Week 10: IT WORKS!

Hey guys, welcome back to my blog. Since I currently have a fever, I won’t be able to write much for this post but I’ll do my best to cover what I have accomplished.

Starting with fantastic news, my code works! Last week left me pretty demotivated and I really did not know if I was going to be able to get it working. After reading my code over and over again, I was unable to spot where it was going wrong. My code was so messy and unreadable that it was almost impossible to track whether it was math that was wrong or the algorithm that was wrong. I had to organize it. And that was what I spent my weekends doing. I modularized each part of the algorithm, testing each function to make sure none of the math is wrong. I wrote documentation for each of these functions, making sure I clearly understand the dimensions of the input and outputs. I made sure that these functions could work given a wide range of differential equations and trial solutions. After the implementation, I started testing.

Testing was a great success…until I tested the Lorenz system. The algorithm was unable to predict the Lorenz system. This is to be expected because the Lorenz system is a chaotic system. One small change in the initial state can create huge changes in a later state. This means if there is a small error in what the algorithm predicts, it can result in a graph that is entirely different than expected.

After testing the Lorenz system, I was going to implement the BFGS optimizer to see if I was able to get better results, however the day after I fell sick. Hopefully, I will recover enough to start testing some more and implement the BFGS optimizer during the weekends.

Thanks, this is all I have for this week’s blog! See you guys at the Senior Project Presentations!