[cherryteastain]

> Are PINNs the current state of the art in ML methods for solving PDEs? What are their limitations?

I guess in a way they are. They aren't new, they have been around since the 90s [1]. The problem with them is, you typically need to train them on a specific problem (boundary conditions, domain, equation, PDE coefficients etc). Compared to a traditional solver, the training is much slower, and on top of that the results are typically much less accurate. The PDE + NN community has a bit of a problem dealing with this in general [2], there are tons of papers that make NNs look much better at solving PDEs than they are compared to traditional solvers.

[1] https://www.cs.uoi.gr/~lagaris/papers/TNN-LLF.pdf

[2] https://www.nature.com/articles/s42256-024-00897-5