Related papers: Bayesian experimental design for linear elasticity
We discuss the problem of input design for uncertainty reduction in a parameter estimation procedure. Assuming a linear continuous-time control system with noisy measurements, we formulate an objective of variance reduction in a Bayesian…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by…
We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
Optimal experimental design (OED) is the general formalism of sensor placement and decisions about the data collection strategy for engineered or natural experiments. This approach is prevalent in many critical fields such as battery…
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…
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…
In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…
Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…
Design optimisation offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based…
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…
We consider infinite-dimensional Bayesian linear inverse problems governed by time-dependent partial differential equations (PDEs) and develop a mathematical and computational framework for optimal design of mobile sensor paths in this…
Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…
Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data. In many applications, we seek to minimize the uncertainty of a predicted quantity of interest (QoI) based on…
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…