DeepBHCP: Deep neural network algorithm for solving backward heat conduction problems

This paper extends a deep neural network method, a semi-supervised one, to solve backward heat conduction problems which have been long-standing computational challenges due to being ill-posed. The effectiveness and robustness of the methodology are demonstrated through various problems including di...

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Bibliographic Details
Published in:Computer physics communications Vol. 272; p. 108236
Main Authors: Mostajeran, F., Mokhtari, R.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2022
Subjects:
Backward heat conduction problems
Deep neural networks
Ill-posed problems
Inverse problems
Thermal conductivity
Thermal conductivity
Ill-posed problems
Deep neural networks
Inverse problems
Backward heat conduction problems
ISSN:0010-4655, 1879-2944
Online Access:Get full text
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Summary:This paper extends a deep neural network method, a semi-supervised one, to solve backward heat conduction problems which have been long-standing computational challenges due to being ill-posed. The effectiveness and robustness of the methodology are demonstrated through various problems including different types of boundary conditions, several types of time-dependent thermal diffusivity factors, and a variety of domains for two-dimensional tests. In spite of traditional methods, there is no need to apply any regularization technique. According to simulation results, this revolutionary strategy can efficiently and accurately extract the pattern of the solutions even when the noise corruption up to ten percent is imposed on input data. Moreover, when the final time is increased further, this approach is efficient in recovering the data at the initial time, which accentuates the method's robustness. To demonstrate the superiority of the semi-supervised neural network process, we make a comparison with the radial basis functions finite difference (RBF-FD) method which is a localized RBF method.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2021.108236