Artificial Intelligence Reduces a 100,000-Equation Quantum Physics Problem to Only Four Equations
Fnord666 writes:
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 Medvidovi, Alessandro Toschi, et al. Deep Learning the Functional Renormalization Group, Physical Review Letters (DOI: 10.1103/PhysRevLett.129.136402)
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