[atty]

I work on a team that has actually deployed NN based surrogate models into production in industry. We don’t use PINNs for the simple reason that many industrial scale solvers are solving significantly more complex systems than a single global PDE (at least in CFD, perhaps other areas are simpler). For instance, close to the boundaries, the solver our engineers use uses an approximation that does not satisfy conservation of mass and momentum. So when we try to use physical constraints, our accuracy goes down. Even in the cases where we could technically use PINNs we find they are underwhelming, and spending time on crafting better training data sets has always been a better option for us.