Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate

TL;DR

This paper introduces a two-stage neural network approach that learns a differentiable surrogate for physical processes, enabling efficient synthesis of constrained configurations with improved quality and reduced computational cost.

Contribution

The paper proposes a novel autoencoder-based method to learn a differentiable surrogate of complex physical processes for constrained synthesis tasks.

Findings

Outperforms supervised learning in solution quality

Achieves competitive results with direct optimization

Reduces computational cost significantly

Abstract

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.