A computational method to solve for the heat conduction temperature field based on data-driven approach

In this paper, a computational method for solving for the one-dimensional heat conduction temperature field is proposed based on a data-driven approach. The traditional numerical solution requires algebraic processing of the heat conduction differential equations, and necessitates the use of a complex mathematical derivation process to solve for the temperature field. In this paper, a temperature field solution model called HTM (Hidden Temperature Method) is proposed. This model uses an artificial neural network to establish the correspondence relationship of the node temperature values during the iterative process, so as to obtain the "Data to Data" solution. In this work, one example of one-dimensional steady state and three examples of one-dimensional transient state are selected, and the calculated values are compared to those obtained by traditional numerical methods. The mean-absolute error(MAE)of the steady state is only 0.2508, and among the three transient cases, the maximum mean-square error(MSE) is only 2.6875, indicating that the model is highly accurate in both steady-state and transient conditions. This shows that the HTM simulation can be applied to the solution of the heat conduction temperature field. This study provides a basis for the further optimization of the HTM algorithm.