**Thesis Title:** Calibration and Optimization of Computer Models with applications to Acoustics and Materials Discovery

**Advisor:**

Dr. V. Roshan Joseph, School of Industrial and Systems Engineering, Georgia Tech

**Committee Members:**

Dr. C. F. Jeff Wu, School of Industrial and Systems Engineering, Georgia Tech

Dr. Xiaoming Huo, School of Industrial and Systems Engineering, Georgia Tech

Dr. William Brenneman, Statistics and Data Science Department, Procter & Gamble

Dr. Rampi Ramprasad, School of Material Science & Engineering, Georgia Tech

Dr. Chengzhi Shi, School of Mechanical Engineering, Georgia Tech

**Date and Time:** Wednesday, July 14, 2021 @ 01:00pm (EST)

**Meeting URL** (BlueJeans): https://bluejeans.com/241305216

Meeting ID (BlueJeans): 241305216

**Abstract:**

In the past, physical systems/processes/phenomena were studied using expensive and time-consuming physical experiments. However, with the advancement of computational resources, computer models are now used extensively to minimize the need for such experimentation. A computer model provides a cheap alternative to explore the behavior of physical processes in desired scenarios and make inferences. This thesis begins with the topic of model calibration, a method to estimate unknown model parameters, and adjust the model to mimic reality. This is followed by a couple of applications of computer models in the field of material informatics and acoustic metasurface design. Novel machine learning algorithms are developed that leverage the computer models for efficient exploration of the physical processes, optimization of parameters of interest, and making inferences.

In Chapter 1, we propose a novel methodology to obtain a robust experimental design for model calibration. A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting physical experiments. This chapter presents an approach to optimally design such a physical experiment. The problem of optimally

designing a physical experiment, using a computer model, is similar to the problem of finding an optimal design for fitting nonlinear models. However, the problem is more challenging than the existing work on nonlinear optimal design because of the possibility of model discrepancy, that is, the computer model may not be an accurate representation of the true underlying model. Therefore, we propose an optimal design approach that is robust to potential model discrepancies. We show that our designs are better than the commonly used physical experimental designs that do not make use of the information contained in the computer model and other nonlinear optimal designs that ignore potential model discrepancies. We illustrate our approach using a toy example and a real example from the Procter & Gamble company.

In Chapter 2, we present a novel machine learning algorithm for discovering new materials crystal structure. A material is (thermodynamically) stable and exists naturally when its building blocks, i.e., the constituent atoms, are arranged so that the potential energy is (globally) minimized. We aim to find such minimum energy configurations, to discover a new crystal structure. We leverage density functional theory (DFT) to compute the potential energy for a given configuration of the atoms. The problem is challenging because there are infinitely large number of configurations, the DFT code for computing the energy is expensive, and the potential energy surface is highly non-linear and multi-modal. We propose a novel expansion-exploration-exploitation framework to find the global minimum. The space spanned by a few known crystal structure configurations is expanded to obtain a candidate set of configurations. A key feature of this step is that it tends to generate a space-filling design without the knowledge of the boundaries of the domain space. Once a candidate set of configurations is obtained, it is explored and exploited simultaneously, using Bayesian optimization, to find the global minimum of potential energy. Gaussian Process modeling along with the Expected Improvement algorithm is used to iteratively update the model and guide the search towards the global minimum. We show the effectiveness of our methodology on toy examples and a real problem of predicting the crystal structure configuration of Al_{8}.

In Chapter 3, we address the problem of designing acoustic metasurfaces for independent amplitude and phase control of acoustic waves. Acoustic metasurfaces are material structures of subwavelength thickness that are used for modulating propagating sound waves. Several applications of acoustic metasurfaces, such as non-invasive biomedical treatments, require independent phase and amplitude modulation of the reflected and transmitted waves. These reflection and transmission outputs (or acoustic outputs) are governed by the geometry of the acoustic metasurface. We model the geometry of the metasurface as a unit cell with *mn* equal-sized square shaped elements, or a grid-size of *m x n*. Each element can either be empty or filled with solid material leading to a total of 2^{mn} unique geometries! This makes it challenging to identify the relevant geometries for obtaining the desired range of acoustic outputs, which are simulated using the COMSOL Multiphysics software. We leverage the expansion algorithm developed in Chapter 2 to start with a few geometries and iteratively add geometries to the set such that they span the entire range of acoustic outputs using only a small fraction of the total number of possible geometries. The algorithm is modified to identify and eliminate redundancy in the chosen geometries due to various kinds of symmetry and other factors. With our modified expansion algorithm, we were able to identify the smallest grid-size necessary for spanning the entire space of the acoustic outputs using only around 5,000 simulations.