  In design, fabrication, and control problems, we are often faced with the
task of synthesis, in which we must generate an object or configuration that
satisfies a set of constraints while maximizing one or more objective
functions. The synthesis problem is typically characterized by a physical
process in which many different realizations may achieve the goal. This
many-to-one map presents challenges to the supervised learning of feed-forward
synthesis, as the set of viable designs may have a complex structure. In
addition, the non-differentiable nature of many physical simulations prevents
efficient direct optimization. We address both of these problems with a
two-stage neural network architecture that we may consider to be an
autoencoder. We first learn the decoder: a differentiable surrogate that
approximates the many-to-one physical realization process. We then learn the
encoder, which maps from goal to design, while using the fixed decoder to
evaluate the quality of the realization. We evaluate the approach on two case
studies: extruder path planning in additive manufacturing and constrained soft
robot inverse kinematics. We compare our approach to direct optimization of the
design using the learned surrogate, and to supervised learning of the synthesis
problem. We find that our approach produces higher quality solutions than
supervised learning, while being competitive in quality with direct
optimization, at a greatly reduced computational cost.
