Projects

Research and Internship Projects

Project, University of Notre Dame, 2025

Guide: Dr. Zhiliang Xu, Professor, ACMS Department, University of Notre Dame, Notre Dame, IN.
About the project: This work is part of my Graduate Research Assistantship at the University of Notre Dame.
- Architected and implemented an Energetic Variational Deep Neural Network (EVNN) solver in PyTorch to model Cahn-Hilliard phase-separation dynamics.
- Ensured model stability and physical consistency by enforcing energy conservation laws directly within the neural network architecture, resulting in more robust and reliable simulations.
- Scaling this EVNN framework to model complex, coupled Cahn–Hilliard–Navier–Stokes systems to improve training stability for high-dimensional fluid dynamics.

Project, Indian Institute of Science Education and Research (IISER), Thiruvananthapuram, Department of Mathematics, 2024

Guide: Dr. K. R. Arun, School of Mathematics, IISER Thiruvananthapuram, India
About the project: This work was conducted as part of my Master’s thesis at IISER Thiruvananthapuram.
- In this project, we designed and analyzed a finite volume scheme for the barotropic Euler equations with the congestion pressure law and performed the singular limit termed as the hard congestion limit at the discrete level.
- The developed scheme was an entropy stable and asymptotic preserving. We also obtained a-priori estimates on the relevant unknowns. We lastly, proved the efficiency of the numerical scheme by testing various numerical examples.

Project, National Institute of Science Education and Research (NISER), Bhubaneswar, 2023

Guide: Dr. Anupam Pal Choudhury, School of Mathematics, NISER Bhubaneswar, India About the project: This work was done during my Summer Research Intern position at NISER Bhubaneswar.
In this project, I studied scalar conservation laws and how they model physical phenomena with a particular emphasis on traffic dynamics.
I learned about weak (or integral) solutions, Rankine-Hugoniot condition, and entropy conditions.

Class Project, University of Notre Dame, 2025

Course: ACMS 60792 Numerical hemodynamics and Uncertainty Quantifciation
Semester: Spring 2025
Instructor: Dr. Daniele E. Schiavazzi
Project Title: Impact of hemodynamic parameters on rupture risk in abdominal aortic aneurysm: Emphasis on wall shear stress-derived indicators
Investigated AAA Hemodynamics Through WSS-Derived parameters: This project focused on analyzing the role of wall shear stress (WSS) and its derived parameters, TAWSS, OSI, ECAP, and RRT, in the progression and rupture risk of abdominal aortic aneurysms (AAAs), enhancing understanding of disturbed blood flow patterns.
Utilized SimVascular for Computational Modeling: A representative AAA model and a virtually repaired version were studied using SimVascular to compute key hemodynamic metrics, offering insights into how arterial geometry influences shear stress and potential rupture sites.
Read the full project report (PDF).