Related papers: A computational framework for infinite-dimensional…
Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
Inverse problems are often ill-posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is…
Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…
Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…
We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…
We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…
We propose to use techniques from Bayesian inference and deep neural networks to translate uncertainty in seismic imaging to uncertainty in tasks performed on the image, such as horizon tracking. Seismic imaging is an ill-posed inverse…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…
We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the…