Encoding Invariances in Deep Generative Models

TL;DR

This paper introduces InvNet, a generative model that efficiently encodes known invariances into data distributions, improving modeling in physics simulations, image generation, and microstructure reconstruction.

Contribution

InvNet is a novel approach that incorporates known invariances into generative models via adversarial training, enhancing data efficiency and modeling accuracy.

Findings

Successfully generates images with fixed motifs.

Effectively solves nonlinear PDEs.

Reconstructs microstructures with desired properties.

Abstract

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori} known; for example, in complex physics simulations, the training data obey universal laws encoded as well-defined mathematical equations. In this paper, we propose a new generative modeling approach, InvNet, that can efficiently model data spaces with known invariances. We devise an adversarial training algorithm to encode them into data distribution. We validate our framework in three experimental settings: generating images with fixed motifs; solving nonlinear partial differential equations (PDEs); and reconstructing two-phase microstructures with desired statistical properties. We complement our experiments with several theoretical results.