Temperature field inversion of heat-source systems via physics-informed neural networks

Temperature field inversion of heat-source systems (TFI-HSS) with limited observations is essential to monitor the system health. Although some methods such as interpolation have been proposed to solve TFI-HSS, those existing methods ignore correlations between data constraints and physics constraints, causing the low precision. In this work, we develop a physics-informed neural network-based temperature field inversion (PINN-TFI) method to solve the TFI-HSS task and a coefficient matrix condition number based position selection of observations (CMCN-PSO) method to select optima positions of noise observations. For the TFI-HSS task, the PINN-TFI method encodes constrain terms into the loss function, thus the task is transformed into an optimization problem of minimizing the loss function. In addition, we have found that noise observations significantly affect reconstruction performances of the PINN-TFI method. To alleviate the effect of noise observations, the CMCN-PSO method is proposed to find optimal positions, where the condition number of observations is used to evaluate positions. The results demonstrate that the PINN-TFI method can significantly improve prediction precisions and the CMCN-PSO method can find good positions to acquire a more robust temperature field.