My academic journey and research experiences have centered around the intersection of numerical analysis, partial differential equations, and scientific computing, with a strong motivation to address real-world problems through mathematical modeling and computation. During my undergraduate and master’s studies, I worked on the mathematical modeling of subsurface fluid flow systems, where I developed a solid foundation in differential equations and numerical methods. This early experience sparked my long-term interest in the development of efficient computational techniques for solving complex physical and biological systems.

As a PhD student in Applied Mathematics, I have continued to expand my expertise by working on problems involving heat and mass transfer, fluid dynamics, and the numerical solution of partial differential equations. My recent work includes the development and analysis of finite difference and finite element schemes for simulating flow behavior in dual-permeability porous media using Newtonian and Oldroyd-B fluid models. These studies have involved stability and convergence analysis, as well as implementation using high-performance computing tools.

In addition to traditional applied mathematics topics, I have also developed an active interest in emerging areas at the interface of data science and statistics. I have explored methods in artificial intelligence (AI), causal inference, conformal prediction, and biostatistics, especially as they relate to uncertainty quantification and predictive modeling in complex systems.

My future research goals lie in continuing this multidisciplinary direction by integrating modern computational methods with data-driven approaches. I aim to contribute to the advancement of robust and scalable numerical methods that can be used in diverse fields such as environmental modeling, biomedical engineering, and industrial simulations. Specifically, I intend to:

• Develop adaptive and stable numerical solvers for nonlinear PDE systems;

• Apply data-assimilation techniques to improve model accuracy in real-world applications;

• Investigate machine learning tools for enhancing numerical simulations;

• Contribute to open-source scientific computing frameworks.

By combining mathematical theory, numerical algorithms, and statistical insights, I hope to contribute meaningfully to the field of applied mathematics and create tools that can support evidence-based decision-making across various domains.