
Preconditioned training of normalizing flows for variational inference in inverse problems
Obtaining samples from the posterior distribution of inverse problems wi...
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A transportbased multifidelity preconditioner for Markov chain Monte Carlo
Markov chain Monte Carlo (MCMC) sampling of posterior distributions aris...
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Variational Inference for Computational Imaging Inverse Problems
We introduce a method to infer a variational approximation to the poster...
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Multifidelity Bayesian Neural Networks: Algorithms and Applications
We propose a new class of Bayesian neural networks (BNNs) that can be tr...
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Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows
In inverse problems, we often have access to data consisting of paired s...
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The frontier of simulationbased inference
Many domains of science have developed complex simulations to describe p...
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Multifidelity Computer Model Emulation with HighDimensional Output: An Application to Storm Surge
Hurricanedriven storm surge is one of the most deadly and costly natura...
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Learning by example: fast reliabilityaware seismic imaging with normalizing flows
Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of illposed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for largescale inverse problems, such as seismic imaging. Our main contribution is a datadriven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low and highfidelity migrated images. In our numerical example, we obtain highfidelity images from the Parihaka dataset and lowfidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reversetime migration image. Next, by feeding this lowfidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a highfidelity image including a first assessment of the image's reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current image and assess its reliability.
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