AI Solves Schrodinger's Equation (phys.org) 67
An anonymous reader quotes a report from Phys.Org: A team of scientists at Freie Universitat Berlin has developed an artificial intelligence (AI) method for calculating the ground state of the Schrodinger equation in quantum chemistry. The goal of quantum chemistry is to predict chemical and physical properties of molecules based solely on the arrangement of their atoms in space, avoiding the need for resource-intensive and time-consuming laboratory experiments. In principle, this can be achieved by solving the Schrodinger equation, but in practice this is extremely difficult. Up to now, it has been impossible to find an exact solution for arbitrary molecules that can be efficiently computed. But the team at Freie Universitat has developed a deep learning method that can achieve an unprecedented combination of accuracy and computational efficiency.
The deep neural network designed by [the] team is a new way of representing the wave functions of electrons. "Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei," [Professor Frank Noe, who led the team effort] explains. "One peculiar feature of electronic wave functions is their antisymmetry. When two electrons are exchanged, the wave function must change its sign. We had to build this property into the neural network architecture for the approach to work," adds [Dr. Jan Hermann of Freie Universitat Berlin, who designed the key features of the method in the study]. This feature, known as 'Pauli's exclusion principle,' is why the authors called their method 'PauliNet.' Besides the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of the innovative success of PauliNet is that it integrates these properties into the deep neural network, rather than letting deep learning figure them out by just observing the data. "Building the fundamental physics into the AI is essential for its ability to make meaningful predictions in the field," says Noe. "This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on." The results were published in the journal Nature Chemistry.
The deep neural network designed by [the] team is a new way of representing the wave functions of electrons. "Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei," [Professor Frank Noe, who led the team effort] explains. "One peculiar feature of electronic wave functions is their antisymmetry. When two electrons are exchanged, the wave function must change its sign. We had to build this property into the neural network architecture for the approach to work," adds [Dr. Jan Hermann of Freie Universitat Berlin, who designed the key features of the method in the study]. This feature, known as 'Pauli's exclusion principle,' is why the authors called their method 'PauliNet.' Besides the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of the innovative success of PauliNet is that it integrates these properties into the deep neural network, rather than letting deep learning figure them out by just observing the data. "Building the fundamental physics into the AI is essential for its ability to make meaningful predictions in the field," says Noe. "This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on." The results were published in the journal Nature Chemistry.
The AI looked inside (Score:4, Funny)
...and now the cat is dead and the AI doesn't give a shit.
Re: The AI looked inside (Score:1)
Re: The AI looked inside (Score:1)
Well "the AI" is a tensor mapper, configured by certain humans.
It has as much individual thought as a news media watching voter.
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We need someone to develop an AI and call it Weird AI Yankovic.
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We need someone to develop an AI and call it Weird AI Yankovic.
That joke works on platforms that are stupid enough to use sans-serif fonts. Why do so many persist in that, when we all have high-def screens now, even on phones?
Helvetica is just one step removed form Comic Sans.
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Re: The AI looked inside (Score:2)
Found the UI 'designer' for Chinese apps that use Times Roman or another ugly serif font.
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On the issue of small text, I found that they were the cause of 80% of my migraines (the other being a lack of sleep). Once I increase the text size to 120%, 140% of what they were, I found that 80% of migraines simply disappeared. I've never needed glasses
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Because sans-serif fonts are, generally speaking, easier for me to read with these tired old eyes.
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Are you replying about "the AI" or the news media watching voter?
Re: The AI looked inside (Score:2)
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Given the quality of responses to this article, a dogs watching television analogy would be more appropriate.
Re: The AI looked inside (Score:2)
So now we are on Snowball VI?
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Re: The AI looked inside (Score:1)
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We are tired of hearing about that fucktard. Take it to reddit.
Re: Trumps fault (Score:1)
Well, unfortunately Congress chose to spend way too much money on TDS items, and the State governments largely did the same.
