The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measuremen...The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.展开更多
By simultaneously introducing a finite-difference-based numerical loss term and a clustering-reconstruction mechanism,we propose an enhanced physics-informed neural network named the informed reconstruction-oriented n...By simultaneously introducing a finite-difference-based numerical loss term and a clustering-reconstruction mechanism,we propose an enhanced physics-informed neural network named the informed reconstruction-oriented numerical network(IRON-Net)and subsequently apply it to the Manakov equations-a well-known two-component nonlinear physical model.Numerical experiments are conducted on a dataset containing eight analytical solu-tions with noise.The results indicate that,compared to conventional PINNs and other mainstream algorithms,IRON-Net demonstrates significant advantages in training accuracy,convergence rate,and robustness,achiev-ing a stepwise improvement in the neural network’s ability to enforce physical constraints.Additional ablation experiments further confirm the necessity of the consistency constraint within IRON-Net.This study provides an effective approach for modeling and parameter identification in complex nonlinear optical systems as well as other nonlinear physical scenarios.展开更多
This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the...This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.展开更多
This research analyzed a snowfall process in north China during February 12-13, 2022. By using synoptic and numerical analysis, it is concluded that this snowfall process was mainly caused by trough, low-level vortex,...This research analyzed a snowfall process in north China during February 12-13, 2022. By using synoptic and numerical analysis, it is concluded that this snowfall process was mainly caused by trough, low-level vortex, shear line and Siberian High. Meanwhile, an easterly wind that transports water vapor from the Bohai to North China, was the water resource of the snowfall process. Relative humidity in the low atmosphere was above 80%, providing an excellent humidity condition for snowfall. Positive vorticity and convergence induced upward motion, which offered conditions for snowfall. Numerical reconstruction is also used to show the range and the intensity of the snowfall process.展开更多
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the i...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the interior interface of the inhomogeneous cavity by means of many internal measurements of the near-field data.Numerical examples are carried out to illustrate the practicability of the inversion algorithm.展开更多
Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles wi...Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles with different kinds of boundary conditions.Based on the establishment of the well-posedness result of the direct problem,we intend to develop a modified factorization method to simultaneously reconstruct both the support of the inhomogeneous conductive medium and the shape and location of various impenetrable obstacles by means of the far-field data for all incident plane waves at a fixed wave number.Numerical examples are carried out to illustrate the feasibility and effectiveness of the proposed inversion algorithms.展开更多
The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different as...The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.展开更多
We present a Fizeau interferometer using a microscopic objective as a tool for surface contouring without the need for a numerical lens for reconstruction. The interferometer is associated with a telescope system to f...We present a Fizeau interferometer using a microscopic objective as a tool for surface contouring without the need for a numerical lens for reconstruction. The interferometer is associated with a telescope system to feature the object with collimated light. The experiment is conducted on two objects possessing different step heights.The phase maps from the captured off-axis holograms are calculated numerically, which allows us to deduce the contours of the objects. The great advantages of the presented technique are that it can be done in real time and there is no need for numerical lenses for micro-objects reconstruction.展开更多
文摘The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.
基金supported by the Hubei Provincial Natural Science Foundation(Grant No.2023AFB873)the National Natural Science Foun-dation of China(Grant Nos.12505006,11975172,122611-31495,and 12381240286).
文摘By simultaneously introducing a finite-difference-based numerical loss term and a clustering-reconstruction mechanism,we propose an enhanced physics-informed neural network named the informed reconstruction-oriented numerical network(IRON-Net)and subsequently apply it to the Manakov equations-a well-known two-component nonlinear physical model.Numerical experiments are conducted on a dataset containing eight analytical solu-tions with noise.The results indicate that,compared to conventional PINNs and other mainstream algorithms,IRON-Net demonstrates significant advantages in training accuracy,convergence rate,and robustness,achiev-ing a stepwise improvement in the neural network’s ability to enforce physical constraints.Additional ablation experiments further confirm the necessity of the consistency constraint within IRON-Net.This study provides an effective approach for modeling and parameter identification in complex nonlinear optical systems as well as other nonlinear physical scenarios.
