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This paper introduces for the first time, to the best of our knowledge, theBayesian Physics-Informed Neural Networks for applications in power systems.Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages ofPhysics-Informed Neural Networks (PINNs), being robust to noise and missingdata, with Bayesian modeling, delivering a confidence measure for their output.Such a confidence measure can be very valuable for the operation of safetycritical systems, such as power systems, as it offers a degree oftrustworthiness for the neural network output. This paper applies the BPINNsfor robust identification of the system inertia and damping, using a singlemachine infinite bus system as the guiding example. The goal of this paper isto introduce the concept and explore the strengths and weaknesses of BPINNscompared to existing methods. We compare BPINNs with the PINNs and the recentlypopular method for system identification, SINDy. We find that BPINNs and PINNsare robust against all noise levels, delivering estimates of the system inertiaand damping with significantly lower error compared to SINDy, especially as thenoise levels increases.

Bayesian Physics-Informed Neural Networks for Robust System Identification of Power Systems