So they compare speed to traditional methods (1000x faster) and accuracy to previous deep learning methods (30% lower error rate), which leads me to think it's still much less accurate than...
So they compare speed to traditional methods (1000x faster) and accuracy to previous deep learning methods (30% lower error rate), which leads me to think it's still much less accurate than traditional methods. I remember a similar buzzworthy article about ML solving the 3-body problem much faster than traditional methods, but to like 5 orders of magnitude lower accuracy, making the end result impractical for real-world applications. Maybe that's not the case here, since they seem excited about real-world applications.
edit: looked for a comparison in the paper, all i found is:
We do not compare against traditional solvers (FEM/FDM) orneural-FEM type methods since our goal is to produce an efficient operator approximation that can be usedfor downstream applications.
From the article: [...] Here is the paper and discussion on Twitter.
From the article:
[...] researchers at Caltech have introduced a new deep-learning technique for solving [partial differential equations] that is dramatically more accurate than deep-learning methods developed previously. It’s also much more generalizable, capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining. Finally, it is 1,000 times faster than traditional mathematical formulas, which would ease our reliance on supercomputers and increase our computational capacity to model even bigger problems.
[...]
One research topic Anandkumar is particularly excited about: climate change. Navier-Stokes isn’t just good at modeling air turbulence; it’s also used to model weather patterns. “Having good, fine-grained weather predictions on a global scale is such a challenging problem,” she says, “and even on the biggest supercomputers, we can’t do it at a global scale today. So if we can use these methods to speed up the entire pipeline, that would be tremendously impactful.”
So they compare speed to traditional methods (1000x faster) and accuracy to previous deep learning methods (30% lower error rate), which leads me to think it's still much less accurate than traditional methods. I remember a similar buzzworthy article about ML solving the 3-body problem much faster than traditional methods, but to like 5 orders of magnitude lower accuracy, making the end result impractical for real-world applications. Maybe that's not the case here, since they seem excited about real-world applications.
edit: looked for a comparison in the paper, all i found is:
whatever that means
I wonder if a quick approximation can be used to speed up a more precise calculation?
From the article:
[...]
Here is the paper and discussion on Twitter.