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Cuchulainn
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Re: Universal Approximation theorem

May 13th, 2021, 5:44 pm

Cuchulainn, perhaps something for you: https://arxiv.org/abs/1711.10561
modulo the physics part! (-:
There's also a Part II article.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl
 
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katastrofa
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Re: Universal Approximation theorem

May 13th, 2021, 6:25 pm

I anticipated you'd guess it yourself.
 
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Cuchulainn
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Re: Universal Approximation theorem

May 13th, 2021, 7:06 pm

I anticipated you'd guess it yourself.
Well, there's not much in I (read it), so II looks likes a fix.
I'll get back with a report, My kind of area.

Pity they used Physics example to camoflage the lack mathematical/numerical foundations.

Part III?
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl
 
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katastrofa
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Re: Universal Approximation theorem

May 13th, 2021, 8:40 pm

Who knows where the truth foundations lie? Maybe they are accidentally right.
 
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Cuchulainn
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Re: Universal Approximation theorem

May 13th, 2021, 8:51 pm

Who knows where the truth foundations lie? Maybe they are accidentally right.
At first glance the intuition might be OK.. But no substitute for maths.
Like Dirac becoming respectable due to Schwartz and Sobolev.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Cuchulainn
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Re: Universal Approximation theorem

May 15th, 2021, 1:42 pm

I have read articles I and II (I == II almost everywhere..). It's basically BS. I am not going to waste my time with a review but if you have technical questions I will try to answer. I love technical discussions.
The KO punch is when the authors use TensorFlow for AD. It's like a kid with a new toy.

Cognoscenti say

"Concerning AD : from one to thousands dimensions, neural networks are always behind, for all performance indicators and all tests that I performed. It is also lacking of math foundations. I am just more and more confident that this technology is basically crap, but benefit of huge investments and marketing."

More generally, AD is probably a dead-end technology going forward (my words).
def f(t, x):
u = u(t, x)
u_t = tf.gradients(u, t)[0]
u_x = tf.gradients(u, x)[0]
u_xx = tf.gradients(u_x, x)[0]
f = u_t + u*u_x - (0.01/tf.pi)*u_xx
return f
Finally, the term "Physics Informed Deep Learning" is vacuous.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl