Related papers: Efficient Bayesian inversion for shape reconstruct…

We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…

Scatterometry is a tested method for measuring periodic semiconductor structures. Since the sizes of modern semiconductor structures have reached the nanoscale regime, the challenge is to determine the shape of periodic nanostructures with…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…

The recent development of scintillation crystals combined with $\gamma$-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography (CST). The associated inverse problem rises many…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…

Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the…

The surrogate matrix methodology delivers low-cost approximations of matrices (i.e., surrogate matrices) which are normally computed in Galerkin methods via element-scale quadrature formulas. In this paper, the methodology is applied to a…

Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate…

In this paper, a novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics is developed for predicting the response of engineering systems and complex physical phenomena. The method utilizes…

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…