  Multimode optical fibers (MMFs) have gained renewed interest in the past
decade, emerging as a way to boost optical communication data-rates in the
context of an expected saturation of current single-mode fiber-based networks.
They are also attractive for endoscopic applications, offering the possibility
to achieve a similar information content as multicore fibers, but with a much
smaller footprint, thus reducing the invasiveness of endoscopic procedures.
However, these advances are hindered by the unavoidable presence of disorder
that affects the propagation of light in MMFs and limits their practical
applications. We introduce here a general framework to study and avoid the
effect of disorder. We experimentally find an almost complete set of optical
channels that are resilient to disorder induced by strong deformations. These
deformation principle modes are obtained by only exploiting measurements for
weak perturbations. We explain this effect by demonstrating that, even for a
high level of disorder, the propagation of light in MMFs can be characterized
by just a few key properties. These results are made possible thanks to a
precise and fast estimation of the modal transmission matrix of the fiber which
relies on a model-based optimization using deep learning frameworks.
