Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation an...Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation and display of the sensitivity kernel will be different.Unfortunately,in the past,both perspectives give the same name to their quantity computed/displayed,and that has caused some confusion.To distinguish between the two,their perspective should be added to the names.This paper focuses only on the perspective of the Forward Problem where the input parameters are known.The Perturbation method has been successfully used in the computation of the sensitivity kernels of observations on 1D and 3D viscosity variations from the Forward perspective.One aim of this paper is to review and clarify the physics of the Perturbation method and bring out some important aspects of this method that have been misunderstood or neglected.Another aim is to present sensitivity kernels from the Perturbation method using 3D(both radially and laterally heterogeneous)Earth models with realistic ice history.These new results are now suitable for future comparison with those from new methods using the Forward perspective.Finally,the sensitivity computations for realistic ice histories on a 3D Earth is reviewed and used to search for optimal locations of new GIA observations.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which posses...The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.展开更多
Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performan...Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.展开更多
文摘Sensitivity of observational data is important in the study of Glacial Isostatic Adjustment(GIA).However,depending on whether sensitivity is used for the Inverse Problem or the Forward Problem,the final formulation and display of the sensitivity kernel will be different.Unfortunately,in the past,both perspectives give the same name to their quantity computed/displayed,and that has caused some confusion.To distinguish between the two,their perspective should be added to the names.This paper focuses only on the perspective of the Forward Problem where the input parameters are known.The Perturbation method has been successfully used in the computation of the sensitivity kernels of observations on 1D and 3D viscosity variations from the Forward perspective.One aim of this paper is to review and clarify the physics of the Perturbation method and bring out some important aspects of this method that have been misunderstood or neglected.Another aim is to present sensitivity kernels from the Perturbation method using 3D(both radially and laterally heterogeneous)Earth models with realistic ice history.These new results are now suitable for future comparison with those from new methods using the Forward perspective.Finally,the sensitivity computations for realistic ice histories on a 3D Earth is reviewed and used to search for optimal locations of new GIA observations.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
文摘The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.
基金Supported by the National Key Research and Development Program of China(No.2023YFC3008200)the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(No.SML2022SP505)。
文摘Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.
