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Title: Solving Bayesian Inverse Problems via Variational Autoencoders
In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-constrained framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty. Numerical results for an elliptic PDE-constrained Bayesian inverse problem are provided to verify the proposed framework.  more » « less
Award ID(s):
1808576 1845799
NSF-PAR ID:
10288556
Author(s) / Creator(s):
Editor(s):
Joan Bruna, Jan S
Date Published:
Journal Name:
Proceeding of Machine Learning Research, 2nd Annual Conference on Mathematical and Scientific Machine Learning
Volume:
145
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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