Week 0: Using Neural Networks to Solve Systems of Ordinary Differential Equations

Hello everybody, my name is Zheyu and welcome to my first blog!

My project is designing neural networks to solve systems of ordinary differential equations(ODEs). This project is aimed at using a different approach to systems of ODEs which may have an efficiency and accuracy factor times faster than that of traditional numerical algorithms, such as RDK4. 

By testing multiple ways of modeling neural networks and comparing the resulting accuracy and efficiency, I strive to find which structures give the best solution. ODEs can be used to model many worldly phenomenon, and being able to solve them with greater accuracy and speed would lead to better predictions in events such as weather, fluid flow, population growth, spread of disease, and more. With many applications in the real world, neural networks can help supply society with more accurate predictions to act on. Better predictions of the spread of disease can lead to better policies. Better predictions of population growth can lead to more foresight in housing and infrastructure. More accurate modeling of fluids can lead to better fluid animation in video games and animation.

The first step towards my project is to learn and build my foundations in both linear algebra and neural networks. I have some books and courses lined up and I will start learning next week. I can’t wait to start the experimentation phase after I strengthen my foundations!