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DeepONet: A deep NN-based model to approximate linear and nonlinear operators
- syadegari 6y agoIs it just me or the wordings of the article sound too generic/unspecific to someone else?
- syadegari 6y agoLinks to one of the papers: - https://arxiv.org/pdf/1910.03193.pdf https://arxiv.org/pdf/1910.03193.pdf - https://www.nature.com/articles/s42256-021-00302-5 https://www.nature.com/articles/s42256-021-00302-5
- jhrmnn 6y agoFor 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.
- boromi 6y agoExactly, I'm not sure why we need a new fancy name for this obvious task.
- amelius 6y agoHow 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 https://en.wikipedia.org/wiki/Discrete_Poisson_equation
- vsskanth 6y agoHow do they compare or relate to differential neural nets (diffeqflux) ?