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We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion.
An implementation of the reconstruction algorithm of a nachman for the 2d inverse conductivity problem
S. Siltanen, J. Mueller, and D. Isaacson · 2000
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Patial Differential Equations
L.C. Evans · 2010
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Linear and Nonlinear Inverse Problems with Practical Applications
J. Mueller and S. Siltanen · 2012
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Software available from tensorflow.org
TensorFlow: Large-scale machine learning on heterogeneous systems, 2015 · 2015
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Solving differential equations using neural networks
M. M. Chiaramonte and M. Kiener · 2017
Earlier work this paper cites.
A review of convolutional neural networks for inverse problems in imaging
M. T. McCann, K. H. Jin, and M. Unser · 2017
Cited alongside, same era.
Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2017
Cited alongside, same era.
DGM: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spiliopoulos · 2017
Cited alongside, same era.
A deep learning framework for single-sided sound speed inversion in medical ultrasound
M. Feigin, D. Freedman, and B. W. Anthony · 2018
Cited alongside, same era.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and E. Weinan · 2018
Later among the works it cites.
Switchnet: A neural network model for forward and inverse scattering problems
Y. Khoo and L. Ying · 2018
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NETT: Solving inverse problems with deep neural networks
H. Li, J. Schwab, S. Antholzer, and M. Haltmeier · 2018
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Using deep neural networks for inverse problems in imaging
A. Lucas, M. Iliadis, R. Molina, and A. K. Katsaggelos · 2018
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