Biography

I am Eric, a 3rd year graduate student in Mathematics at Purdue University. My current research interests are in dynamical systems and machine learning methods. In the summer of 2025, I worked on data-driven machine learning surrogate models (data-driven closure models) and data assimilation, where I conducted a parametric study of 100 samples of data of an SIQR epidemic model. In the summer of 2023, I worked on generative artificial intelligence and mathematical algorithms, where I applied clustering methods and principal component analysis (PCA) to determine the optimal autoencoder for sequences of unlabeled data. I earned my Bachelor of Science degree in Mathematics from the University of Puerto Rico, Mayagüez Campus, where I was a research assistant in number theory and abstract algebra. After completing my graduate studies, I aspire to become a mathematical research scientist, and outside of academics I like to make origami figures and play percussion instruments.

Academic Status

PhD Student - 3rd

Research Area/Department

Applied Mathematics; Data Science; Machine Learning/AI; Mathematics

Major/Specialty

Dynamical systems, Machine Learning, Mathematical Algorithms

Degrees Earned or in Progress

B.S. in Mathematics (University of Puerto Rico, Mayagüez Campus, 2023) M.S. in Mathematics (Purdue University, expected December 2025/June 2026) Ph.D. in Mathematics (Purdue University, expected June 2029)

Academic Preparation

MA54300 - Dynamical Systems and Ordinary Differential Equations MA59500OT - Computational Optimal Transport and Deep Generative Models MA59500MM - Intro. to Mathematical Modeling MA54600 - Intro. to Functional Analysis

Research/Publications

I have participated in summer programs, which have given me the opportunity to publish some research papers. During the summer of 2025, I was a research intern in the Computing & Information Science Research Foundation at Sandia National Laboratories (Livermore, California), as part of the 2025 URA-Sandia Graduate Student Summer Fellowship, where I worked on data-driven machine learning surrogate models (data-driven closure models) and data assimilation. My job over the summer was to conduct a parametric study of 100 samples of data belonging to the optimization step of an SIQR epidemic model. This research is currently being written as part of either a technical report publication within Sandia, or submitted to a journal or conference proceeding. During the summer of 2023, I participated in the 2023 MIT Lincoln Laboratory Summer Research Program, where I worked on unsupervised machine learning under Group 39 of Division 3, as part of the National GEM Consortium Fellowship Employer Sponsor Internship. My tasks were to find optimal clusterings of a numerical dataset belonging to the dynamics of player moves of a basketball game. This was done via autoencoders with Long-Short Term Memory structure. I successfully found the optimal clustering that best described the encoded dataset, and this research has been published as part of the 2024 Proceedings of the IEEE Conference on Games.

Research/Academic Interests

My interests currently lie in dynamical systems, data-driven modeling, machine learning and mathematical algorithm development. I am particularly interested on the mathematical modeling aspect of physical phenomena and the development of machine learning techniques to study these complex systems.

Computational and Data Science Areas

Applied Mathematics; Artificial Intelligence and Intelligent Systems; Atmospheric Sciences; Informatics, Analytics and Information Science; Other Computer and Information Sciences

Motivation

I want to participate in the Sustainable Horizons Institute-Sustainable Research Pathways program because it will help me connect with laboratory research scientists, professors, and students interested in my areas of research. I am currently in my fifth semester of the graduate program in Mathematics at Purdue University, where I have taken the core courses, such as Abstract Algebra and Measure Theory, as well as courses in applied math, like Dynamical Systems and Mathematical Modeling. For the Fall 2025 semester, I will take courses in Probability and Numerical Ordinary Differential Equations, since they overlap with my interests in Machine Learning and Dynamical Systems. These courses will prepare me to obtain knowledge that can be applied to research that is of interest to the National Artificial Intelligence Research Resource Pilot program. Through the program, I hope to learn about other areas of research that might be of interest as well. My overall goal once I finish my graduate studies is to become a mathematical research scientist and work as a researcher in a laboratory, solving problems that are of national interest.

Lightning Talk Title

Dynamics and Machine Learning: Best of Two Worlds

Keywords (Maximum 20 words)

Dynamical Systems; Machine Learning; Mathematical Modeling; Applied Mathematics