Biography

I'm a third-year Applied Mathematics PhD student with a minor in Artificial Intelligence at Oregon State University. My research interest is in the field of computational mathematics, more specifically, developing and implementing numerical methods and developing numerical simulations for complex physical systems and real-world problems. My current work focuses on the Spectral Finite Element Method for linear dispersive metamaterials. My ongoing work explores the dispersion, stability and convergence analysis of the Drude and Lorenz Metamaterial Model. I have experience in coding in Python, MATLAB. I have worked with software such as Maple, Mathematica, Pandas, and Jupyter Notebook. Along with finite element methods, I have worked with finite difference methods, finite volume methods and inverse problems.

Academic Status

PhD Student - 3rd

Research Area/Department

Applied Mathematics; Machine Learning/AI

Major/Specialty

Computational Mathematics (Numerical Methods and Simulations), Artificial Intelligence

Degrees Earned or in Progress

Ph.D. Mathematics, minor - Artificial Intelligence, Oregon State University, expected 2028. MSc Mathematics, University of Delhi, 2022. BSc Mathematics, St. Xaviers college, Mumbai, 2020

Academic Preparation

I have completed courses on Computational Wave Propagation, Inverse Problems, Finite Element Methods, Introduction to Artificial Intelligence, Nonlinear coupled PDEs. I'm in progress of finishing the Machine Learning and Probabilistic Graphical Model course. In winter term, I will be taking the Deep Learning and Reinforsement Learning classes.

Research/Publications

My current research is being conducted at Oregon State University as a part of my Ph.D. program.

Research/Academic Interests

My research interest focuses on Computational Mathematics. I work on developing, implementing, and analyzing numerical methods and simulations for complex physical phenomena and their practical applications. My ongoing research applies the spectral finite element method to examine the dispersive characteristics of metamaterials. In this project, we have formulated generalized dispersion relations for Drude and Lorenz metamaterial models in two dimensions. We conducted convergence analyses of first, second, and third order Nédélec elements, both analytically and numerically, and established generalized convergence orders for higher order edge elements. The project includes a detailed stability analysis of spectral FEM for metamaterials. We use Python and MATLAB to develop the simulations for metamaterials. In addition to my work with finite element methods, I am also interested in explicit and implicit finite difference methods, operator splitting methods, and optimization. Furthermore, I am keen to explore Artificial Intelligence techniques to rigorously assess and compare the accuracy of computational results.

Computational and Data Science Areas

Applied Mathematics; Artificial Intelligence and Intelligent Systems; Fluid and Plasma Physics

Motivation

Sustainable Research Pathways is an outstanding program that allows me to collaborate with distinguished researchers and advance both my mathematical and computational skills. This program closely aligns with my research goals, offering opportunities to engage with ongoing research projects and acquire practical experience. Presenting research at conferences helps me expand my network and offers valuable feedback on my work. Overall, this program provides me with a unique opportunity to learn, implement innovative ideas, and strengthen my career.

Lightning Talk Title

Numerical Modeling and Simulation of Wave Phenomena in Complex Systems

Keywords (Maximum 20 words)

FEM; Numerical Modeling; Neural Network; Deep Learning; Wave Phenomena; Python; MATLAB; Multiscale Materials; High-Order Methods; Simulation; Implementation; Finite Difference