Melissa Butler
PhD Candidate
Department of Mathematics and Statistics & School of Computing
University of Wyoming, Laramie, WY
PhD Candidate
Department of Mathematics and Statistics & School of Computing
University of Wyoming, Laramie, WY
Computational and Applied Mathematics, Data Science, Scientific Computing, Machine Learning, Network Science, Anomaly Detection, Modeling, Random Matrix Theory, Human Mobility Patterns
Complex systems are found in many real world applications and understanding the structural properties is crucial for detecting anomalous behavior in the system. Here we represent complex systems by a series of nodes and edges. This approach allows the application of spectral properties to detect anomalies. We plant a series of densely connected anomalies into systems that have community structure and quantify the ability of spectral methods to detect the anomalies.
Code RepositoryUnderstanding human mobility during disastrous events is crucial for emergency planning and disaster management. We develop a methodology to construct time-varying, multilayer networks where edges encode observed movements between spatial regions (census tracts) and network layers encode movement categories by industry sectors (e.g., schools, hospitals). Using the 2021 Texas winter storm as a case study, we find that people markedly reduced movements to ambulatory healthcare services, restaurants, and schools, but prioritized movements to grocery stores and gas stations. Additionally, we study the predictability of nodes' in- and out-degrees in the multilayer networks, which encode movements into and out of census tracts. Inward movements prove harder to predict than outward movements, especially during the storm. Our findings on the reduction, prioritization, and predictability of sector-specific movements aim to support mobility-related decisions during future extreme weather events.
The study of fluid flow through partially saturated porous media is critical to agriculture, construction, waste disposal, and other significant fields and is an extremely complex process, described by Richards equation. Richards equation is of great interest due to the lack of closed form solutions and the difficulties with numerical approximations. This paper explores finite volume method for approximating Richards equation and quantifies the uncertainty effect of transpiration and evaporation on land surface. A stochastic process is used to simulate uncertainty and the effect on water content was analyzed.
I developed a collection of scientific machine learning projects focused on automated model selection and physics-informed neural networks. This work includes meta-learning algorithms for optimizing machine learning pipelines (model choice, preprocessing, and hyperparameters), PINN implementations for solving initial value problems, and machine learning methods applied to fluid dynamics modeling. Together these projects explore how data-driven methods can be integrated with physical structure and numerical modeling.
I developed a collection of numerical methods projects focused on differential equations and computational mathematics. This includes object-oriented finite element software in MATLAB for solving boundary value problems, a C++ implementation of the conjugate gradient method for differential systems, and additional work in polynomial approximation and B-spline methods. These projects emphasize numerical stability, algorithm design, and scientific computing techniques.
M. Butler, A. Khan, F. Afrifa, Y. Hu, and D. Taylor (2026) Multilayer networks characterize human-mobility patterns by industry sector for the 2021 Texas winter storm. Accepted to NPJ Complexity. [arXiv]
M. Sejunti, M. Butler, Y. Hu, and D. Taylor Predictability of human movement in multilayer mobility networks. In preparation