Since it is time-consuming to print every extruder path we generate in the last step onareal printer,webuild asimulation system byusing Bullet [22]tohelp usgenerate fiber paths. Finally, we run the tuned simulators on the generated extruder paths. Wesplitthedatasetinto90%training(9,000paths),5%validation(500paths), and 5% testing (500 paths), and we use the Adam optimizer [54]with alearning rate of 1 10 3, a learning rate exponential decay of 0.95 per epoch, and a batch size of 1 (path). Therobothasanoriginalheight of 10 and an original width of 0.5, and its bottom is fixed. The stretch ratios are restricted to be between 0.8 and 1.2.

We first learn the decoder: a differentiable surrogate that approximates the many-to-one physical realization process.

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 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 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.