If ALL of Congress and the Senate (and the same for State governments) were disposed of by Jan 1 and it was pointed out to the replacements that the same would happen to them unless they worked for Americans, no one else, not themselves, not special interests, then maybe things might get better.
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If by "things" you mean deceptions, then yes, I'm sure that would make "things" better.
Interesting, but has one major flaw (Score:5, Interesting)
The method is interesting, but has two major flaws, which shares with DFT.
The first one is that it's not variational. What do I mean by that? One important property of some quantum chemistry methods is that the more you increase the number of degrees of freedom in optimisation, the more accurate you become, and with the guarantee that you will always be a little bit worse in one clear direction. If it were a pixelated image, imagine increasing the resolution. The image would become closer and closer to the truth, and predictably so. There's never a case where you increase the resolution and the colours change wildly.
The second problem is that there's no clear way to improve the method. Some methods are simple: more degrees of freedom, better results. Not so with DFT, not so with this method. You are basically throwing everything in a big cauldron, mix with some fitted coefficients, and hope for the best. You have no clear direction on what to do next in order to get better results. It's like comparing ray tracing, which is slow, but very, very realistic, with 3d graphic tricks to make games, where the results are fast, but hardly as photorealistic as a ray traced image that took hours to render.
Now, these shortcomings have not stopped big achievements, and in fact most computations today are performed with DFT mostly because it gives very good results for minimal computational cost on large molecules, but from the formal point of view, quantum chemists are blind, and these methods don't shed new light on optimisation tricks. They are almost empirical methods that you accept pretty much at face value and hope for the best.
Re: Interesting, but has one major flaw (Score:2)
Since you seem to know a fair bit ...
Could you kindly point me to something that *actually* explains the "Pauli exclusion priciple"?
Because everything I found states it as an a unexplained rule. I know enough quantum field theory to follow PBS SpaceTime in my sleep, but math is a deliberate obfuscation for people that work like me. I'd need something that can make sense of it visually (or in terms of structured memes, as in mental objects).
TFS hints at it having something to do with a changing sign? That te
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From what I remember though, is that Pauli merely managed to formulate rules from empirical chemistry observation.
When he came up with a formulation that explained observed electron groupings and chemical reactions, the math indicated that no 2 electrons could occupy the same quantum state at the same time without a null wavefunction.
As it turns out, this math has held up to rather silly levels of testing, and almost all physical and c
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And there remains no explanation of what causes this behaviour, other than that the math works.
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And there remains no explanation of what causes this behaviour, other than that the math works.
That's literally the entire standard model.
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Oh great, there's one random Slashdot poster who can explain it all. All you need is attitude, right, that's it.
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"there remains no explanation of what causes this behaviour" ... "That's literally the entire standard model." -- hard to be dumber than this.
You know the biggest problem is with stupid people? They do not know they are stupid. On the contrary, they think that everybody else is stupid for not agreeing with their stupid pronouncements. But the proof of your stupidity is right there engraaved on the internet, leaving no room for doubt.
Look, just don't offer opinions about quantum mechanics. Please stick to MM
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"there remains no explanation of what causes this behaviour" ... "That's literally the entire standard model." -- hard to be dumber than this.
Not at all. It's a pure statement of fact.
The Standard Model's explanation for why we have particles at certain energy regimes is simply "The math says there must be"
We then test, and holy shit- there is.
Your ignorance doesn't make my statement dumb.
Go back to school, fuckstick.
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You're a fucking goof. Read the thread again, there are people with a clue in it. Not you,.
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Even Physicists Don’t Understand Quantum Mechanics [nytimes.com] But not to worry because some random asshat on Slashdot thinks he does.
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This shouldn't come as a surprise to anyone, given previous interactions with you.
You have a habit of saying shit so fucking stupid and wrong that one can only assume you walk through your life in a constant haze of confusion.
Don't you have an AMD thread somewhere to go shill? Want to educate us all again about how path-tracing works?
Come on dude. Spare yourself the indignity of the roast. Disappear.
Re: Interesting, try Eugene Khutoryansky (Score:2)
Since you're familiar with PBS Space Time, try this youtube video:
https://www.youtube.com/watch?v=Zlp2GQ3OLeE [youtube.com]
What causes the Pauli Exclusion Principle? by Eugene Khutoryansky.
I won't say I understand it completely either, but this brings me closer than anything else I've seen. From the video:
...if we have an anti-symmetric spatial wavefunction, then when we place the particles together in the same box, the two parts of the wavefunction will cancel each other out, and we will get a probability of zero everywhere...
There's an animation showing this in the video.
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Here's one:
https://physics.stackexchange.... [stackexchange.com]
Basically, you have creation (a) and annihilation (a dagger) operators which operate on "states" (notation |n> where n is the number of particles). Fermions (spin 1/2 particles) and bosons (integer spin particles) follow different statistics.
For bosons, you can create a state with N particles by applying the creation operator N times on the empty ground state |0> so that |1> = a|0> and |2> = a|1> etc. The bosonic creation operator works like a
Re: Interesting, but has one major flaw (Score:5, Informative)
The simple answer: it just is like that. It's an experimental fact of nature that two electrons cannot share the same quantum mechanical properties. Pauli came to realize this when trying to match up electron numbers in the periodic table (or rather: had to make this assumption to be able to create a working theory). Usually, if everything else is the same (the space they're in, the energy levels etc), they at least differ in their spin -- that's a QM property that can be roughly imagined like the electrons "spinning" along their own axis. Arbitrarily, you'd say "+", or "up" for ccw-rotation, and "-" or "down" for clockwise rotation.
The complex answer: after Pauli made this assumtion, a lot of stuff in physics began to just "make sense" if that assumption was true.
There are many ways to derive that formally, but they all came after the postulate of Pauli. There are also some equivalent (mathematical/physical( expressions of the same fact, like:
- Wave functions of Fermions (electrons) are anti-symmetric, i.e. they change signs when two particles are exchanged
- Fermions (electrons) obey the Pauli-Dirac statistics, which can be derived from the Grand-Canonical Ensemble of thermodynamics (you can google that)
- Two electrons on the same energy level in a system must have different spin...
But these are not essential, they are just consequences of their respective mathematics. The essential part is: it just "is" like that, that's what Nature does. And was Pauli who realized / guessed that first.
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We don't really know. All we know is that electrons are represented in a four dimensional space: three spatial coordinates and one spin coordinate (which is _not_ a physical rotation of the electron) and that there is a function, the wavefunction, that describes the behavior of many electrons. This function _must_ be antisymmetric (it must change sign) if you swap two electrons. It is a constraint of nature, specifically of particles with half spin like electrons. Particles that have integer spin (e.g. the
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> Could you kindly point me to something that *actually* explains the "Pauli exclusion priciple"?
This physics video has an excellent visualization of the math: https://www.youtube.com/watch?... [youtube.com]
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The method is interesting, but has two major flaws, which shares with DFT.
The purpose was not to reach perfect accuracy but to be accurate enough to be useful while being computationally relevant. This is similar to how they made a neural network the accurately calculate planetary orbits while considering lots of other bodies. The results it generated were not exact but they were radically faster than existing methods.
The level of accuracy they aiming for is equal to or greater than DFT. However, if you have no constraints on computational power or time then go ahead and compu
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By DFT do you mean Discrete Fourier Transform? Is increasing the degrees of freedom like increasing the sampling rate? The Nyquist rate?
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DFT in this context is Density Functional Theory. Here, you work with functionals of the electronic spatial density.
Re:Interesting, Thanks (Score:1)
Thanks for clarifying that.
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Surely this is the entire problem of the current state of AI. We haven't got a clue what they are doing.
The learning, such as on pictures of cats, appears to create a statistically efficient way to determine if a picture is of a cat.
And it does, and quite well. But sometimes not. And we don't really know why.
