Fig. 5.

Results of coupling FEM and DeepONet for the Poisson equation. (a–b) Model predictions from the FEM and DeepONet with the corresponding absolute errors in ${\Omega }_{FEM}$ and ${\Omega }_{NN}$. (c) Model predictions at the interfaces (${u|}_{{\Gamma }_1}$ and ${u|}_{{\Gamma }_2}$) and the true solution (red line). The relative errors of model predictions at the interfaces are far less than 1%. Please see Fig. 4 for ${\Omega }_{NN}$ and ${\Omega }_{FEM}$.