Research

My research lies at the intersection of applied mathematics, computation, and data-driven modeling, with an emphasis on developing mathematically grounded methods that address real-world problems. Over the course of my career, my research program has evolved both in scope and methodology. Trained originally in numerical analysis and partial differential equations, my early work focused on fast and accurate finite difference methods for fractional and nonlinear diffusion problems. Since then, my research has expanded to include structure-preserving numerical schemes for ordinary and partial differential equations, as well as applied data science and machine learning approaches to classification and prediction problems arising in finance, genetics, education, and other contexts. A unifying theme across this evolution is the translation of mathematical theory and tools into computationally effective models, with an emphasis on interpretability, robustness, and real-world relevance.

Current Research Directions

These days, one major strand of my research focuses on numerical analysis and differential equations, particularly the development of structure-preserving finite difference schemes for nonlinear and fractional models. My work on nonstandard finite difference (NSFD) methods addresses fundamental issues of stability, accuracy, and qualitative consistency in models arising from diffusion, reaction–diffusion systems, and related applications. In a series of publications, I have demonstrated how carefully designed discretizations can preserve essential properties of the underlying continuous systems—such as positivity, boundedness, and long-term behavior—that are often lost under standard schemes, especially for large step sizes or long-time simulations. This line of research emerges from my broader interest in numerical methods that respect the mathematical structure of the problems they approximate, rather than merely achieving formal accuracy.

A second major strand of my research focuses on data science, machine learning and artificial intelligence, where I apply statistical learning and deep learning techniques to high-dimensional classification and prediction problems. My work in this area includes educational data mining, rare-event prediction in financial time series, and gene expression classification using convolutional neural network architectures. These projects emphasize careful model design, validation, and interpretation, with particular attention to robustness and ethical use of data. Several of my recent publications explore how machine learning models can be deployed responsibly in domains where decisions have real human consequences, reinforcing my commitment to mathematically informed, transparent, and socially aware modeling.

Although these research directions span different application areas, they are connected by a shared methodological core: mathematical modeling, algorithmic design, and computational experimentation. Across both numerical analysis and machine learning, I prioritize reproducibility, interpretability, and explicit consideration of the assumptions embedded in models and data.

Research and Scientific Service

An important dimension of my development as a researcher has been the opportunity to contribute beyond my immediate disciplinary boundaries. In 2025, I was honored to be selected as one of only twenty-five fellows as an AAAS Science & Technology Policy Fellow at the National Institute of Standards and Technology (NIST), where my work sits at the interface of applied mathematics, artificial intelligence, and national policy priorities. At NIST, I work within the Office of Advanced Manufacturing, contributing to analytical and technical efforts that support resilient, data-driven manufacturing systems.

In this role, I participate in initiatives connected to the AI for Resilient Manufacturing Notice of Funding Opportunity (NOFO), engaging with questions related to trustworthy AI, data standards, and the translation of advanced analytical methods into manufacturing practice. This experience has deepened my perspective on how mathematical and computational research can inform large-scale systems, public–private partnerships, and national research agendas. It has also reinforced my interest in applied, interdisciplinary work that connects rigorous mathematics with decision-making at institutional and policy levels.

Undergraduate Student Involvement

Student involvement is part of my research agenda. I have experience mentoring undergraduate researchers through independent studies, capstone courses, and externally funded research programs. My projects are intentionally designed to be modular, allowing students to contribute meaningfully at different stages of mathematical maturity. Undergraduate students often begin with computational experiments, numerical simulations, or exploratory data analysis, and progressively move toward theoretical analysis, algorithmic refinement, or model validation. Two of my publications include undergraduate coauthors, reflecting my commitment to engaging students in authentic research rather than isolated exercises.

Note: My paper (with co-author) On Analytical, Computational and Historical Developments of Statistics and Its Applications appeared in the International Journal of Applied and Computational Mathematics in 2015. Please note the following typographical error in the paper:

• page 14, Equation 38: which should read as: