DeepONet: A deep NN-based model to approximate linear and nonlinear operators(techxplore.com)
techxplore.com
DeepONet: A deep NN-based model to approximate linear and nonlinear operators
https://techxplore.com/news/2021-04-deeponet-deep-neural-network-based-approximate.html
4 comments
For practical purposes, functionals are just infinite-dimensional functions. In practice, a function is always represented numerically using a finite basis (grid, splines, Fourier), so functionals become just high-dimensional functions. At which point we are back to ordinary machine learning. So I’m not sure what’s the point here.
Exactly, I'm not sure why we need a new fancy name for this obvious task.
How well does this scale? Say I have a discrete Poisson equation for some 3d geometry [1], how does the solution time compare to fast multigrid methods, for increasing matrix size?
[1] https://en.wikipedia.org/wiki/Discrete_Poisson_equation
[1] https://en.wikipedia.org/wiki/Discrete_Poisson_equation
Is it just me or the wordings of the article sound too generic/unspecific to someone else?
Links to one of the papers:
- https://arxiv.org/pdf/1910.03193.pdf
- https://www.nature.com/articles/s42256-021-00302-5
- https://arxiv.org/pdf/1910.03193.pdf
- https://www.nature.com/articles/s42256-021-00302-5
How do they compare or relate to differential neural nets (diffeqflux) ?