When I implemented the Hamiltonian network, I got some questions that I didn't understand.
When outputting Hamiltonian H by NN with input x = (q, p)
Let H = f (x) and let f be an NN with parameter θ.
L = (∂H/∂p --dp/dt) ^ 2 + (∂H/∂q --dq/dt) ^ 2
I would like to define and ask how to calculate the gradient ∂L/∂θ at θ.
∂L/∂θ = (∂L/∂H) (∂H/∂p) (∂p/∂θ)
I want to calculate, but since neither p nor q is a function of θ, I think that ∂p/∂θ cannot be calculated.
How is the θ gradient of the loss function calculated?
It's a mathematical question, so it may be out of place, but I couldn't find any other place to ask, so I asked.
Answer # 1
If p and q do not depend on θ
∂L/∂θ = (∂H/∂p)/∂θ + (∂H/∂q)/∂θ
Therefore, I think that there is no choice but to partially differentiate ∂H/∂p and ∂H/∂q with θ.
Certainly stackoverflow seems out of place.
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