Machine learning for nonlinear materials characterization and modeling

Abstract

Materials scientists and engineers broadly aim to study materials by analyzing their structures, performance, properties, and synthesis methods using a variety of characterization techniques. This thesis aims to develop broadly applicable data-driven techniques to advance the study of materials by improving characterization and modeling of nonlinear materials. Nonlinear materials are generally challenging to understand because of the difficulty associated with solving the relevant governing differential equations. Furthermore, many systems in materials science and engineering are governed by boundary value problems wherein certain conditions are specified at the points within or boundaries of the system. In this work, we develop two data-driven modeling approaches for boundary value problems (BVPs) involving nonlinear differential equations and one characterization technique for time-frequency analysis of a nonlinear phase evolution system. The data-driven modeling approaches can be used to understand the underlying physics, enable predictive modeling of the system, and are broadly applicable to any BVPs. The time-frequency analysis technique improves the time-frequency resolution of traditional techniques, enables analysis of nonstationary time series signals, and can be used on any multimodal nonstationary signal. Further, it is extremely useful for analyzing cantilever-based imaging modalities that are extremely common in materials science such as atomic force microscopy.