  This paper introduces for the first time, to the best of our knowledge, the
Bayesian Physics-Informed Neural Networks for applications in power systems.
Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of
Physics-Informed Neural Networks (PINNs), being robust to noise and missing
data, with Bayesian modeling, delivering a confidence measure for their output.
Such a confidence measure can be very valuable for the operation of safety
critical systems, such as power systems, as it offers a degree of
trustworthiness for the neural network output. This paper applies the BPINNs
for robust identification of the system inertia and damping, using a single
machine infinite bus system as the guiding example. The goal of this paper is
to introduce the concept and explore the strengths and weaknesses of BPINNs
compared to existing methods. We compare BPINNs with the PINNs and the recently
popular method for system identification, SINDy. We find that BPINNs and PINNs
are robust against all noise levels, delivering estimates of the system inertia
and damping with significantly lower error compared to SINDy, especially as the
noise levels increases.
