Fig. 4. Image classification with diverse physical systems.

We trained PNNs based on three physical systems (mechanics, electronics and optics) to classify images of handwritten digits. a, The mechanical PNN: the multimode oscillations of a metal plate are driven by time-dependent forces that encode the input image data and parameters. b, The mechanical PNN multilayer architecture. c, The validation classification accuracy versus training epoch for the mechanical PNN trained using PAT. The same curves are shown also for a reference model where the physical transformations implemented by the speaker are replaced by identity operations. d, Confusion matrix for the mechanical PNN after training. e–h, The same as a–d, respectively, but for a nonlinear analogue-electronic PNN. i–l, The same as a–d, respectively, for a hybrid physical–digital PNN based on broadband optical SHG. The final test accuracy is 87%, 93% and 97% for the mechanical, electronic and optics-based PNNs, respectively.