Session: 01-10-01: Machine Learning, Artificial Intelligence, and Deep Learning in Dynamics, Vibrations, and Control

Paper Number: 165982

Machine Learning Approaches for Designing 1-D Elastic Superlattices With Non-Conventional Topological Acoustic Waves 

Optimal development of acoustic devices requires selecting numerous design parameters that control the device structure, material properties, and acoustic wave behavior. For complex devices, the design parameter space becomes so vast that exploring all combinations becomes impractical and resource-intensive, both experimentally and computationally. This is particular true when searching for topological properties of acoustics waves which are non-conventional. In this paper, we propose using Machine Learning (ML) techniques to accelerate the design of topological acoustic devices with a large number of design parameters. Our approach enables efficient parameter space exploration to identify promising parameters or confidence ranges that lead to desired performance characteristics. To bypass the exhaustive search, we reformulate the problem as classification and employ ML to identify parameter subspaces associated with high-performance of acoustic devices. We illustrate our approach with a one-dimensional elastic superlattice system, where the goal is to search for design parameters associated with non-conventional topological phases of acoustic waves. We formulate this as a binary classification problem where the two classes indicate whether phase transition occurs or not. We generate data using one-dimensional (1D) 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 mathematical technique to automatically label the generated data as 1 (phase transition occurs) or 0 (phase transition doesn't occur), which significantly scales up the experimental capacity.  We train classifiers using various supervised learning methods, including logistic regression, support vector machine, feedforward neural network (FNN), and XGBoost, and evaluate their performance. Our preliminary results demonstrate test accuracy and F1 scores exceeding 95%. Recognizing that accuracy is dependent on the training sample size, we analyze the tradeoff between the sample size and prediction accuracy to determine an optimal balance, which is particularly important when data generation faces constraints in similar applications. Upon identifying an "ideal" set of parameters, we leverage ML further to estimate wave numbers and frequencies associated with phase transitions. For this task, we implement Gaussian Process Regression (GPR) and Feedforward Neural Network (FNN) approaches. GPR offers uncertainty quantification for its predictions, which is valuables for stability. Using 4000 samples, we achieve a Mean Absolute Percentage Error below 10%. These encouraging results from our 1D elastic superlattice experiments provide strong motivation to extend our methodology to 2D superlattice systems. The increased parameter dimensionality in 2D configurations presents forbidden challenges for conventional methods, highlighting the advantage of our ML approach for efficiently exploring complex parameter spaces and their associated properties.

Presenting Author: Kamaljeet Singh University of Arizona

Presenting Author Biography: Kamaljeet Singh is a PhD student in the Statistics & Data Science program at the University of Arizona, with a minor in Systems & Industrial Engineering. He is currently working as a Graduate Research Assistant with the New Frontiers of Sound (NewFos) center at the University of Arizona. His research focuses on the application of machine learning in materials science. He holds a master's degree in Statistics from Panjab University and a bachelor's degree in Statistics and Mathematics from Kurukshetra University. His broader research interests include statistical learning theory and machine learning theory.

Authors:

Kamaljeet Singh University of Arizona
Hao Helen Zhang University of Arizona
Pierre Deymier University of Arizona
Keith Runge University of Arizona
Pierre Lucas University of Arizona