Related papers: Inverse problem in cylindrical electrical networks
We propose a new method that uses deep learning techniques to solve the inverse problems. The inverse problem is cast in the form of learning an end-to-end mapping from observed data to the ground-truth. Inspired by the splitting strategy…
We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group is a Weyl field, that is isomorphic to a skew field of some…
We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…
We address the discrete inverse conductance problem for well-connected spider networks; that is, to recover the conductance function on a well-connected spider network from the Dirichlet-to-Neumann map. It is well-known that this inverse…
This work derives explicit series reversions for the solution of Calder\'on's problem. The governing elliptic partial differential equation is $\nabla\cdot(A\nabla u)=0$ in a bounded Lipschitz domain and with a matrix-valued coefficient.…
For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the neural network approach to solving optimization problems such as variational inequality, monotone inclusion, and…
We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
In this paper we examine an inverse problem in the modular theory of von Neumann algebras in the case of finite factors. First we give a characterization of cyclic and separating vectors for finite factors in terms of operators associated…
Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the…
Let $A, B$ be invertible, non-commuting elements of a ring $R$. Suppose that $A-1$ is also invertible and that the equation $$[B,(A-1)(A,B)]=0$$ called the fundamental equation is satisfied. Then an invariant $R$-module is defined for any…
We develop linear discretization of complex analysis, originally introduced by R. Isaacs, J. Ferrand, R. Duffin, and C. Mercat. We prove convergence of discrete period matrices and discrete Abelian integrals to their continuous…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
We prove that the Dirichlet-to-Neumann map of the linear wave equation determines the topological, differentiable and conformal structure of the underlying Lorentzian manifold, under mild technical assumptions. With more stringent geometric…
We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
We present a directed percolation inverse problem for diode networks: Given information about which pairs of nodes allow current to percolate from one to the other, can one find a configuration of diodes consistent with the observed…