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We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…
Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interfaces, of superconducting thin films and of electronic…
This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was…
We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…
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…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…
With a super-high-efficient numerical algorithm, we are able to self-consistently calculate the Green's function in the renormalized-ring-diagram approximation for a two-dimensional electron system with long-range Coulomb interactions. The…
The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical…
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics…
We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
The reconstruction of electrical current densities from magnetic field measurements is an important technique with applications in materials science, circuit design, quality control, plasma physics, and biology. Analytic reconstruction…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…
Resistive-capacitive (RC) networks are used to model various processes in engineering, physics or biology. We consider the problem of recovering the network connection structure from measured input-output data. We address this problem as a…