Related papers: Multi-parameter identification in systems of PDEs …
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…
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…
Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…
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,…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In particular, we consider derivative-based sensitivity analysis of…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
We present an interval-based approach for parameter identification in structural static inverse problems. The proposed inverse formulation exploits the Interval Finite Element Method (IFEM) combined with adjoint-based optimization. The…
We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state…
All inverse problems rely on data to recover unknown parameters, yet not all data are equally informative. This raises the central question of data selection. A distinctive challenge in PDE-based inverse problems is their inherently…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…