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In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…
Mathematics demonstrates that an ideally evolving magnetic field has an exponentially increasing sensitivity to non-ideal effects for all but truly exceptional evolutions. On a time scale that depends only logarithmically on the magnitude…
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…
A novel mathematical approach has been developed to complete the inversion of the Biot-Savart law in one- and two-dimensional cases from measurements of the perpendicular component of the magnetic field using the well-developed…
Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the…
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…
We study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable, but also on the solution itself. We prove existence, uniqueness and continuous dependence results for…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields.…
The non-destructive estimation of doping concentrations in semiconductor devices is of paramount importance for many applications ranging from crystal growth, the recent redefinition of the 1kg to defect, and inhomogeneity detection. A…
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…