  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.
