https://arxiv.org/abs/2205.03017

Generative Adversarial Neural OperatorsWe propose the generative adversarial neural operator (GANO), a generativemodel paradigm for learning probabilities on infinite-dimensional functionspaces. The natural sciences and engineering are known to have many types ofdata that are sampled from infinite-dimensional function spaces, whereclassical finite-dimensional deep generative adversarial networks (GANs) maynot be directly applicable. GANO generalizes the GAN framework and allows forthe sampling of functions by learning push-forward operator maps ininfinite-dimensional spaces. GANO consists of two main components, a generatorneural operator and a discriminator neural functional. The inputs to thegenerator are samples of functions from a user-specified probability measure,e.g., Gaussian random field (GRF), and the generator outputs are synthetic datafunctions. The input to the discriminator is either a real or synthetic datafunction. In this work, we instantiate GANO using the Wasserstein criterion andshow how the Wasserstein loss can be computed in infinite-dimensional spaces.We empirically study GANO in controlled cases where both input and outputfunctions are samples from GRFs and compare its performance to thefinite-dimensional counterpart GAN. We empirically study the efficacy of GANOon real-world function data of volcanic activities and show its superiorperformance over GAN.arxiv.org


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