I'm working on this webpage and hope to get it done by mid-June. I have to take care of several other tasks, unrelated to this website, in the meantime.
If you are curious, I used a dense neural network with two hidden layers. One layer contained 128 nodes and the other 64 nodes. (I'll experiment with other configurations when I get a chance.) When applied to the test data, the network predicted the mode share variable with a mean squared error of 0.00048 and a mean absolute error of 0.01526. Again, I'll experiment with other configurations to see if I can get the algorithm to predict better.