There is a problem of constructing a PINN based on an integro-differential equation in Tensorflow. Its simplified form is shown on the picture. The function h has no analytical solution. The differential part is calculated quickly with AutoDiff, but there is a problem with the integral part. In the full formulation, I need to calculate several double and triple integrals. I calculate them by finite differences, which makes the calculation slow down a lot. Is there any way to get away from finite-difference integration in the problem shown in the picture? I would be grateful for a hint or an example of a similar solution.

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Hi @VO_G. Have you looked into neural network quadrature to handle the integral part of your integro-differential equation?

Thanks for the tip, tagoma. That should do it.