MACHINE LEARNING APPROACHES FOR DESIGNING 1-D ELASTIC SUPERLATTICES WITH NON-CONVENTIONAL TOPOLOGICAL ACOUSTIC WAVES

The design and development of acoustic devices requires exploring and selecting a large number of parameters associated with the device structure, material properties and the behavior of the acoustic wave within these materials. In some cases, the number of underlying parameters can be so large, making it impractical and resource-intensive to explore all possible parameter combinations experimentally or computationally. In this paper, we propose the use of Machine Learning (ML) techniques to accelerate the design and optimization of acoustic devices. Our approach facilitates efficient exploration of the parameter space, enabling the identification of optimal parameters or a confidence range that achieves the desired performance characteristics. This innovative methodology minimizes the reliance on exhaustive experimentation, offering a faster and more cost-effective pathway to the development of high-performance acoustic devices. More specifically, we study a one-dimensional elastic superlattice which supports acoustic waves exhibiting non-conventional topologies. We formulate the parameter search problem as a binary classification problem, where the two classes indicate whether a phase change occurs or does not occur. We generate data using one-dimensional elastic superlattice equations, where the 1D elastic superlattice consists of alternating layers of materials 1 and 2 with densities (ρ₁, ρ₂), sound speeds (c₁, c₂), and segment lengths (d₁, d₂). We also develop a self-labeling technique that can automatically label the data as 1 (phase change occurs) and 0 (phase change does not occur). This binary classification problem is solved using machine learning methods, including logistic regression, support vector machine, feedforward neural network (FNN) and XGBoost. We achieve a test accuracy and F1 score of at least 95%. However, as accuracy depends on the number of training samples, we analyze the trade-off between the sample size and accuracy to find a balance, considering that data generation may be limited in similar problems. Once a “good" parameter subspace is identified, we solve another prediction problem to estimate the wave number and frequency of acoustic waves exhibiting zero amplitude associated with a 180 change in geometric phase (Berry connection), a signature of non-conventional topology. We use Gaussian Process Regression (GPR) and a Feedforward Neural Network (FNN) for this task. GPR provides uncertainty estimates alongside its predictions, which is particularly valuable in this setting. With a data size of 4000, we achieve a Mean Absolute Percentage Error of less than 10 The promising results from the 1D elastic superlattice motivate us to extend the methodology to 2D or high-D superlattices. The increased number of parameters in high-D systems poses challenges for traditional methods, making our approach ideal for exploring the properties of different parameter combinations.