Related papers: Solving High-dimensional Inverse Problems Using Am…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace…
We propose an instance-wise adaptive sampling framework for constructing compact and informative training datasets for supervised learning of inverse problem solutions. Typical learning-based approaches aim to learn a general-purpose…
To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
We consider the solution of nonlinear inverse problems where the forward problem is a discretization of a partial differential equation. Such problems are notoriously difficult to solve in practice and require minimizing a combination of a…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula,…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
This paper presents normalizing flows for incremental smoothing and mapping (NF-iSAM), a novel algorithm for inferring the full posterior distribution in SLAM problems with nonlinear measurement models and non-Gaussian factors. NF-iSAM…
We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…