Encoding Invariances in Deep Generative Models

Date
2019-06-04
Authors
Hegde, Chinmay
Shah, Viraj
Joshi, Ameya
Ganapathysubramanian, Baskar
Ghosal, Sambuddha
Pokuri, Balaji
Sarkar, Soumik
Ganapathysubramanian, Baskar
Hegde, Chinmay
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Mechanical Engineering
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Mechanical EngineeringElectrical and Computer EngineeringPlant Sciences Institute
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.

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This is a pre-print of the article Shah, Viraj, Ameya Joshi, Sambuddha Ghosal, Balaji Pokuri, Soumik Sarkar, Baskar Ganapathysubramanian, and Chinmay Hegde. "Encoding Invariances in Deep Generative Models." arXiv preprint arXiv:1906.01626 (2019). Posted with permission.

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