Solving Composable Constraints for Inverse Design Tasks

Phillip Williams, Brooks Paige

Keywords: Inverse Design, Conditional Generation, Constrained Optimization, Deep Learning, Neural Networks, Signed Distance Functions

TL;DR: We provide a novel mechanism for composing arbitrary constraints and then efficiently solving them for two large families of models

Abstract:

Inverse design tasks are an important category of problem in which we want to identify some input vector $x$ satisfying some desirable properties. In this paper we propose a mechanism for representing inequality constraints as Signed Distance Functions (SDFs). SDFs permit efficient projection of points into the solution region as well as providing a mechanism for composing constraints via boolean set operations. In this paper, we provide theoretical motivation for Signed Distance Functions (SDFs) as an implicit representation of inequality constraints. Next, we provide analysis demonstrating that SDFs can be used to efficiently project points into solution regions. Additionally, we propose two novel algorithms for computing SDFs for wide families of machine learning models. Finally, we demonstrate practical utility by performing conditional image generation using MNIST and CelebA datasets, and computational drug design using the ZINC-250K dataset. From the experimental results, we note that the composable constraints can reliably and efficiently compute solutions to complex inverse design tasks with deep learning models.

Primary Area: optimization

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Submission Number: 11710