Related papers: Interval-based parameter identification for struct…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…

In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation…

This work addresses the problem of missing data in time-series analysis focusing on (a) estimation of model parameters in the presence of missing data and (b) reconstruction of missing data. Standard approaches used to solve these problems…

We consider the approximation of elliptic eigenvalue problem with an immersed interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix-Raviart…

This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…

We consider an elliptic linear-quadratic parameter estimation problem with a finite number of parameters. A novel a priori bound for the parameter error is proved and, based on this bound, an adaptive finite element method driven by an a…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning…

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

We present a scalable and efficient framework for the inference of spatially-varying parameters of continuum materials from image observations of their deformations. Our goal is the nondestructive identification of arbitrary damage,…

Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long standing problem until recently. It was shown that if consistent spatial basis functions are used, one…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…