rachnog/neural-networks-for-differential-equations

UNIVR PDE course project and just for fun

neural-networks-for-differential-equations's Issues

d_neural_network derivative is off

def d_neural_network_dx(W, x, k=1):
return np.dot(np.dot(W[1].T, W[0].T**k), sigmoid_grad(x))

I believe that the derivative ought to be
return np.dot(np.multiply(W[1], W[0].T), sigmoid_grad(np.dot(x, W[0]) )
to remain consistent with chain rule,

Though, I am intrigued that you were able to get the same amount of convergence in spite of this.

a function

def d_neural_network_dx(W2, x):
return np.dot(np.dot(W2[1].T, W2[0].T), sigmoid_grad(x)

They come from (5) in the paper “Arti ial Neural Networks for Solving Ordinary and Partial Di erential Equations”. While I think it is not right since it sigma(z) not sigma(x)? But it’s amazing that the results is right.

do you have a network for solving system of ODEs