Purpose of summing over frequencies in adjoint optimization example

[niccolot]

Hello, in tutorial 3 of adjoint optimization (03-Filtered_Waveguide_Bend) the backprop of the mapping/filtering is done by giving to autograd tensor_jacobian_product the derivatives summed by the frequencies in the nlopt cost function wrapper definition:

gradient[:] = tensor_jacobian_product(mapping, 0)(
            v, eta_i, cur_beta, np.sum(dJ_du, axis=1)
        )  # backprop

I wanted to ask if this reducing strategy was chosen for a particular reason instead of others (e.g. np.mean(dJ_du, axis=1)), thank you in advance.

[smartalecH]

In this case, the FOM is a linear combination of the frequency components. The individual scaling of each frequency (whether it's a mean or something arbitrary) is extracted via autograd and injected into the adjoint current sources. So all that's left is the actual sum.

The reason we don't hardcode the sum is because there are cases where you don't want to formulate an FOM that is a linear combination of the frequencies (eg the epigraph of a minimax, as described in the meep adjoint paper).