Don't even get me started on DFT :-) (Score:5, Interesting)
To the uninitiated: the Schroedinger equation describes the energy (landscape) of a physical system. Basically it has two parts: the kinetic and the potential energy. The kinetic energy is fairly simple, just account for all particles and multiply each by its mass/square-speed ratio like "m/2*v^2" -- Schroedinger is non-relativistic. But the potential energy is complicated for any system with more than 2 particles because all the particles influence all the other particles. So the energy of the system influences its quantum mechanical state, which influences its energy etc...
DFT (Density Functional Theory) is one method to estimate essential parts of the potential energy using cargo cult physics. (Obviously, I'm simplifying a lot here... ;-). You have a few dozen methods to do that, of which, for any given problem, roughly 50% are waaay off, 30% are mostly off, 15% are ??? and 5% are kinda ok-ish. The trick with every problem is to find those 5% -- or invent a new cargo cult method -- which fits your data. Now the issue with DFT is that, if your physical problem changes even slightly, you're back to square 1; you need to find another 5% of methods that fit. If you want to slightly improve your results, you're back to square 1. If you sneeze while you do it, you're back to square 1.
You cannot improve on your previous result because the DFT estimation methods are not based on systematic insights about your system; and if you do happen to find a method that gives good results, you cannot derive any new insights from that, because it's sheer luck that your calculations matched your experiment.
So, what's the value in DFT?
Well... yeah. That is precisely my point :-)
To be fair, DFT always comes in pairs with an experimetnal result: once you have a calculation to match your data, you can publish a paper and say "look, I did the experiment, I have a (DFT-based) solution for a Schroedinger equation, so most likely there's physics inside". This is valuable in and of itself, to a certain degree, because it's better than nothing. Also, it tells you that "simple", straight-forward quantum mechanics is enough for your data (as opposed to: strong quantum correlations, phase transitions, etc).
But that's about it; it adds just as much to actualy physical insight as sneezing on your notebook while TeX-ing a paper would.
So... *shrug*... I guess that means: nice paper, but useless physics they got there. Might be useful to advance AI, though... :-)
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I think you have a bit too pessimistic of a view of DFT. Sure, it has very real limits on what it can actually achieve, and there are a lot of people who think DFT results are gospel, which is bad in my opinion -- but you can actually motivate (but not derive!) DFT from more fundamental principles. The main problem DFT has is that you can't actually quantify the error you're making compared to a true solution of the Schroedinger eqution -- unlike e.g. basic pertubation theory, which typically yields much wo
Re: Don't even get me started on DFT :-) (Score:2)
I don't disagree with most of your criticisms, but I do disagree with the degree to which it applies.
Yeah... well... why let fact get in the way of a good rant, right? *shrug* :-)
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Thanks for that. You explained nicely how DFT fills much the same role in quantum physics as valence bond theory does in chemistry. That is, a bunch of rules of thumb and unreliable heuristics without a whole lot of predictive value. When it breaks, as it does in nearly every interesting situation, someone invents a new bunch of ad hoc rules with no apparent basis in physics.
Re: Interesting, but has one major flaw (Score:5, Informative)
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OK, that might just be a bad analogy, but if there are very small areas of an image having a spectrum of different colors, then a low resolution image would just show a large grey pixel, while moving to higher resolutions would bring the individual colors to light.
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I doubt that you have any idea how many degrees of freedom this model encompasses. Talented bullshitter, enough to convince the casually ignorant.
So it't not really an universal function. (Score:2)
But a specialized function with some SWMM (shitty weight matrix multipication) in it.
Professor Frank Noe (Score:2)
how is it tranined? (Score:2)
TFA states:
"Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei,"
"capable of learning of the complex patterns" ??? My undrestanding of ANN is that you have to feed it a lot of known solutions (assocotions) and then "tune it" so it "answers" correctly for most of the stimulai.
What was the training "stimulai" here?
Thanks for the "news"! (Score:2)
Published three months ago.
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Published three months ago.
Yes but if you do a slashplaceian transform, you’ll see the story frequency is every few weeks.
Exactly who is this Al person anyway? (Score:1)
My opinion (Score:1)