Estimating the boundary conditions for 3D transient heat conduction by bidirectional long short-term memory network and attention mechanism

Estimating boundary conditions for three-dimensional transient heat conduction problems is a challenging task in science and engineering. The innovative integration of deep learning algorithm and finite element method provides a promising approach for addressing intricate challenges and enhancing the efficiency of problem solutions. Specifically, a novel framework based on bidirectional long short-term memory network and attention mechanism is proposed to accurately identify transient thermal boundary conditions for three-dimensional complex physical models. The bidirectional long short-term memory network is able to simultaneously combine the forward and backward information of the current moment. And the attention mechanism can improve the ability of the network to extract important features. Therefore, the proposed framework can further improve the performance of the network. The training datasets are obtained by the finite element method. The network is tested using different complex physical models and data to evaluate its performance. Compared with other network models, such as recurrent neural network, gated recurrent unit, long short-term memory network and bidirectional long short-term memory network, the proposed method outperforms others in terms of accuracy. Besides, the predicting time is also acceptable. The stability and effectiveness of the proposed method are verified by analyzing the effects of the number of sample points and the data noise. It is credible that the proposed scheme is effective in estimating three-dimensional transient nonlinear thermal boundary conditions.