  The large spatial/temporal/frequency scale of geoscience and remote-sensing
datasets causes memory issues when using convolutional neural networks for
(sub-) surface data segmentation. Recently developed fully reversible or fully
invertible networks can mostly avoid memory limitations by recomputing the
states during the backward pass through the network. This results in a low and
fixed memory requirement for storing network states, as opposed to the typical
linear memory growth with network depth. This work focuses on a fully
invertible network based on the telegraph equation. While reversibility saves
the major amount of memory used in deep networks by the data, the convolutional
kernels can take up most memory if fully invertible networks contain multiple
invertible pooling/coarsening layers. We address the explosion of the number of
convolutional kernels by combining fully invertible networks with layers that
contain the convolutional kernels in a compressed form directly. A second
challenge is that invertible networks output a tensor the same size as its
input. This property prevents the straightforward application of invertible
networks to applications that map between different input-output dimensions,
need to map to outputs with more channels than present in the input data, or
desire outputs that decrease/increase the resolution compared to the input
data. However, we show that by employing invertible networks in a non-standard
fashion, we can still use them for these tasks. Examples in hyperspectral
land-use classification, airborne geophysical surveying, and seismic imaging
illustrate that we can input large data volumes in one chunk and do not need to
work on small patches, use dimensionality reduction, or employ methods that
classify a patch to a single central pixel.
