Encoding Invariances in Deep Generative Models
This addresses the problem of data scarcity in generative modeling for domains like physics and materials science, but it is incremental as it builds on existing GAN frameworks.
The paper tackles the challenge of training generative adversarial networks (GANs) with limited data by incorporating known invariances, such as physical laws, into the model. It introduces InvNet, which achieves efficient modeling in tasks like image generation, PDE solving, and microstructure reconstruction, though no concrete numbers are provided.
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.