(a) Training starts by encoding an image as a vector of current source densities in the FDFD simulation. This step is followed by an iterative process to solve for the electric field in a nonlinear medium. Next, we use the ASM to calculate the gradient, which is then used to update the level-set function and consequently, the medium itself. Here we use mini-batch SGD (explained in the supplementary materials section of Ref. [17]). In training with mini-batches, we sum the cost functions calculated for different images in the same batch and compute the gradients. (b)–(d) show an NNM in training after 1, 33, and 66 training iterations, respectively. (After iteration 66, the medium has already seen each of the training samples at least once, since we are using batches of 100 images.) At each step, the boundary between the host material and the inclusions is shown, along with the field distribution for the same randomly selected digit 8. Also, the accuracy of the medium on the test set can be seen for that particular stage in training.
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