We develop a theoretical analysis for special neural network architectures, termed operator
recurrent neural networks, for approximating nonlinear functions whose inputs are linear …

In this paper, we study the inverse boundary value problem for the wave equation with a
view towards an explicit reconstruction procedure. We consider both the anisotropic problem …

We develop a factorization method to obtain an explicit characterization of a (possibly
nonconvex) Dirichlet scattering object from measurements of time-dependent causal …

We present the results of numerical testing on determination of the sound speed c in the
acoustic equation u tt-c 2Δ u= 0 by the boundary control method. The inverse data is a …

This work concerns the inverse scattering problems of imaging unknown/inaccessible
scatterers by transient acoustic near-field measurements. Based on the analysis of the …

We develop a linearized boundary control method for the inverse boundary value problem of
determining a density in the acoustic wave equation. The objective is to reconstruct an …

Let $(N, g) $ be a Riemannian manifold with the distance function $ d (x, y) $ and an open
subset $ M\subset N $. For $ x\in M $ we denote by $ D_x $ the distance difference function …

We consider an inverse obstacle problem for the acoustic transient wave equation. More
precisely, we wish to reconstruct an obstacle characterized by a Dirichlet boundary condition …

Based on the direct sampling method, this paper solves the inverse acoustic wave scattering
problem from the transient scattered field. Two indicator functions can be obtained to …

We introduce a new algorithm to construct travel time distances between a point in the
interior of a Riemannian manifold and points on the boundary of the manifold, and describe …