Energy-preserving POD-Galerkin ROM with neural closure for Navier–Stokes, improving stability and long-time accuracy.

PINNs produce approximate PDE solutions but carry no certificate of accuracy. This paper provides one — and shows that the standard residual-only approach is provably insufficient for penalty-based…

This repository implements **P1 and P2 Lagrange finite element methods from scratch** on unstructured triangular meshes, applied to three canonical PDE problems

This project implements a complete Bayesian inversion pipeline for recovering the spatially varying diffusion coefficient $a(x)$ in the 1D elliptic PDE

This repository serves as my academic GitHub profile, highlighting my research interests, projects, and contributions in Applied Mathematics, Scientific Machine Learning (SciML), and Physics-Inform…

Do neural operators generalize when the geometry is non-trivial — L-shaped domains with corner singularities, annular regions, and domains with internal holes?

Hybrid statistical and LSTM-based models for anomaly detection in time-dependent dynamical systems.

Master’s thesis on generalized intuitionistic fuzzy soft sets and mathematical frameworks for uncertainty modeling.

Physics-Informed Neural Network solvers for convection–diffusion equations with conservation-law enforcement and numerical analysis.

This project focuses on a comprehensive time series analysis of Chicago taxi trip data.

Implemented statistical methods and LSTM models for anomaly detection on complex time series data. Achieved improved detection accuracy by 25\%, outperforming traditional anomaly detection techniques.