How is the loss evaluated?

[edoardo100]

I have a question related to the loss evaluation in deepXDE.

Let us take the example for deepONet in https://deepxde.readthedocs.io/en/latest/demos/operator/antiderivative_aligned.html.
If I understand properly the network is defined in

m = 100
dim_x = 1
net = dde.nn.DeepONetCartesianProd(
    [m, 40, 40],
    [dim_x, 40, 40],
    "relu",
    "Glorot normal",
)

and the loss will have a term like y_true-y_pred, with y_true and y_pred arrays representing the pde solution as calculated a priori and the predicted solution. Now, if my interpretation is correct, y_true should have length equal to 100 along one axis, while y_pred, in the example provided, will be of length 40 along the same axis.
My question is: how is the loss actually evaluated? Is there a sort of interpolation step for one of the vectors involved or am I missing something?

Thank you in advance

[lululxvi]

See the papers: https://doi.org/10.1038/s42256-021-00302-5, https://doi.org/10.1016/j.cma.2022.114778