Fig. 3. Physics-aware training.

a, PAT is a hybrid in situ–in silico algorithm to apply backpropagation to train controllable physical parameters so that physical systems perform machine-learning tasks accurately even in the presence of modelling errors and physical noise. Instead of performing the training solely within a digital model (in silico), PAT uses the physical systems to compute forward passes. Although only one layer is depicted in a, PAT generalizes naturally to multiple layers (Methods). b, Comparison of the validation accuracy versus training epoch with PAT and in silico training, for the experimental SHG-PNN depicted in Fig. 2b. c, Final experimental test accuracy for PAT and in silico training for SHG-PNNs with increasing numbers of physical layers. The length of error bars represent two standard errors.