This repository holds the code used for our Mathematics Capstone Project on neural networks and neural ordinary differential equations (ODEs).

With the goal to fully understand the algorithms and to feature the strengths of the Julia language, we build our own implementation framework of neural networks and neural ODEs using as few external packages as possible.

• Neural Network Source Code
• Neural ODE Source Code

For neural ODEs, we rely on Julia's packages DifferentialEquations, Flux, and Zygote. Dependencies can be found in our Project.toml and Manifest.toml files.

We conduct a few simple experiments as proofs of concept of our implementations. The Lotka-Volterra example is adapted from Julia's DiffEqFlux package for neural ODEs.

• Neural Network Classifier Example
• Lotka-Volterra Example
• Sine Approximation Comparisons