My Research
My research primarily focuses on development of projection-based reduced-order models (ROMs) for computational physics simulations and their use in sensitivity analysis and uncertainty quantification. In my dissertation work I have developed methodologies for proper-orthogonal based decomposition (POD) ROMs to improve their reliability, sensitivity accuracy, and allow for sensitivity analysis of boundary conditions. I have applied this work to models of both chemical reactors and incompressible Navier-Stokes flows. In my undergraduate and master's work I also developed ecological models of disease transmission for Lyme and Chagas disease. In addition to this work I also have extensive experience in model verification and randomized linear algebra methods.
Hyper-Reduction of Non-Linear Sources in ROMs
Summary: Mathematical models of chemical reactor are critical to a wide varitiey of industries including biofuels, pharmaceuticals, and waste remediation. Models of these systems are typically advection dominated with nonlinear source terms to model chemcial reactions and often include recirculation of heat or reactants. Reduced-order models (ROMs) are a common appraoch to quickly model these reactors for control and uncertainty quantification. However, we document previously unidentified limitations in convergence of projection-based ROMs for these models. We also develop a hyper-reduction approach for nonlinear source terms that improves reliability of projection-based ROMs without increasing computational cost.
Collaborating Authors: Ralph C. Smith (North Carolina State University), Hangjie Ji (North Carolina State University)
Sensitivity Equation Projection in POD-ROMs
Summary: Proper Orthogonal Decomposition-based Reduced Order Models (POD-ROMs) are a common model reduction approach for many computational physics applications. They often have improved stability compared to other projection-based ROM approaches and require significantly less data than surrogate methods such as neural networks. However, they can often have signficant errors estimating parameter sensitivities with standard finite-differences since the solution basis of the full-order model is often not a suitable basis for the model sensitivities. We use a new approach of projecting the POD basis onto the model sensitivity equations to better inform computed ROM coefficients with parameter sensitivity information. We test this approach on a chemical reactor model to determine the fidelity in FOM sampling required to accurately capture the parameter sensitivities and how the necessary fidelity compares to standard finite-differences.
Collaborating Author: Ralph C. Smith (North Carolina State University)
Boundary Penalties for Sensitivity Analysis (In Review)
Title: Efficient Quantification of Fluid Flow Parameter Sensitivity Using Reduced-Order Modeling [Paper Submission]
Abstract: Sensitivity analysis for computational fluid dynamics (CFD) simulations is often required for many applications but complicated by the computational cost of simulation codes. For many applications, the computational cost of quantifying the simulation's sensitivity to physical parameters (e.g., body surface roughness) and hyperparameters (e.g., subiteration convergence criterion) can be intractable for even a single simulation. Reduced-order modeling significantly reduces the computational cost of simulating fluid flows by solving on a reduced solution space informed by prior simulation data. In this work, fluid reduced-order models using boundary penalties are developed and utilized to quantify flow sensitivity to physical parameters, boundary conditions, and model hyperparameters. The proposed reduced-order modeling approach allows sensitivity analysis and uncertainty quantification of boundary conditions and enables more informed CFD frameworks.
Collaborating Authors: Michael W. Lee (NASA Langley), Ralph C. Smith (North Carolina State University)
Funding: This work was funded under NASA's AEROFUSION-MLUQ grant (Contract No. 80LARC21CA003)
Chagas Disease (Master's Thesis)
Title: Sylvatic and Domestic T. cruzi Transmission Cycles and Chagas Disease Risk in New Orleans, Louisiana
Summary: My research on Chagas Disease focuses on building an ordinary differential equation host-vector model of the transmission of T. cruzi, the caussative agent of Chagas disease, the New Orleans area. I seek to use it first to take the limited data sampling for the New Olreans area to construct an estimation of the number of infected vectors in homes, which is where human infections almost exculsively originate. I will also use the model to identify optimal steps of the transmission pathway for intervention so that we can develop new ways for reducing human risk. I have also conducted literature reviews of human case data to estimate the risk for human infection in Louisiana
Advisors: Dr. James Mac Hyman (Math, Tulane), Dr. Claudia Herrera (Tropical Medicine, Tulane), Dr. Eric Dumonteil (Tropical Medicine, Tulane), Dr. Zhuolin Qu (Math, Tulane)
Lyme Disease (Published)
Title: Cost Benefit Analysis of Vaccination in Tick-Mouse Transmission of Lyme Disease [PDF]
Abstract: Lyme disease is one of the most prevalent and fastest growing vector-borne bacterial illnesses in the United States, with over 25,000 new confirmed cases every year. Humans contract the bacterium Borrelia burgdorferi through the bite of the tick Ixodes scapularis. The tick can receive the bacterium from a variety of small mammal and bird species, but the white-footed mouse Peromyscus leucopusis is the primary reservoir in the northeastern United States, especially near human settlement. The tick’s life cycle and behavior depend greatly on the season, with different stages of tick biting at different times. Reducing the infection in the tick-mouse cycle may greatly lower human Lyme incidence in some areas. However, research on the effects of various mouse-targeted interventions is limited. One particularly promising method involves administering vaccine pellets to white-footed mice through special bait boxes. In this study, we develop and analyze a mathematical model consisting of a system of nonlinear difference equations to understand the complex transmission dynamics and vector demographics in both tick and mice populations. We evaluate to what extent vaccination of white-footed mice can affect Lyme incidence in I. scapularis, and under which conditions this method is cost-effective in preventing Lyme disease. We find that, in areas with high human risk, vaccination can eliminate mouse-tick transmission of B. burgdorferi while saving money.
Collaborating Authors: Daniel Carrera-Pineyro, Adam Litzler, Andrea McCormack, Josean Velazquez-Molina, Anuj Mubayi, Karen Rıos-Soto, Christopher Kribs