Artificial intelligence reduces a 100,000-equation quantum physics problem to only four equations

phys.org ^ | SEPTEMBER 26, 2022 | Thomas Sumner,

[BenLurkin]

For even a modest number of electrons and cutting-edge computational approaches, the problem requires serious computing power. That's because when electrons interact, their fates can become quantum mechanically entangled: Even once they're far apart on different lattice sites, the two electrons can't be treated individually, so physicists must deal with all the electrons at once rather than one at a time. With more electrons, more entanglements crop up, making the computational challenge exponentially harder.

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

[Hootowl99]

The math logic for working with interactions will make your head spin. Back in day while in college, I had a prof that had an equation of state (ideal gas law) with modifications incorporating multi component interactions named after him. Much more than half a dozen interactions, you had to switch to a computer to do the work. It took lots of sheets of paper to work this by hand for the simplest of cases.

I can’t imagine the computer horsepower to do 100,000 interactions. I wonder if the derivation strategy for these new equations could hint of possible paths for applications going beyond the electron entanglement system in the OP article.

[Governor Dinwiddie]

I've been told that every moon mission had slide rules aboard for sanity checks.

[Mathews]

6th...

[SunkenCiv]

Thanks BenLurkin.

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