Fetching the paper…
Reading the bibliography…
We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa).
The mathematics of computerized tomography
F. Natterer · 1986
Earlier work this paper cites.
A perfectly matched layer for the absorption of electromagnetic waves
J.-P. Berenger · 1994
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
Earlier work this paper cites.
Partial differential equations with numerical methods
S. Larsson and V. Thomée · 2003
Earlier work this paper cites.
Reducing the dimensionality of data with neural networks
G. E. Hinton and R. R. Salakhutdinov · 2006
Earlier work this paper cites.
Hadamard, Khatri-Rao, Kronecker and other matrix products
S. Liu and G. Trenkler · 2008
Earlier work this paper cites.
A fast butterfly algorithm for the computation of Fourier integral operators
E. Candès, L. Demanet, and L. Ying · 2009
Earlier work this paper cites.
Sparse fourier transform via butterfly algorithm
L. Ying · 2009
Earlier work this paper cites.
Recurrent neural network based language model
T. Mikolov, M. Karafiát, L. Burget, J. Černockỳ, and S. Khudanpur · 2010
Earlier work this paper cites.
Inverse acoustic and electromagnetic scattering theory
D. Colton and R. Kress · 2013
Earlier work this paper cites.
On the difficulty of training recurrent neural networks
R. Pascanu, T. Mikolov, and Y. Bengio · 2013
Cited alongside, same era.
Adam: A method for stochastic optimization
D. Kingma and J. Ba · 2014
Cited alongside, same era.
Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
Cited alongside, same era.
Butterfly factorization
Y. Li, H. Yang, E. R. Martin, K. L. Ho, and L. Ying · 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.
Solving parametric pde problems with artificial neural networks
Y. Khoo, J. Lu, and L. Ying · 2017
Later among the works it cites.
Interpolative butterfly factorization
Y. Li and H. Yang · 2017
Later among the works it cites.
PDE-net: Learning PDEs from data
Z. Long, Y. Lu, X. Ma, and B. Dong · 2017
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
Closest in time.
Approximate separability of the green’s function of the Helmholtz equation in the high frequency limit
B. Engquist and H. Zhao · 2018
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Deep learning
I. Goodfellow, Y. Bengio, and A. Courville · 2016
Cited alongside, same era.
Solving the quantum many-body problem with artificial neural networks
G. Carleo and M. Troyer · 2017
Cited alongside, same era.
Keras (2015)
F. Chollet · 2017
Cited alongside, same era.
Deep potential: A general representation of a many-body potential energy surface
J. Han, L. Zhang, R. Car, et al · 2017
Cited alongside, same era.
Y. Fan, L. Lin, L. Ying, and L. Zepeda-Núnez · 2018
Closest in time.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and E. Weinan · 2018
Closest in time.
Solving for high dimensional committor functions using artificial neural networks
Y. Khoo, J. Lu, and L. Ying · 2018
Closest in time.
Butterfly-net: Optimal function representation based on convolutional neural networks
Y. Li, X. Cheng, and J. Lu · 2018
Closest in time.