Practical uncertainty quantification for space-dependent inverse heat conduction problem via ensemble physics-informed neural networks

Inverse heat conduction problems (IHCPs) are problems of estimating unknown quantities of interest (QoIs) of the heat conduction with given temperature observations. The challenge of IHCPs is that it is usually ill-posed since the observations are noisy, and the estimations of QoIs are generally not unique or unstable, especially when there are unknown spatially varying QoIs. In this study, an ensemble physics-informed neural network (E-PINN) is proposed to handle function estimation and uncertainty quantification of space-dependent IHCPs. The distinctive characteristics of E-PINN are ensemble learning and adversarial training (AT). Compared with other data-driven UQ approaches, the suggested method is more than straightforward to implement and also achieves high-quality uncertainty estimates of the QoI. Furthermore, an adaptive active sampling (AS) strategy based on the uncertainty estimates from E-PINNs is also proposed to improve the accuracy of material field inversion problems. Finally, the proposed method is validated through several numerical experiments of IHCPs.