Numerical Solution of Inverse Problems by Weak Adversarial Networks
- URL: http://arxiv.org/abs/2002.11340v2
- Date: Sat, 5 Sep 2020 16:19:26 GMT
- Title: Numerical Solution of Inverse Problems by Weak Adversarial Networks
- Authors: Gang Bao, Xiaojing Ye, Yaohua Zang, Haomin Zhou
- Abstract summary: We leverage the weak formulation of PDE in the given inverse problem, and parameterize the solution and the test function as deep neural networks.
As the parameters are updated, the network gradually approximates the solution of the inverse problem.
- Score: 6.571303769953873
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We consider a weak adversarial network approach to numerically solve a class
of inverse problems, including electrical impedance tomography and dynamic
electrical impedance tomography problems. We leverage the weak formulation of
PDE in the given inverse problem, and parameterize the solution and the test
function as deep neural networks. The weak formulation and the boundary
conditions induce a minimax problem of a saddle function of the network
parameters. As the parameters are alternatively updated, the network gradually
approximates the solution of the inverse problem. We provide theoretical
justifications on the convergence of the proposed algorithm. Our method is
completely mesh-free without any spatial discretization, and is particularly
suitable for problems with high dimensionality and low regularity on solutions.
Numerical experiments on a variety of test inverse problems demonstrate the
promising accuracy and efficiency of our approach.
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