基金supported by the National Natural ScienceFoundation of China Grant(11871416,12171057)the Natural Science Foundation of Shandong Province Grant(ZR2019MA027)。
文摘This paper is concerned with inverse acoustic scattering in an inhomogeneous medium with a conductive boundary condition and the unknown buried impenetrable objects inside.Using a variational approach,we establish the well-posedness of the direct problem.For the inverse problem,we shall numerically reconstruct the inhomogeneous medium from the far-field data for different kinds of cases.For the case when a Dirichlet boundary condition is imposed on the buried object,the classical factorization method proposed in[1]is justified as valid for reconstructing the inhomogeneous medium from the far-field data.For the case when a Neumann boundary condition is imposed on the buried object,the classical factorization method of[1]cannot be applied directly,since the middle operator of the factorization of the far-field operator is only compact.In this case,we develop a modified factorization method to locate the inhomogeneous medium with a conductive boundary condition and the unknown buried objects.Some numerical experiments are provided to demonstrate the practicability of the inversion algorithms developed.
文摘This research analyzed a snowfall process in north China during February 12-13, 2022. By using synoptic and numerical analysis, it is concluded that this snowfall process was mainly caused by trough, low-level vortex, shear line and Siberian High. Meanwhile, an easterly wind that transports water vapor from the Bohai to North China, was the water resource of the snowfall process. Relative humidity in the low atmosphere was above 80%, providing an excellent humidity condition for snowfall. Positive vorticity and convergence induced upward motion, which offered conditions for snowfall. Numerical reconstruction is also used to show the range and the intensity of the snowfall process.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871416,12171057)by the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA027)+1 种基金supported by the National Natural Science Foundation of China(Grant Nos.11971273,12126426)by the Natural Science Foundation of Shandong Province(Grant No.ZR2018MA004).
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous cavity.We shall develop a modified factorization method to reconstruct the shape and location of the interior interface of the inhomogeneous cavity by means of many internal measurements of the near-field data.Numerical examples are carried out to illustrate the practicability of the inversion algorithm.
基金supported by the National Natural Science Foundation of China Grant(Grant Nos.11871416,12171057)by the Natural Science Foundation of Shandong Province(Grant No.ZR2019MA027).
文摘Consider the inverse scattering of time-harmonic acoustic waves by a mixed-type scatterer consisting of an inhomogeneous penetrable medium with a conductive transmission condition and various impenetrable obstacles with different kinds of boundary conditions.Based on the establishment of the well-posedness result of the direct problem,we intend to develop a modified factorization method to simultaneously reconstruct both the support of the inhomogeneous conductive medium and the shape and location of various impenetrable obstacles by means of the far-field data for all incident plane waves at a fixed wave number.Numerical examples are carried out to illustrate the feasibility and effectiveness of the proposed inversion algorithms.
基金partially supported by the Basal-CMM Project,the Fondecyt Grant(No.1130317,1111012,1140773)"Agence Nationale de la Recherche" Project CISIFS(No.ANR-09-BLAN-0213-02)partially supported by ECOS-CONICYT C13E05 and Basal-CeBiB
文摘The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.
基金supported by the Chinese Academy of Sciences Fellowship for Postdoctoral and Visiting Scholars from Developing Countries
文摘We present a Fizeau interferometer using a microscopic objective as a tool for surface contouring without the need for a numerical lens for reconstruction. The interferometer is associated with a telescope system to feature the object with collimated light. The experiment is conducted on two objects possessing different step heights.The phase maps from the captured off-axis holograms are calculated numerically, which allows us to deduce the contours of the objects. The great advantages of the presented technique are that it can be done in real time and there is no need for numerical lenses for micro-objects reconstruction.
