Oh I see, I missed the major point that the training data is basically incomplete to model the entire relationship.

Why embed priors into neural networks, doesn’t Bayesian Modeling using MCMC do pretty much what this is attempting to do? We did something similar to this in one of my courses although we didn’t get to spend enough time on it so forgive me if my questions are stupid. I also would need someone to walk me through a motivating example for a PINN because I’d just get lost in generalities otherwise. I get the example, but am failing to see the larger use case.