Right,

Here we introduce a hybrid in situ–in silico algorithm, called physics-aware training, that applies backpropagation to train controllable physical systems. Just as deep learning realizes computations with deep neural networks made from layers of mathematical functions, our approach allows us to train deep physical neural networks made from layers of controllable physical systems, even when the physical layers lack any mathematical isomorphism to conventional artificial neural network layers.

To my naive understanding, and please someone correct me if I'm wrong, the point is that they are not controlling the parameters that compute the NN forward pass directly (hence "no mathematical isomorphism to conventional NNs"), but "hyper-parameters" that guide the physical system to do so. For example, rotation angles of mirrors, or distance between filters, instead of intensity values of light. This leads to the non-linear transformations happening in situ, while simpler transformations in the backprop are still computed in-silico.