Related papers: Bayesian experimental design for linear elasticity
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a…
Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…
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…
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…
The aim of magnetorelaxometry imaging is to determine the distribution of magnetic nanoparticles inside a subject by measuring the relaxation of the superposition magnetic field generated by the nanoparticles after they have first been…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…
We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the…
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
This work considers sequential edge-promoting Bayesian experimental design for (discretized) linear inverse problems, exemplified by X-ray tomography. The process of computing a total variation type reconstruction of the absorption inside…
While many advanced statistical methods for the design of experiments exist, it is still typical for physical experiments to be performed adaptively based on human intuition. As a consequence, experimental resources are wasted on…
We study the inverse boundary value problem for the linear elastic wave equation in three-dimensional isotropic medium. We show that both the Lam\'e parameters and the density can be uniquely recovered from the boundary measurements under…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…
We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
We consider an inverse boundary value problem for a nonlinear elastic wave equation which was studied in [de Hoop, Uhlmann, Wang. Math. Ann. (2019) doi:10.1007/s00208-018-01796-y]. We show that all the parameters appearing in the equation…
Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…