Fetching the paper…
Reading the bibliography…
This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging.
Ultrasonic reflectivity tomography: reconstruction with circular transducer arrays
S. J. Norton and M. Linzer · 1979
Earlier work this paper cites.
Nonlinear two-dimensional elastic inversion of multioffset seismic data
P. Mora · 1987
Earlier work this paper cites.
Acoustical detection of high-density krill demersal layers in the submarine canyons off georges bank
C. Greene, P. Wiebe, J. Burczynski, and M. Youngbluth · 1988
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
G. Cybenko · 1989
Earlier work this paper cites.
Fast wavelet transforms and numerical algorithms I
G. Beylkin, R. Coifman, and V. Rokhlin · 1991
Earlier work this paper cites.
Artificial neural networks in the solution of inverse electromagnetic field problems
S. R. H. Hoole · 1993
Earlier work this paper cites.
Perfectly matched layer for the FDTD solution of wave-structure interaction problems
J.-P. Berenger · 1996
Earlier work this paper cites.
Estimation of multiple scattering by iterative inversion, part ii: Practical aspects and examples
D. Verschuur and A. Berkhout · 1997
Earlier work this paper cites.
Inverse acoustic and electromagnetic scattering theory
D. L. Colton, R. Kress, and R. Kress · 1998
Earlier work this paper cites.
Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory
A. Kirsch · 1999
Earlier work this paper cites.
Mathematical problems in radar inverse scattering
B. Borden · 2001
Earlier work this paper cites.
The linear sampling method and the music algorithm
M. Cheney · 2001
Earlier work this paper cites.
AILU for Helmholtz problems: a new preconditioner based on the analytic parabolic factorization
M. J. Gander and F. Nataf · 2001
Earlier work this paper cites.
Inverse scattering series and seismic exploration
A. B. Weglein, F. V. Araújo, P. M. Carvalho, R. H. Stolt, K. H. Matson, R. T. Coates, D. Corrigan, D. J. Foster, S. A. Shaw, and H. Zhang · 2003
Earlier work this paper cites.
General elastic wave scattering problems using an impedance operator approach-ii. two-dimensional isotropic validation and examples
T. Hulme, A. Haines, and J. Yu · 2004
Earlier work this paper cites.
Advances in iterative methods and preconditioners for the Helmholtz equation
Y. A. Erlangga · 2008
Earlier work this paper cites.
Neural network inverse modeling and applications to microwave filter design
H. Kabir, Y. Wang, M. Yu, and Q.-J. Zhang · 2008
Earlier work this paper cites.
The factorization method for inverse problems
A. Kirsch and N. Grinberg · 2008
Earlier work this paper cites.
Fast directional algorithms for the Helmholtz kernel
B. Engquist and L. Ying · 2010
Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
Earlier work this paper cites.
Quantitative microwave imaging for breast cancer detection using a planar 2.45 ghz system
T. Henriksson, N. Joachimowicz, C. Conessa, and J.-C. Bolomey · 2010
Earlier work this paper cites.
The linear sampling method in inverse electromagnetic scattering
F. Cakoni, D. Colton, and P. Monk · 2011
Earlier work this paper cites.
Sweeping preconditioner for the Helmholtz equation: hierarchical matrix representation
B. Engquist and L. Ying · 2011
Cited alongside, same era.
Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers
B. Engquist and L. Ying · 2011
Cited alongside, same era.
Why it is difficult to solve Helmholtz problems with classical iterative methods
O. G. Ernst and M. J. Gander · 2012
Cited alongside, same era.
Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups
G. Hinton, L. Deng, D. Yu, G. E. Dahl, A. r. Mohamed, N. Jaitly, A. Senior, V. Vanhoucke, P. Nguyen, T. N. Sainath, and B. Kingsbury · 2012
Cited alongside, same era.
ImageNet classification with deep convolutional neural networks
A. Krizhevsky, I. Sutskever, and G. E. Hinton · 2012
Cited alongside, same era.
A unified deep artificial neural network approach to partial differential equations in complex geometries
J. Berg and K. Nyström · 2018
Later among the works it cites.
Looking back on inverse scattering theory
D. Colton and R. Kress · 2018
Later among the works it cites.
The deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
W. E and B. Yu · 2018
Later among the works it cites.
A multiscale neural network based on hierarchical matrices
Y. Fan, L. Lin, L. Ying, and L. Zepeda-Núñez · 2018
Later among the works it cites.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
Later among the works it cites.
Deep potential: A general representation of a many-body potential energy surface
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. I. Hussein, M. J. Leamy, and M. Ruzzene · 2014
Cited alongside, same era.
Deep learning of the tissue-regulated splicing code
M. K. K. Leung, H. Y. Xiong, L. J. Lee, and B. J. Frey · 2014
Cited alongside, same era.
Sequence to sequence learning with neural networks
I. Sutskever, O. Vinyals, and Q. V. Le · 2014
Cited alongside, same era.
Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
Cited alongside, same era.
Deep neural nets as a method for quantitative structure-activity relationships
J. Ma, R. P. Sheridan, A. Liaw, G. E. Dahl, and V. Svetnik · 2015
Cited alongside, same era.
A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks
K. Rudd and S. Ferrari · 2015
Cited alongside, same era.
Deep learning in neural networks: An overview
J. Schmidhuber · 2015
Cited alongside, same era.
J. Han, L. Zhang, R. Car, and W. E · 2018
Later among the works it cites.
SwitchNet: a neural network model for forward and inverse scattering problems
Y. Khoo and L. Ying · 2018
Later among the works it cites.
PDE-net: Learning PDEs from data
Z. Long, Y. Lu, X. Ma, and B. Dong · 2018
Later among the works it cites.
Using deep neural networks for inverse problems in imaging: beyond analytical methods
A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos · 2018
Later among the works it cites.
Hidden physics models: Machine learning of nonlinear partial differential equations
M. Raissi and G. E. Karniadakis · 2018
Later among the works it cites.
Image reconstruction based on convolutional neural network for electrical resistance tomography
C. Tan, S. Lv, F. Dong, and M. Takei · 2018
Later among the works it cites.
Unsupervised deep learning algorithm for PDE-based forward and inverse problems
L. Bar and N. Sochen · 2019
Closest in time.
BCR-Net: a neural network based on the nonstandard wavelet form
Y. Fan, C. O. Bohorquez, and L. Ying · 2019
Closest in time.
A multiscale neural network based on hierarchical nested bases
Y. Fan, J. Feliu-Fabà, L. Lin, L. Ying, and L. Zepeda-Núñez · 2019
Closest in time.
Solving electrical impedance tomography with deep learning
Y. Fan and L. Ying · 2019
Closest in time.
Solving optical tomography with deep learning
Y. Fan and L. Ying · 2019
Closest in time.
Meta-learning pseudo-differential operators with deep neural networks
J. Feliu-Faba, Y. Fan, and L. Ying · 2019
Closest in time.
Solving for high-dimensional committor functions using artificial neural networks
Y. Khoo, J. Lu, and L. Ying · 2019
Closest in time.
A theoretical analysis of deep neural networks and parametric PDEs
G. Kutyniok, P. Petersen, M. Raslan, and R. Schneider · 2019
Closest in time.
Variational training of neural network approximations of solution maps for physical models
Y. Li, J. Lu, and A. Mao · 2019
Closest in time.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Closest in time.