MLO4EMD
Machine learning-based optimization for extreme metamaterials design

Invited Session

Time Slot: Friday Morning

Room: 003

Chair: Giorgio Gnecco

Designing a broadband GRIN lens through a deep learning based data-driven method

Time: 11:30

Amir Darabi (Georgia Institute of Technology), Leamy Michael Georgia Institute of Technology

Controlling flexural waves in thin plates is a challenging task with implications for a variety of applications in acoustic problems. One of the most fascinating problems in such medium is optimizing the amount of focused wave intensity in the focal area for gradient-index (GRIN) acoustic lenses [1], for energy harvesting purposes. Recently, machine learning techniques have been utilized extensively to solve variety of problems in physical sciences and engineering. As such, we use numerically produced data to predict the shape of a discrete lens, formed from a lattice of circular scatterers in a thin aluminum plate, for given focal shapes. For each of these lenses, the inclusion diameters and their locations are varied randomly to obtain different lens shapes. In support of such concepts, twenty one thousands different lens shapes are considered, and the corresponding wave fields are computed numerically using multiple scattering formulation. Next, nineteen thousand of these recorded wavefields (each of them 200 *200 pixels) are input into a ResNet [2] with twenty layers to train the convolutional neural network to predict the shape of the lens. In addition, the last two thousands samples are used as the test set to evaluate the performance of the network. In order to train the network, ADAM optimizer algorithm with the learning rate of 0.001 is chosen, along with the categorical crossentropy as the loss function, and batch size of thirty two. After running the algorithm for three hundred iterations (each with fifty epochs) the designed network successfully is trained with the loss of 1E-4 and the accuracy of 0.987 percent. Next, the performance of the trained network is tested with the two thousand validation test, to obtain the accuracy of 0.97 with the loss being equal to 2E-3. Finally, three different wave field responses are input to the trained network to predict the shape of the desired lens. The proposed idea herein can be extended to other media such as phononic devices, air, Bulk waves, electromagnetic waves, optical Bulk waves and photonics by changing the phase velocity of the medium.

[1] Darabi, Amir, and Michael J. Leamy. “Analysis and experimental validation of an optimized gradient-index phononic-crystal lens.” Physical Review Applied 10.2 (2018): 024045.
[2] He, Kaiming, et al. “Deep residual learning for image recognition.” Proceedings of the IEEE conference on computer vision and pattern recognition. 2016.

Voronoi recursive binary trees for the optimization of nonlinear functionals

Time: 11:50

Danilo Macciò (Institute of Marine Engineering, National Research Council of Italy), Francesco Rebora, Cristiano Cervellera

We propose an algorithm for the approximate solution of general nonlinear functional optimization problems through recursive binary Voronoi tree models. Unlike typical binary tree structures commonly employed for classification and regression problems, where splits are performed parallel to the coordinate axes, here the splits are based on Voronoi cells defined by a pair of centroids. Models of this kind are particularly suited to functional optimization, where the optimal solution function can easily be discontinuous even for very smooth cost functionals. In fact, the flexible nature of Voronoi recursive trees allows the model to adapt very well to possible discontinuities. In order to improve efficiency, accuracy and robustness, the proposed algorithm exploits randomization and the ensemble paradigm. To this purpose, an ad hoc aggregation scheme is proposed. Simulation tests involving various test problems, including the optimal control of a crane-like system, are presented, showing how the proposed algorithm can cope well with discontinuous optimal solutions and outperform trees based on the standard split scheme.

On dispersion curve coloring

Time: 12:10

Giorgio Gnecco (IMT School for Advanced Studies, Lucca), Andrea Bacigalupo, Maria Laura De Bellis, Federico Nutarelli

A novel automatic technique for smooth curve coloring – i.e., curve identification – in the presence of curve intersections is presented. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, when these are written as functions of a scalar parameter. The algorithm develops the one proposed in [1]. Specifically, it is based on a first-order finite difference approximation of the curves and a prediction/correction steps sequence. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving a Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming formulation is analyzed. The proposed algorithm is applied to mechanical filters made of metamaterials, also known as metafilters [2]. Its output is shown to be in excellent agreement with the desired smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out.

[1] Gnecco, G.: An algorithm for curve identification in the presence of curve intersections. Mathematical Problems in Engineering, vol. 2018, article ID 7243691, 7 pages (2018).
[2] Bacigalupo, A., Gnecco, G., Lepidi, M., Gambarotta, L.: Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization. Computer Methods in Applied Mechanics and Engineering, vol. 375, article ID 113623, 22 pages (2021).