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 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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper extends a semi-supervised deep neural network method to solve ill-posed backward heat conduction problems, which have long been a computational challenge. The methodology's effectiveness and robustness are demonstrated through various tests, including different boundary conditions, thermal diffusivity factors, and domains. Unlike traditional methods, no regularization technique is required. Simulation results show that this revolutionary strategy can efficiently and accurately extract solution patterns even with up to ten percent noise corruption in the input data. Additionally, as the final time is increased, the method remains efficient in recovering the initial time data, demonstrating its robustness. A comparison with the localized radial basis functions finite difference (RBF-FD) method supports the superiority of the semi-supervised neural network approach.