Bayesian physics informed neural networks (PINNs) [R]

Hi! I’m trying to understand Bayesian physics-informed neural networks (PINNs).

I have a relatively solid understanding of standard PINNs, but I’m confused about what changes when they are made Bayesian.

Specifically:

• Which components are treated probabilistically?
• Is uncertainty placed only on the neural network parameters (weights and biases), or also on the data, boundary/initial conditions, or physical parameters? Or does this depend on the specific use case? Or model developed?

I’d appreciate any intuition or references that clarify how uncertainty is modeled in Bayesian PINNs!