Applied projects

Applied, computational, and quantitative work — the numerical, optimization, and machine-learning toolkit behind my research, used to build and ship concrete tools. Several projects are still in progress.

Physics-Informed Neural Operators for Option Pricing

Learned solution operators for European option pricing under the Black–Scholes PDE. Benchmarks a Fourier Neural Operator against deep, convolutional, and vanilla neural-operator baselines, with a physics-informed loss that bakes the governing PDE into training. Includes feasibility studies, hyperparameter and loss-weight ablations, and evaluation on real market data from WRDS. Built in PyTorch. code Work in progress; a second option-pricing model is currently under construction.

Multi-Material Print Path Planning

A Rural Postman Problem solver that plans continuous toolpaths covering every edge of a lattice while minimizing non-printing “jump” travel, achieving up to 18% printing-time reduction for multi-material structures. Handles per-material nozzle offsets and exports G-code for direct printing. Utilizing Python, NetworkX, NumPy, SciPy. details

Differentiable Thermal Simulation & Learned Surrogates

Building a differentiable thermal-simulation framework for metal additive manufacturing and learned surrogate models that accelerate it, turning slow forward solves into fast, gradient-enabled tools for inverse process design and optimization. Work in progress; details to follow upon publication.

Technical Skills

• Programming: Python (NumPy, Pandas, Scikit-learn, PyTorch), MATLAB, C++
• Mathematics: Partial differential equations, finite element analysis, numerical methods, optimization, stochastic & time-series modeling