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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 11:41 am

Better and worse than others.

Figure 1 is a howler. Computer scientists love their polynomials., so they do.

// It would be interesting to hear view from the fluid dynamics experts on the forum.
Last edited by Cuchulainn on August 26th, 2018, 11:57 am, edited 1 time in total.
 
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ISayMoo
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Re: DL and PDEs

August 26th, 2018, 11:56 am

What should have they used instead?

(Looking at the authors' backgrounds, most of them are chemists/physicists, not computer scientists.)
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 12:09 pm

What should have they used instead?

(Looking at the authors' backgrounds, most of them are chemists/physicists, not computer scientists.)
Your question is way too premature. 
 
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Paul
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Re: DL and PDEs

August 26th, 2018, 12:12 pm

There's a lot of running before walking in this field. It's very tempting because it's easy to sit down and programme without thinking too deeply and get some 'results.' Nothing very new in that, it's been common in finance for decades (a finance degree makes people think they are mathematicians).

But it's easy to criticise. What would the baby-steps version of DL/PDEs (or any maths) look like? What would be the first problem 'translated'?
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 12:45 pm

But it's easy to criticise. What would the baby-steps version of DL/PDEs (or any maths) look like? What would be the first problem 'translated'?

Good question. The part I am having difficulty with (and which no one had formulated it seems) can be summarised as:

understand the problem
what's input and desired output
devise a plan
Carry out plan (+ a scoped down 101 case)
Review results

These are fundamental questions that should be made explicit. It makes the article more accessible for the rest of us.

Modest proposal; Before Burgers, KS, Kdv (that almost no one knows) etc. why not do the heat equation (that everyone knows) from A-Z? 

For the record, I have given some proposals regarding other DL_PDEarticles to authors and ZERO response. I've run out of pearls at this stage..
 
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ISayMoo
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Re: DL and PDEs

August 26th, 2018, 3:30 pm

I think part of the interest in the "difficult" equations comes from domain experts (i.e. not ML people, not numerican analysis people) who would like to make their life easier by applying ML to a problem they need to solve anyway.

But there are also ML people trying to make themselves useful to other disciplines.

Why don't they test on the heat equation first? I suspect because the existing methods are so good that it's a hard benchmark to beat. And ML people have this unfortunate "beat the benchmark" mentality engrained deeply now in them. ML methods may not be as good as hand-optimised methods on simple problems, but they could be better on very complex problems where hand-tuning is too expensive. But that's not very convincing to the reader, is it? What a conundrum ;-)
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 3:32 pm

Why don't they test on the heat equation first? I suspect because the existing methods are so good that it's a hard benchmark to beat.

This is a wrong answer. As I already mentioned, you do the heat equation to show how it works. to quote Halmos again and again

the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case. 

This is a most depressing thread.Show me how the 'process' works for a simple case and I will work out the rest myself. The (unrefereed?) articles to date are not of a standard that I can extract the essence of the problem from them.

And ML people have this unfortunate "beat the benchmark" mentality engrained deeply now in them
Not only in ML.

It's all as clear as mud to me at this stage.
 
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ISayMoo
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Re: DL and PDEs

August 26th, 2018, 4:36 pm

Well, this paper has been peer-reviewed, but it's even worse (methodologically).
 
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Paul
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Re: DL and PDEs

August 26th, 2018, 5:00 pm

Can’t we do the ML version of the heat equation here and now?
 
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ppauper
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Re: DL and PDEs

August 26th, 2018, 5:36 pm

Kdv (that almost no one knows)
I thought everyone knew the KdV equation
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 7:01 pm

Can’t we do the ML version of the heat equation here and now?
I'm in. Who else is coming on board? And who does what?
IMO if we have solved the heat equation all the way then it would clear things up.
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 7:05 pm

Well, this paper has been peer-reviewed, but it's even worse (methodologically).
As Wittgenstein would say: it is a (wordy) description, not an explanation. 
Where'e the meat?

// There's a superviser, article reviewer in my DNA, so I tend to look for holes in the mathematics. 
 
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Cuchulainn
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Re: DL and PDEs

August 26th, 2018, 7:10 pm

Kdv (that almost no one knows)
I thought everyone knew the KdV equation
It's a bit esoteric. Of course, applied maths degrees do this before lunch tiime.
On a related note, I see Peter Lax is still with us (born 1926). 
 
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Paul
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Re: DL and PDEs

August 26th, 2018, 8:47 pm

Can’t we do the ML version of the heat equation here and now?
I'm in. Who else is coming on board? And who does what?
IMO if we have solved the heat equation all the way then it would clear things up.
I’m in. What’s the procedure? Naive training on known solutions? Or representing differentiation using DLs?
 
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katastrofa
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Re: DL and PDEs

August 27th, 2018, 11:15 am

Well, this paper has been peer-reviewed, but it's even worse (methodologically).
Imho, ML computing can develop its full potential only if it parts with the reductionist approach. The paper sounds like a first step in the right direction.
BTW, why computer science bros don't try to apply Galois connection in ML? They should be familiar with formal concept analysis. I'll ask this question on linkedin, where everybody (except me) is an ML expert these days.
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