Related papers: Bayesian identification of material parameters in …
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of…
Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we…
The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a…
In this work, we investigate the estimation of a parameter $f$ in PDEs using Bayesian procedures, and focus on posterior distributions constructed using Gaussian process priors, and its variational approximation. We establish contraction…
This paper deals with a polymeric matrix composite material. The matrix behaviour is described by the modified Rabotnov's nonlinear viscoelastic model assuming the material is nonlinear viscoelastic. The parameters of creep and…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…
There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
The development of new materials typically involves a process of trial and error, guided by insights from past experimental and theoretical findings. The inverse design approach for soft-matter systems has the potential to optimize specific…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming…
We study the Bayesian inverse problem of inferring the permeability of a porous medium within the context of a moving boundary framework motivated by Resin Transfer Molding (RTM), one of the most commonly used processes for manufacturing…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…