Related papers: Full-waveform inversion in three-dimensional PML-t…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
The inverse problem we consider is to reconstruct the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. A main difficulty of this problem is…
Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Seismic waves bring information from the physical properties of the earth to the surface. Full waveform inversion (FWI) is a local optimization technique which tries to invert the recorded wave fields to the physical properties. An…
We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…
The perfectly matched layer (PML) is a very popular tool in the truncation of wave scattering in unbounded domains. In Chandler-Wilde & Monk et al. 2009, the author proposed a conjecture that for scattering problems with rough surfaces, the…
We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
This paper concerns the reconstruction of multiple elastic parameters (Lam\'e parameters and density) of an inhomogeneous medium embedded in an infinite homogeneous isotropic background in $\mathbb{R}^2$. The direct scattering problem is…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse…
In this paper, we have proposed a dispersive formulation of scalar-based meshless method for time-domain analysis of electromagnetic wave propagation through left-handed (LH) materials. Moreover, we have incorporated Berenger's perfectly…
This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, the proposed method…
Producing reliable acoustic subsurface velocity models still remains the main bottleneck of the oil and gas industry's traditional imaging sequence. In complex geological settings, the output of conventional ray-based or wave-equation-based…
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…
Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has…
A Finite-Difference Time-Domain (FDTD) scheme with Perfectly Matched Layers (PMLs) is considered for solving the time-dependent Schr\"{o}dinger equation, and simulate the ionization of an electron initially bound to a one-dimensional…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [22, 18]…