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.

翻译：在设计、制造和控制方面,我们常常面临合成任务,即我们必须产生一个能满足一系列制约的物体或组合,同时最大限度地发挥一种或多种客观功能。合成问题典型的特点是物理过程,许多不同的实现都可能实现这个目标。这一多对一的地图对监督地学习进料合成提出了挑战,因为一套可行的设计可能具有复杂的结构。此外,许多物理模拟的无差别性质妨碍了高效的直接优化。我们用一个两阶段神经网络结构来解决这两个问题,我们可以把它视为一个自动编码器。我们首先学习解码器:一个不同的替代器,可以接近多到一个实际实现过程。我们然后学习从目标到设计的编码,同时使用固定的解码器来评估实现的质量。我们评价了两个案例研究的方法:在添加制造过程中的极端路径规划,以及软机器人的反向运动。我们比较了我们的方法是直接优化设计的方法,在进行高额的模拟时,我们用高额的模型学习了高额的计算方法。