https://phys.org/news/2022-09-artificial-intelligence-equation-quantum-physics.html
Using artificial intelligence, physicists have compressed a daunting quantum problem that until now required 100,000 equations into a bite-size task of as few as four equations—all without sacrificing accuracy. The work, published in the September 23 issue of Physical Review Letters, could revolutionize how scientists investigate systems containing many interacting electrons. Moreover, if scalable to other problems, the approach could potentially aid in the design of materials with sought-after properties such as superconductivity or utility for clean energy generation.
[...] One way of studying a quantum system is by using what's called a renormalization group. That's a mathematical apparatus physicists use to look at how the behavior of a system—such as the Hubbard model—changes when scientists modify properties such as temperature or look at the properties on different scales. Unfortunately, a renormalization group that keeps track of all possible couplings between electrons and doesn't sacrifice anything can contain tens of thousands, hundreds of thousands or even millions of individual equations that need to be solved. On top of that, the equations are tricky: Each represents a pair of electrons interacting.
Di Sante and his colleagues wondered if they could use a machine learning tool known as a neural network to make the renormalization group more manageable. The neural network is like a cross between a frantic switchboard operator and survival-of-the-fittest evolution. First, the machine learning program creates connections within the full-size renormalization group. The neural network then tweaks the strengths of those connections until it finds a small set of equations that generates the same solution as the original, jumbo-size renormalization group. The program's output captured the Hubbard model's physics even with just four equations.
"It's essentially a machine that has the power to discover hidden patterns," Di Sante says. "When we saw the result, we said, 'Wow, this is more than what we expected.' We were really able to capture the relevant physics."
Journal Reference:
Domenico Di Sante, Matija Medvidović, Alessandro Toschi, et al. Deep Learning the Functional Renormalization Group, Physical Review Letters (DOI: 10.1103/PhysRevLett.129.136402)
(Score: 5, Funny) by Rosco P. Coltrane on Wednesday September 28 2022, @04:34PM (20 children)
Here, in front of your very eyes, I'm gonna reduce 1,000,000 equations to a single one. Ready? Here we go:
x+2 = 3
x+3 = 4
x+4 = 5
... (just imagine this goes on for a while eh?)
x+999,999 = 1,000,000
x+1,000,000 = 1,000,001
x+1,000,001 = 1,000,002
And now... ready?
x = 1
(Score: 5, Interesting) by JoeMerchant on Wednesday September 28 2022, @05:13PM (19 children)
I worked for a guy who used to say "most jobs given to supercomputers are actually just inefficient algorithms that could be done on a regular computer if people would fix the algorithm."
He paid us to convert his Matlab code to parallelized C++ to run on a supercomputer. After some time with a profiler, we reduced the run time of his algorithm by 100x and had it running acceptably quickly on a 2 core laptop.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 0) by Anonymous Coward on Wednesday September 28 2022, @05:56PM (10 children)
The article is a bit weird. Is their claim that no human without AI assistance could find a single optimization from 100,000 equations to four (or as few as four? is there wiggle-room in how many equations are needed?)? Or is it just that an AI did it that is fantastic, not that humans could do it themselves? I find that part a bit unclear.
(Score: 5, Insightful) by Freeman on Wednesday September 28 2022, @06:03PM (9 children)
AI did it, now we only need one super smart math guy. Can fire the rest of the team.
Joshua 1:9 "Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee"
(Score: 4, Interesting) by JoeMerchant on Wednesday September 28 2022, @09:03PM (5 children)
There are a lot of problems that are easy to check the solution, once you have it, but hard to find the solution.
A lot of AI involves checking a ton of options and optimizing toward some desired result - this may have been the result of trying lots and lots and lots of combinations and coming up with something that humans just don't have the patience for, anymore.
Ever pick up an old mathematics text, like from the 1800s? Full of sine, exp, and other much more esoteric tables calculated out to 6 digits or more? Ever think about how that was made? Ain't nobody got time for that, anymore.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 5, Insightful) by hendrikboom on Wednesday September 28 2022, @09:14PM (4 children)
I've seen a book of mathematical tables from the early 1900's.
Sines, cosines, others (even Bessel functions if I recall correctly) calculated to about 20 duodecimals.
Yes, duodecimals.
Base twelve.
The amount of work this involved is mind-boggling.
(Score: 3, Informative) by gnuman on Thursday September 29 2022, @08:44AM (3 children)
If by early 1900s, you said up to 1970s, you would be correct.
https://www.amazon.com/-/en/Samuel-Selby-dp-B0020D2PBW/dp/B0020D2PBW/ [amazon.com]
Calculators didn't become commoditized until ICs became commoditized. So, look no earlier than 1980s for accessible, cheap way of calculating these things.
Yeah, the world changes rather fast and we take it for granted. And if we are not careful, it can change back to era predating the math tables very quickly.
(Score: 1, Interesting) by Anonymous Coward on Thursday September 29 2022, @12:26PM
I was taught how to use log tables for calculating when I was in the 10th grade in the early 80s.
(Score: 2) by Immerman on Thursday September 29 2022, @01:42PM
What do personal calculators have to do with lookup tables? I mean, aside from being the death of them?
The whole point of lookup tables for mathematical functions is that there *wasn't* a cheap, accessible way to calculate the results.
If you wanted to calculate lookup tables in the good old days (tm) you hired computers. Human ones, possibly aided by mechanical adding machines or simple calculators if you had the budget for such novelties. Eventually, once vacuum tubes matured, your room full of computers working for days was replaced by 10 minutes on a mainframe running through your punchcard program and print out the resulting tables, much cheaper, but still expensive and inconvenient by most people's standards.
By the time electronic calculators hit the scene the cost of computing the tables was negligible if you had access to a digital computer, but most people didn't. Until eventually more complex ICs became cheap enough to enable most high school students to own "scientific" calculators that could calculate the most common functions (trig and maybe log) on the fly (or at least interpolate between points in a sparse internal lookup table).
At which point computing standalone lookup tables became kind of pointless.
(Score: 2) by hendrikboom on Saturday October 01 2022, @02:34PM
I'm not sure of the date of publication, but I think it was around 1910 or 1920.
(Score: 1, Interesting) by Anonymous Coward on Wednesday September 28 2022, @10:35PM (2 children)
> now we only need one super smart math guy.
Sorry Steinmetz is dead. And if he was alive, you can bet that GE would guard him and his services with everything they've got:
https://www.britannica.com/biography/Charles-Proteus-Steinmetz [britannica.com]
(Score: 0) by Anonymous Coward on Thursday September 29 2022, @04:48PM (1 child)
Here's a puzzler for you smart 21st C math majors: vectors with complex coefficients. WTF's that, now?
[1 0] sure that makes sense. How about [i 0]? Fuck you, that's what it means.
(Score: 2) by maxwell demon on Thursday September 29 2022, @09:45PM
Easy: That's ℂn
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by Freeman on Wednesday September 28 2022, @05:58PM
That is hilarious and goes to show that smart people do dumb stuff too. If nothing else, due to the fact that X thing isn't what they do. Sure a mathematician may be good at math. Doesn't mean they're good at programming a calculator.
Joshua 1:9 "Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee"
(Score: 2) by turgid on Wednesday September 28 2022, @07:33PM (6 children)
Were you cheaper than the plug-in for MATLAB that spews out hundreds of thousands of lines of spaghetti C for teency weency models? It's really impressive and "professional."
I refuse to engage in a battle of wits with an unarmed opponent [wikipedia.org].
(Score: 2) by JoeMerchant on Wednesday September 28 2022, @09:06PM
Yeah, only because we were programming graphic UIs for the stuff and the Matlab converted C spaghetti doesn't stick to that wall no matter how hard you throw it.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 1, Interesting) by Anonymous Coward on Wednesday September 28 2022, @10:39PM (4 children)
> plug-in for MATLAB that spews out hundreds of thousands of lines of spaghetti C for teency weency models?
My understanding (could be wrong) is that the Matlab compiler links to a huge library of pre-compiled functions, so even tiny models produce a large executable. Pretty sure this was the case ~10 years ago but don't know what they are doing now.
(Score: 1, Touché) by Anonymous Coward on Thursday September 29 2022, @12:28PM (3 children)
But since we're talking about Mathworks here, that is probably by design. It spits out ugly huge executables; however, for $1,200/yr (and $4,000 up front), they'll sell you the "Reasonable-Sized Executable Toolbox."
(Score: 1, Informative) by Anonymous Coward on Thursday September 29 2022, @09:12PM (2 children)
They wanted to sell me a plugin for reading "Microsoft Excel spreadsheet CSV files."
(Score: 1, Interesting) by Anonymous Coward on Thursday September 29 2022, @10:14PM (1 child)
Just heard from a co-worker that Matlab/Mathworks recently quit supporting some part(s) of their interchange with Excel. The comment in the Matlab docs is that Microsoft changed the COM interface, so call Microsoft if you want this feature of Matlab to work like it used to work.
Maybe someone here can confirm this and add some detail, it was passed to me as a corporate battle that might be worth some popcorn...
(Score: 3, Touché) by JoeMerchant on Friday September 30 2022, @02:03AM
When Octave started doing everything I needed from Matlab, the whole license issue became extremely disinteresting to me.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2) by stretch611 on Wednesday September 28 2022, @05:00PM (1 child)
I guess P = NP [wikipedia.org]
Unless they are wrong
Now with 5 covid vaccine shots/boosters altering my DNA :P
(Score: 2) by JoeMerchant on Wednesday September 28 2022, @09:04PM
Just because it's NP doesn't mean you _can't_ find the solution by brute force. This was "only" 100,000 equations, relatively small by modern supercomputer standards, and an awful lot of AI is just hitting the problem with a really big compute hammer.
Україна досі не є частиною Росії Слава Україні🌻 https://news.stanford.edu/2023/02/17/will-russia-ukraine-war-end
(Score: 2, Informative) by khallow on Wednesday September 28 2022, @06:57PM (2 children)
(Score: 0) by Anonymous Coward on Wednesday September 28 2022, @07:58PM (1 child)
This should work on large populations too, the keystone of effective crowd control with a single taser.
(Score: 1) by khallow on Thursday September 29 2022, @12:01AM
Renormalization is in large part about how things/dynamics can change with scale. Number of people is another change in scale. So I wouldn't be surprised if some automated mass control thing does rely, here and there, on renormalization.