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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
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Blog Post number 4
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
project
Differential Equations
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.
An Asymptotic Preserving and Energy Stable Scheme for the Euler System with Congestion Constraint
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.
Impact of hemodynamic parameters on rupture risk in abdominal aortic aneurysm: Emphasis on wall shear stress-derived indicators
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).
Deep Learning for Multiscale Models
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.
publications
talks
Energetic Variational Neural Network Discretization of the Cahn-Hilliard Equation
Published:
In this talk, I presented a structure-preserving Lagrangian algorithm for solving the Cahn-Hilliard equation. The algorithm employs neural networks as tools for spatial discretization. The proposed scheme is constructed based on the energy-dissipation law directly. This guarantees the monotonic decay of the system’s free energy, which avoids unphysical states of solutions and is crucial for the long-term stability of numerical computations. To address challenges arising from interface problems, we introduce an adaptive sampling method for better capturing the diffuse-interface. Moreover, we solve for the incremental of the flow map. This approach is computationally memory-efficient. The proposed neural network-based scheme is mesh-free, allowing us to solve gradient flows in high dimensions. Numerical experiments are presented to demonstrate the accuracy and energy stability of the proposed numerical schemes.
teaching
Probability and Statistics for Data Science (DS 60505)
Graduate course, University of Notre Dame, Department of Data Science, 2024
As a Teaching Assistant, my main job is to held office hours and grade homework.
Introduction to Numerical Analysis (ACMS 20350)
Undergraduate course, University of Notre Dame, ACMS Department, 2024
As a Teaching Assistant, my main job is to held office hours and grade homework.
Scientific Programming (ACMS 40210 and ACMS 60210)
Undergraduate and Graduate course, University of Notre Dame, ACMS Department, 2025
As a Teaching Assistant, my main job is to held office hours and grade homework.
Numerical Analysis (ACMS 40390)
Undergraduate course, University of Notre Dame, ACMS Department, 2025
As a Teaching Assistant, my main job is to held office hours and grade homework.
Nonlinear Dynamical Systems (ACMS 60630 and ACMS 40630)
Graduate and Undergraduate course, University of Notre Dame, ACMS Department, 2025
As a Teaching Assistant, my main job is to held office hours and grade homework.
Numerical Analysis I (ACMS 60690)
Graduate course, University of Notre Dame, ACMS Department, 2025
As a Teaching Assistant, my main job is to held office hours and grade homework.
Probability and Statistics for Data Science (DS 60505)
Graduate course, University of Notre Dame, Department of Data Science, 2025
As a Teaching Assistant, my main job is to held office hours and grade homework.