A kernel machine learning for inverse source and scattering problems
DOI10.1137/23m1597381MaRDI QIDQ6561303
Publication date: 25 June 2024
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
stabilityinverse problemneural networkprolate spheroidal wave functionskernel machinetarget identification
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Other functions coming from differential, difference and integral equations (33E30) Other special orthogonal polynomials and functions (33C47) Approximation by other special function classes (41A30) Numerical methods for inverse problems for integral equations (65R32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Prolate spheroidal wave functions of order zero. Mathematical tools for bandlimited approximation
- A qualitative approach to inverse scattering theory
- Kernel methods in machine learning
- Functions of positive and negative type, and their connection with the theory of integral equations.
- Basis of a general theory of linear integral equations (First communication).
- Support-vector networks
- On an artificial neural network for inverse scattering problems
- Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions
- Ball prolate spheroidal wave functions in arbitrary dimensions
- Theoretical foundations of the potential function method in pattern recognition learning
- The Mathematics of Computerized Tomography
- An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
- Reducing the Dimensionality of Data with Neural Networks
- Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves
- An Introduction to the Mathematical Theory of Inverse Problems
- Analysis of spectral approximations using prolate spheroidal wave functions
- A Novel Method for Solving the Inverse Scattering Problem for Time-Harmonic Acoustic Waves in the Resonance Region
- Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty-V: The Discrete Case
- Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
- A Factorization Method for Multifrequency Inverse Source Problems with Sparse Far Field Measurements
- A simple method for solving inverse scattering problems in the resonance region
- On a Hybrid Approach for Recovering Multiple Obstacles
- Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems
- Inverse Acoustic and Electromagnetic Scattering Theory
- SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
- Learning representations by back-propagating errors
- Algorithm 840: computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions---prolate elements
- Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
- Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
- Theory of Reproducing Kernels
- Inverse Scattering Theory and Transmission Eigenvalues, Second Edition
- Single Mode Multi-Frequency Factorization Method for the Inverse Source Problem in Acoustic Waveguides
- Data-Driven Basis for Reconstructing the Contrast in Inverse Scattering: Picard Criterion, Regularity, Regularization, and Stability
- A direct sampling-based deep learning approach for inverse medium scattering problems
- Deterministic-statistical approach for an inverse acoustic source problem using multiple frequency limited aperture data
Related Items (1)
This page was built for publication: A kernel machine learning for inverse source and scattering problems
