shape optimizations are implemented with the objective function of the entropy generation in flow passage for 2D and 3D laminar flows. In the 3D optimal case, this method is validated by supersonic turbine design case with and without mass flow rate constraint. The numerical results testify the accuracy of this adjoint method, which includes only the boundary integrals, and furthermore, the universality and portability of this adjoint system for inverse designs and shape optimizations are demonstrated.