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Solving Bayesian Inverse Problems via Variational Autoencoders
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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-informed 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.
Forward citations
Cited by 2 Pith papers
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Distributional Inverse Homogenization
Statistics of microstructure are identifiable from bulk-property distributions via generative-model calibration under periodic and stochastic homogenization.
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A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization
Paired autoencoders with linear latent-space maps, interpreted through Bayes risk minimization, give theory and experiments for inverse problems and beat an end-to-end baseline when paired training data are scarce.
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