  Deep learning has become an area of interest in most scientific areas,
including physical sciences. Modern networks apply real-valued transformations
on the data. Particularly, convolutions in convolutional neural networks
discard phase information entirely. Many deterministic signals, such as seismic
data or electrical signals, contain significant information in the phase of the
signal. We explore complex-valued deep convolutional networks to leverage
non-linear feature maps. Seismic data commonly has a lowcut filter applied, to
attenuate noise from ocean waves and similar long wavelength contributions.
Discarding the phase information leads to low-frequency aliasing analogous to
the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the
phase content can stabilize training and improve the generalizability of neural
networks. While it has been shown that phase content can be restored in deep
neural networks, we show how including phase information in feature maps
improves both training and inference from deterministic physical data.
Furthermore, we show that the reduction of parameters in a complex network
outperforms larger real-valued networks.
