  Intelligent biological systems are characterized by their embodiment in a
complex environment and the intimate interplay between their nervous systems
and the nonlinear mechanical properties of their bodies. This coordination, in
which the dynamics of the motor system co-evolved to reduce the computational
burden on the brain, is referred to as ``mechanical intelligence'' or
``morphological computation''. In this work, we seek to develop machine
learning analogs of this process, in which we jointly learn the morphology of
complex nonlinear elastic solids along with a deep neural network to control
it. By using a specialized differentiable simulator of elastic mechanics
coupled to conventional deep learning architectures -- which we refer to as
neuromechanical autoencoders -- we are able to learn to perform morphological
computation via gradient descent. Key to our approach is the use of mechanical
metamaterials -- cellular solids, in particular -- as the morphological
substrate. Just as deep neural networks provide flexible and
massively-parametric function approximators for perceptual and control tasks,
cellular solid metamaterials are promising as a rich and learnable space for
approximating a variety of actuation tasks. In this work we take advantage of
these complementary computational concepts to co-design materials and neural
network controls to achieve nonintuitive mechanical behavior. We demonstrate in
simulation how it is possible to achieve translation, rotation, and shape
matching, as well as a ``digital MNIST'' task. We additionally manufacture and
evaluate one of the designs to verify its real-world behavior.
