End-to-end learning can use both approximate and accurate training data, if the model can learn how to mix them correctly. It turns out that Neural Operators offer a perfect solution when such multi-fidelity and multi-resolution data is available, and can learn with high data efficiency.

Our latest paper surprisingly shows that it is not the case! End to end also requires less training data compared to methods that keep existing numerical solvers and augment with AI. Where do savings come from? The approach that augments AI relies only on fully accurate expensive training data.

We have seen end-to-end approach win in areas like weather forecasting. It is significantly better for speed: 1000-million x faster than numerical simulations in many areas such as fluid dynamics, plasma physics etc. But a big argument against it is the need for expensive training data.

Popular prescription is to augment AI into existing workflows rather than replace them, e.g., keep the approximate numerical solver for simulations, and use AI only to correct its errors in every time step. Other extreme is to completely discard the existing workflow and replace it fully with AI.

Thanks to my co-authors David Pitt, Robert Joseph George, Jiawwei Zhao, Cheng Luo, Yuandong Tian, Jean Kossaifi, @anima-anandkumar.bsky.social, and @caltech.edu for hosting me this spring!
Paper: arxiv.org/abs/2501.02379
Code: github.com/neuraloperat...