[HN Gopher] DeepONet: A deep NN-based model to approximate linea...
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       DeepONet: A deep NN-based model to approximate linear and nonlinear
       operators
        
       Author : djoldman
       Score  : 22 points
       Date   : 2021-04-12 23:18 UTC (1 days ago)
        
 (HTM) web link (techxplore.com)
 (TXT) w3m dump (techxplore.com)
        
       | amelius wrote:
       | 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
        
       | syadegari wrote:
       | Is it just me or the wordings of the article sound too
       | generic/unspecific to someone else?
        
         | syadegari wrote:
         | Links to one of the papers:
         | 
         | - https://arxiv.org/pdf/1910.03193.pdf
         | 
         | - https://www.nature.com/articles/s42256-021-00302-5
        
       | jhrmnn wrote:
       | 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.
        
         | boromi wrote:
         | Exactly, I'm not sure why we need a new fancy name for this
         | obvious task.
        
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       (page generated 2021-04-14 23:01 UTC)