Differentiate through complex differential equation

autograd
1

Hi!
I’m currently working an a problem that is related to a differential equation, in which a complex-valued term appears, so the solution to the differential equation will also be complex-valued. The equation looks like this:

y’’(t) + (A(t) + j*B(t))**2 * y(t) = 0

… with j being the complex unit. I want my neural network to predict the coefficient B so that my solution y satisfies some specific conditions. For that I would like to solve the differential equation with the predicted B, check the Loss of y and then backpropagate through the DE-Solver to my model. I think this should generally work, but I don’t know how to deal with the complex values, as PyTorch doesn’t have complex numbers implemented yet. Maybe somebody has already worked on similar problems and can help with an advice?

2

Hi @fewagner PyTorch recently added complex numbers support so you can make tensors of complex dtype:
torch.randn(4, 4, dtype=torch.float) and perform operations on them. you can also compute compute complex derivatives, i.e. run backward on loss functions with complex valued parameters. for more reading on complex autograd, check out: https://pytorch.org/docs/stable/notes/autograd.html?highlight=complex%20autograd