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In design, fabrication, and control problems, we are often faced with thetask of synthesis, in which we must generate an object or configuration thatsatisfies a set of constraints while maximizing one or more objectivefunctions. The synthesis problem is typically characterized by a physicalprocess in which many different realizations may achieve the goal. Thismany-to-one map presents challenges to the supervised learning of feed-forwardsynthesis, as the set of viable designs may have a complex structure. Inaddition, the non-differentiable nature of many physical simulations preventsefficient direct optimization. We address both of these problems with atwo-stage neural network architecture that we may consider to be anautoencoder. We first learn the decoder: a differentiable surrogate thatapproximates the many-to-one physical realization process. We then learn theencoder, which maps from goal to design, while using the fixed decoder toevaluate the quality of the realization. We evaluate the approach on two casestudies: extruder path planning in additive manufacturing and constrained softrobot inverse kinematics. We compare our approach to direct optimization of thedesign using the learned surrogate, and to supervised learning of the synthesisproblem. We find that our approach produces higher quality solutions thansupervised learning, while being competitive in quality with directoptimization, at a greatly reduced computational cost.

Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate