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JohnLeM
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 7th, 2019, 12:55 pm

BTW there be no 'h' in Nicolson..
Isn't he this guy ? (kidding, there is no h, you are right).
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 11:29 am

You are not alone! Numerical analysts know these things,

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JohnLeM
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 11:43 am

You are not alone! Numerical analysts know these things,

Image
Ooops... I used CN schemes for years believing that Nicolson was a man ! These schemes are one of the most used schemes in numerical analysis, and I am just noticing right now that it is also a great contribution to gender equality. Thanks for the precision and the history reminder.
 
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 12:18 pm

You're welcome. BTW I see that Jim Douglas Jr. passed  few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.
 
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JohnLeM
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 12:39 pm

You're welcome. BTW I see that Jim Douglas Jr. passed  few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.
Jim Douglas is the one to be credited for ADI methods ? I did not know that either. Thanks again.
Concerning Lax, to me he is a little bit scary : Lax-Milgram, Lax-Wendroff, Lax Friedrichs...all those results are really famous one. My very humble contribution to his work (together with Monsieur Philippe !) is to propose a more general formula than the Hopf-Lax one to solve Jacobi-Bellman equations (the theoretical analysis behind this work is another paper to release :/).
Last edited by JohnLeM on April 8th, 2019, 12:44 pm, edited 1 time in total.
 
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FaridMoussaoui
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 12:43 pm

You should also mention Olga Ladyzhenskaya
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First proof of the convergence of FD schemes for the NS equations.
 
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 1:16 pm

You're welcome. BTW I see that Jim Douglas Jr. passed  few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.
Jim Douglas is the one to be credited for ADI methods ? I did not know that either. Thanks again.
Concerning Lax, to me he is a little bit scary : Lax-Milgram, Lax-Wendroff, Lax Friedrichs...all those results are really famous one. My very humble contribution to his work (together with Monsieur Philippe !) is to propose a more general formula than the Hopf-Lax one to solve Jacobi-Bellman equations (the theoretical analysis behind this work is another paper to release :/).
JD invented ADI with Rachford.
I once gave a talk on my PDE stuff at a conference. At the time the names of those attending the lectures were not known to me; Douglas, Lax, Wendroff, Strang, Kreiss, Dahlquist, Raviart, Janenko, Dahlquist, Cathleen Synge Morawetz. 
Scary 
 
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FaridMoussaoui
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 1:27 pm

The 1955 paper about ADI was Peaceman & Rachford. Peaceman also co-authored a paper with Douglas about ADI.
 
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 4:09 pm

ADE (1950s)

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JohnLeM
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 4:38 pm

ADE (1950s)
? Didn't you quoted in your paper this book as having been written in 1964 ?
 
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FaridMoussaoui
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 6:18 pm

The book in russian was published in 1960. The 1964 was a translation.

The Russian mathematicians publish a lot in russian. So there is some time to be aware of their work if you don't understand russian.

PS: When I said Russians, I meant Soviets ...
Last edited by FaridMoussaoui on April 8th, 2019, 6:39 pm, edited 1 time in total.
 
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 8th, 2019, 6:23 pm

I studied Russian as undergraduate as preparation.. VK Saul'yev was Lithuanian.
I wrote the 1st article on ADE for option pricing., as I did with Alexander Levin on Soviet Spliting.

https://papers.ssrn.com/sol3/papers.cfm ... id=1552926
https://www.researchgate.net/publicatio ... _equations

https://core.ac.uk/download/pdf/39665447.pdf

etc.
 
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Cuchulainn
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Re: Are Artificial Intelligence methods (AKA Neural Networks) for PDEs about to rediscover the wheel ?

April 9th, 2019, 8:46 am

"Soviet Splitting" (aka LOD) is better than ADI.
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