Project Portfolio

Physics-Informed Neural Networks as Numerical Solvers for the Schrödinger Equation

Dates: Jan 2026 - Present

Phonon-Based Calculations of Graphene's Heat Capcity

Developed analytical and numerical phonon models for graphene by constructing and diagonalizing the dynamical matrix of a honeycomb lattice. Computed full phonon dispersion relations including flexural (ZA) modes and implemented Bose–Einstein-based heat capacity calculations in Python. Validated results against experimental data and DFT literature, reproducing characteristic low-temperature T² scaling and analyzing anharmonic effects at high temperatures. Presented my findings in a ten-minute talk.

Tools: Python, Phonons, Lattice Modeling

Dates: Oct 2025 – Dec 2025

Toy NETS Simulation of Rare-Event Dynamics

Implemented a Python simulation comparing standard Langevin dynamics with a drift-augmented “toy NETS” model in a 1D double-well potential (inspired by Albergo and Vanden-Eijnden, 2025). Explored connections between stochastic modeling and rare-event sampling theory.

Tools: Python, Stochastic Differential Equations

Dates: June 2025 – Sept 2025

Energy Levels and Wavefunctions of Alkali Atoms Calculations

Built a finite-difference eigenvalue solver in Python to compute quantum energy spectra using large tridiagonal Hamiltonian matrices. Implemented adaptive convergence and grid-resolution control to ensure numerical stability and precision for large-scale scientific simulations.

Tools: Python, NumPy, SciPy, Numerical Linear Algebra, Quantum Mechanics

Comparing ML Algorithm Detection for Development of an Artificially Intelligent Radiologist

Developed and compared multiple ML models for radiology (ResNets, DenseNets) using Stanford’s MURA dataset of 40,561 MSK radiographs. Performed statistical evaluation (Cohen’s Kappa, ROC curves, AUROC, McNemar’s Test) and visualized AI-generated data. Produced a written research report and presented findings in a ten-minute talk.

Tools: Python, TensorFlow, Keras, OpenCV, scikit-learn, Matplotlib

Dates: Sept 2022 – May 2023