I use the PINN approach to solve elliptic BVPs. The loss function I exploit is a weighted sum of the MSE losses of a set of collocation points in a domain $D$ and of a set of boundary points on on the boundary B, i.e. $L=L_D+w * L_B$. Both $L_D$ and $L_B$ become sufficiently small after a number of iterations (epochs), however the loss L_B is 10 to 100 smaller than $L_D$. On the other hand though, because $w$ has to be around $10-100$ for the network to describe well the boundary, the term $w L_B$ is of the same order of $L_D$. Is this an indicator of overfitting on the boundary data or not?