A sequential sensor selection strategy for hyper-parameterized linear Bayesian inverse problems

by   Nicole Aretz-Nellesen, et al.

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 model variability needs to be taken into account for the experimental design to guarantee that the Bayesian inverse solution is uniformly informative. In this work we link the numerical stability of the maximum a posterior point and A-optimal experimental design to an observability coefficient that directly describes the influence of the chosen sensors. We propose an algorithm that iteratively chooses the sensor locations to improve this coefficient and thereby decrease the eigenvalues of the posterior covariance matrix. This algorithm exploits the structure of the solution manifold in the hyper-parameter domain via a reduced basis surrogate solution for computational efficiency. We illustrate our results with a steady-state thermal conduction problem.



There are no comments yet.


page 1

page 2

page 3

page 4


Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems

We consider hyper-differential sensitivity analysis (HDSA) of nonlinear ...

Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems

We develop a framework for goal oriented optimal design of experiments (...

Sensor Clusterization in D-optimal Design in Infinite Dimensional Bayesian Inverse Problems

We investigate the problem of sensor clusterization in optimal experimen...

Edge-promoting adaptive Bayesian experimental design for X-ray imaging

This work considers sequential edge-promoting Bayesian experimental desi...

Solving Optimal Experimental Design with Sequential Quadratic Programming and Chebyshev Interpolation

We propose an optimization algorithm to compute the optimal sensor locat...

Optimal hybrid parameter selection for stable sequential solution of inverse heat conduction problem

To deal with the ill-posed nature of the inverse heat conduction problem...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.