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Message:

> The AI folks are using this scheme:
> 
> https://www.quantamagazine.org/new-neural-networks-solve-hardest-equations-faster-than-ever-20210419/
> 
> "To model a passenger jet scything through the air, a seismic wave rippling through Earth or the spread of a disease through a population — to say nothing of the interactions of fundamental forces and particles — engineers, scientists and mathematicians resort to “partial differential equations” (PDEs) that can describe complex phenomena involving many independent variables.
> 
> ***
> 
> "Now researchers have built new kinds of artificial neural networks that can approximate solutions to partial differential equations orders of magnitude faster than traditional PDE solvers. And once trained, the new neural nets can solve not just a single PDE but an entire family of them without retraining.
> 
> ***
> 
> "Last year, Anandkumar and her colleagues at Caltech and Purdue University built a deep neural network, called the Fourier neural operator (FNO), with a different architecture that they claim is faster. Their network also maps functions to functions, from infinite-dimensional space to infinite-dimensional space, and they tested their neural net on PDEs. “We chose PDEs because PDEs are immediate examples where you go from functions to functions,” said Kamyar Azizzadenesheli of Purdue.
> 
> ***
> 
> "It also provides solutions at dramatically improved speeds. In one relatively simple example that required 30,000 simulations, involving solutions of the infamous Navier-Stokes equation, the FNO took fractions of a second for each simulation (comparable to DeepONet’s speed, had it been tested on this problem), for a total of 2.5 seconds; the traditional solver in this case would have taken 18 hours."
> 
> Comment: What the article shows in the figures is a two layer setup mimicking our frontal lobe five tier arrangement. It is interesting they refer to their AI units as 'neurons'. But our wiring system offers obvious advantages to follow by AI engineers, although we need computers' high speed, since we operate at biological speeds. Which brings me to my real thought. It is wiring complexity that makes us so different from anything in the past, even the  larger-brain-sized Neanderthals.