Welcome! I’m Maddie Preston, a computational scientist and applied mathematician with a passion for high-performance simulation, numerical modeling, and backend system design. This portfolio hightlights a selection of projects across Python, C++, SQL, Java, and Docker.
My work focuses on translating mathematical theory into efficient, scalable software - with applications ranging from fluid dynamics to machine learning and simulation infrastructure.
Python • Fortran • HPC • Simulation Framework Architecture
A redacted version of my thesis project exploring Monte Carlo methods for solving PDEs in conformally mapped domains. This skeleton highlights the project’s structure, modular code design, and simulation pipeline across multiple geometries. Core numerical routines have been removed for IP protection, but the architecture, workflow, and methodology are documented in detail. Includes reflections, boundary handling logic, and conformal mapping strategies.
Python • Simulation • Reaction/Advection PDEs
A fully runnable Monte Carlo framework for solving 1D PDEs with linear reaction or advection terms. Uses weighted random walks to approximate solutions and compares results against analytical benchmarks. Designed as a simplified environment to test core ideas used in the larger 2D conformal mapping project. Includes visualization tools and configurable parameters for reproducible experiments.
Python • C++ • PyTorch • Simulation + ML
Solves nonlinear PDEs (e.g., Burgers’ Equation) using finite difference methods, then generates training data to fit a neural network surrogate model. Explores numerical stability, approximate accuracy, and model generalization for predictive use cases. Includes visualizations and runtime comparisons.
Python • PyTorch • Computer Vision
A simple convolutional neural network (CNN) trained on MNIST and extended with ResNet-based transfer learning for custom image classification. Includes reproducibility-focused setup, architecture comparisons, and training performance visualizations.
C++ • Numerical Methods • CLI App
A 1D solver for the heat and advection equations using finite difference schemes. Highlights performance tuning, stability analysis (e.g., CFL conditions), and user-configurable simulation parameters through a clean CLI interface.
Python • Docker • REST API
Containerized pipeline for running PDE simulations in isolated environments. Optional REST API allows remote access to pre-defined simulations and result queries. Designed for reproducibility, research deployment, and collaboration.
Java • OOP • Algorithms
A grid-based simulation (e.g., diffusion or particle movement) showcasing object-oriented programming, modular logic, and basic UI/output handling in Java.
Python • SQL • PostgreSQL
Store and query simulation output data using relational databases. Includes table design, data insertion, and exploratory queries using SQL and pandas.
C++ • Language Practice
A sandbox for learning and implementing C++ basics - data structures, file I/O, numerics, and performance comparisons.
Languages: Python • C++ • Java • SQL • Fortran
Tools: PyTorch • NumPy • Git • Jupyter • Docker • PostgreSQL
Domains: Scientific Computing • Machine Learning • Simulation • Backend APIs • HPC
Thanks for visiting! I’m always open to collaboration or feedback. Feel free to reach out.