Solving a problem with indirect measurements

[tito21]

Hi, I am trying to solve an inverse problem where the measurements are not done in the hidden function but through an operation. More concretely I have a set of measurements ${S_i, t_i}$ that are related to the hidden function $u(x, t)$ by:

$$ S(t) = \int u(x,t) dx $$

There is of course a PDE that has to be satisfied by $u(x, t)$ and has a hidden parameter $\lambda(x)$ that depends on space that I would also like to estimate.

In the examples, there is no problem like this and by reading the documentation and code I can't figure a way to implement this. I thought of using a costume loss function, but it needs to have a signature (y_true, y_pred) and I need access to the model to compute the integral.

[lululxvi]

There are similar (but not exactly the same) examples at https://github.com/lululxvi/hpinn

[tito21]

Thanks for your answer, I will look into that examples