  Analog machine learning hardware platforms promise to be faster and more
energy-efficient than their digital counterparts. Wave physics, as found in
acoustics and optics, is a natural candidate for building analog processors for
time-varying signals. Here we identify a mapping between the dynamics of wave
physics, and the computation in recurrent neural networks. This mapping
indicates that physical wave systems can be trained to learn complex features
in temporal data, using standard training techniques for neural networks. As a
demonstration, we show that an inverse-designed inhomogeneous medium can
perform vowel classification on raw audio signals as their waveforms scatter
and propagate through it, achieving performance comparable to a standard
digital implementation of a recurrent neural network. These findings pave the
way for a new class of analog machine learning platforms, capable of fast and
efficient processing of information in its native domain.
