Prof. Anima Anandkumar

Hi. How flexible/sensitive is this framework to the changes in geometries and meshes? For example, say I want to add/remove a feature, like a hole or a fillet, or place an obstacle to divert the flow or change the mesh resolution adaptively in an unsteady simulation.

This learns the operator of PDE. So it doesn't rely on mesh and is not resolution dependent. We see high fidelity super resolution capability in our method.

Thanks for your interest! The current Fourier neural operator implementation relies on FFT, so it's resolution-invariant but only appliable to the uniform grids. For these crazy meshes, check out our graph-based methods https://arxiv.org/abs/2003.03485  https://arxiv.org/abs/2006.09535 

Thank you! I am interested in problems with complex geometries. But uniform grids are not of much help for such problems. Given my limited knowledge in NNs, I am happy to use your model based on graph-based methods as a black-box to run some benchmarks. Could you please share?

Hi Ghenna, I guess Zongyi has already shared them with you in his reply above, no?

Yes, he did share two papers. One of them (2003.03485) considers the Poisson equation only, and the other one (2006.09535) deals only with Poisson and 1D Burger's equation. Those two papers do not deal with Navier-Stokes equations. Correct me if I am wrong.