An attempt to build a whitebox and blackbox neural network model that is able to replicate the Lorenz Attractor (for set parameters)
The data was genereated by generating 100K points by using the Lorenz Equations iteratively (Euler's Method).
There are 3 input variables x(n), y(n) and z(n) and 3 output variables x(n+1), y(n+1) and z(n+1)
Input Dimensions : [3,1]
Hidden Layers: 2 (10 neurons each)
Output Dimensions : [3,1]
- Hidden Layer 1: ReLU
- Hidden Layer 2: ReLU
- Output Layer: Linear
The performance of the 2 models were compared on their ability to reproduce the Lorenz Attractor. While the black box approach was able to was able to roughly reproduce the attractor, the white box model was not able to do so even though it seemed to be learning and updating its weights through back propagation.