Depends on the problems, but in many situations yes. For PDE's you can plug in the proposed solution and calculate the error. Usually you'd do this in a discret

Depends on the problems, but in many situations yes. For PDE's you can plug in the proposed solution and calculate the error. Usually you'd do this in a discretized version of the PDE, but since neural nets are symbolically differentiable you could instead approximate (by sampling) the average error from the real PDE itself.