"The real promise of these methods is to use the universal approximator power of NNs...", still if one is to use a grey-box non-linear model dx/dt = F(x, u, t), why use NNs to characterize F? I would be more comfortable using a polynomial to characterize non-linearity than a "deep" black-box.
Polynomials are much easier to "train" because it is just one linear regression with no iteration. It has also been hinted that NN are in essence polynomial regressions [0]. Furthermore, most activation functions are base on e^x where the actual implementation of e^x in a computer is again a polynomial!
Polynomials are much easier to "train" because it is just one linear regression with no iteration. It has also been hinted that NN are in essence polynomial regressions [0]. Furthermore, most activation functions are base on e^x where the actual implementation of e^x in a computer is again a polynomial!
[0] https://arxiv.org/abs/1806.06850