Scattering Problems Research Articles

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

Bayesian Compressive Sensing With Variational Inference and Wavelet Tree Structure for Solving Inverse Scattering Problems

A Direct Sampling Method Based on the Green’s Function for Time-Dependent Inverse Scattering Problems

A Direct Sampling Method Based on the Green’s Function for Time-Dependent Inverse Scattering Problems

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

Refinement of the Asymptotics of Three Charged Quantum Particles Scattering Problem Solution of the Six-Dimensional Distorted Plane Wave Type

Refinement of the Asymptotics of Three Charged Quantum Particles Scattering Problem Solution of the Six-Dimensional Distorted Plane Wave Type

Nonautonomous Volterra Series Expansion of the Variable Phase Approximation and its Application to the Nucleon-Nucleon Inverse Scattering Problem

Abstract In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the ${}^1S_0$ NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below $1\%$ averaged relative error between the recalculated and the measured phase shifts.

Combination of Methods of Volume and Surface Integral Equations in Problems of Electromagnetic Scattering by Small Thickness Structures

Combination of Methods of Volume and Surface Integral Equations in Problems of Electromagnetic Scattering by Small Thickness Structures

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

Enhanced Deep Learning Approach Based on the Conditional Generative Adversarial Network for Electromagnetic Inverse Scattering Problems

A Kernel Machine Learning for Inverse Source and Scattering Problems

A Kernel Machine Learning for Inverse Source and Scattering Problems

A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

A residual fully convolutional network (Res-FCN) for electromagnetic inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band

Many successful machine learning methods have been developed for electromagnetic (EM) inverse scattering problems. However, so far, their inversion has been performed only at the specifically trained frequencies. To make the machine learning based inversion method more generalizable for realistic engineering applications, this work proposes a residual fully convolutional network (Res-FCN) to perform EM inversion of high contrast scatterers at an arbitrary frequency within a wide frequency band. The proposed Res-FCN combines the advantages of the Res-Net and the fully convolutional network (FCN). Res-FCN consists of an encoder and a decoder: the encoder is employed to extract high-dimensional features from the measured scattered field through the residual frameworks, while the decoder is employed to map from the high-dimensional features extracted by the encoder to the electrical parameter distribution in the inversion region by the up-sample layer and the residual frameworks. Four numerical examples verify that the proposed Res-FCN can achieve good performance in the 2D EM inversion problem for high contrast scatterers with anti-noise ability at an arbitrary frequency point within a wide frequency band.

Acceleration of Trimmed MLFMA Using the PO Method for Large-Scale Scattering Problems

Acceleration of Trimmed MLFMA Using the PO Method for Large-Scale Scattering Problems

An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures

The article contains a study of methods for solving integral equations in the context of acoustic problems. The methodology considered is applied to describe acoustic wave propagation and scattering. Efficient discretization methods are used together with iterative methods to solve the operator equations, including an apparatus for fast multiplication of the resulting post-discretization Toeplitz matrices by a vector using the fast Fourier transform. The theoretical analysis of the proposed numerical algorithm demonstrates its efficiency in terms of the required number of arithmetic operations and the memory footprint of the computing system. The presented numerical simulation demonstrates the possibility of solving the problem of acoustic wave propagation in transparent media using the proposed methods. A visualization of the obtained solutions for a practical problem with a high level of discretization of the solution volume domain is also presented.

Three-Dimension Calculation for the Scattering Problem for Non-Spherical Potential

The interaction of the 238U with a neutron is studied. Correct accounting for the non-spherical shape of the uranium nucleus is in focus. The optical potential is used as a model. It is shown that the spherically symmetric and non-spherical potentials give different scattering patterns, in particular different resonance features of the cross-section. The possibility of using the method as an extension of the particle–rotor model of the nucleus is illustrated.

Algorithms for Solving the Inverse Scattering Problem for the Manakov Model

Algorithms for Solving the Inverse Scattering Problem for the Manakov Model

Physics-informed Deep Learning to Solve 2D Electromagnetic Scattering Problems

The utilization of physics-informed deep learning (PI-DL) methodologies provides an approach to augment the predictive capabilities of deep learning (DL) models by constraining them with known physical principles. We utilize a PI-DL model called the deep operator network (DeepONet) to solve two-dimensional (2D) electromagnetic (EM) scattering problems. Numerical results demonstrate that the discrepancy between the DeepONet and conventional method of moments (MoM) is small, while maintaining computational efficiency.

A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

Deep Neural Network-Oriented Indicator Method for Inverse Scattering Problems Using Partial Data

We consider the inverse scattering problem to reconstruct an obstacle using partial far-field data due to one incident wave. A simple indicator function, which is negative inside the obstacle and positive outside of it, is constructed and then learned using a deep neural network (DNN). The method is easy to implement and effective as demonstrated by numerical examples. Rather than developing sophisticated network structures for the classical inverse operators, we reformulate the inverse problem as a suitable operator such that standard DNNs can learn it well. The idea of the DNN-oriented indicator method can be generalized to treat other partial data inverse problems.

Speckle Pattern Calculation and Scattering Imaging for General Surface Scattering Problem

Speckle Pattern Calculation and Scattering Imaging for General Surface Scattering Problem

Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium

Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium

A Posteriori Error Analysis of the Pml Finite Volume Method for the Scattering Problem by a Periodic Chiral Structure

A Posteriori Error Analysis of the Pml Finite Volume Method for the Scattering Problem by a Periodic Chiral Structure