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Generative Adversarial Neural Operators

Rahman, Md Ashiqur and Florez, Manuel A. and Anandkumar, Anima and Ross, Zachary E. and Azizzadenesheli, Kamyar (2022) Generative Adversarial Neural Operators. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20220714-212515070

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Abstract

We propose the generative adversarial neural operator (GANO), a generative model paradigm for learning probabilities on infinite-dimensional function spaces. The natural sciences and engineering are known to have many types of data that are sampled from infinite-dimensional function spaces, where classical finite-dimensional deep generative adversarial networks (GANs) may not be directly applicable. GANO generalizes the GAN framework and allows for the sampling of functions by learning push-forward operator maps in infinite-dimensional spaces. GANO consists of two main components, a generator neural operator and a discriminator neural functional. The inputs to the generator are samples of functions from a user-specified probability measure, e.g., Gaussian random field (GRF), and the generator outputs are synthetic data functions. The input to the discriminator is either a real or synthetic data function. In this work, we instantiate GANO using the Wasserstein criterion and show how the Wasserstein loss can be computed in infinite-dimensional spaces. We empirically study GANOs in controlled cases where both input and output functions are samples from GRFs and compare its performance to the finite-dimensional counterpart GAN. We empirically study the efficacy of GANO on real-world function data of volcanic activities and show its superior performance over GAN. Furthermore, we find that for the function-based data considered, GANOs are more stable to train than GANs and require less hyperparameter optimization.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.2205.03017arXivDiscussion Paper
ORCID:
AuthorORCID
Rahman, Md Ashiqur0000-0002-2933-2637
Anandkumar, Anima0000-0002-6974-6797
Ross, Zachary E.0000-0002-6343-8400
Azizzadenesheli, Kamyar0000-0001-8507-1868
Additional Information:The authors thank Yuan-Kai Liu for his assistance in preparing the InSAR dataset. The authors would like to thank Zongyi Li and Hongkai Zheng for their valuable inputs. Anima Anandkumar and Zachary E. Ross are supported in part by Carver Mead New Adventures Fund.
Group:Seismological Laboratory
Funders:
Funding AgencyGrant Number
Carver Mead New Adventures FundUNSPECIFIED
Subject Keywords:Function spaces, generative adversarial models, neural operators
Record Number:CaltechAUTHORS:20220714-212515070
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220714-212515070
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115584
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:15 Jul 2022 22:41
Last Modified:15 Jul 2022 22:41

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