Figure 3.

(a) Schematic of the CNN based data-driven GMRES — a convolutional neural network takes as input the permittivity and effective index field and produces as an output the vectors $v_1,v_2\dots v_N$. These vectors are then supplied to the data-driven GMRES algorithm, which produces the full simulated field. (b) Histogram of the residual after 1 and 100 data-driven GMRES iterations evaluated over the evaluation dataset. We consider neural networks trained with both the projection loss function $l_{\mathrm{proj}}$ and residual loss function $l_{\mathrm{res}}$. The vertical dashed lines indicate the mean residual after 1 and 100 iterations of GMRES over the evaluation dataset. (c) Performance of the data-driven GMRES on the evaluation dataset when supplied with the vectors at the output of the convolutional neural networks trained with the projection loss function $l_{\mathrm{proj}}$ and the residual loss function $l_{\mathrm{res}}$. The dotted line shows the mean residual, and the solid colored background indicates the region within ±standard deviation around the mean residual.