[HN Gopher] Lattice Gauge Equivariant Convolutional Neural Networks
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       Lattice Gauge Equivariant Convolutional Neural Networks
        
       Author : amai
       Score  : 25 points
       Date   : 2022-02-03 15:44 UTC (2 days ago)
        
 (HTM) web link (journals.aps.org)
 (TXT) w3m dump (journals.aps.org)
        
       | Llamamoe wrote:
       | Translated into a human language, this means what exactly?
        
         | lumost wrote:
         | They defined a neural network operation which can in principal
         | learn to approximate certain equations used in Nuclear physics
         | and other quantum field theories.
         | 
         | Approximating QFT/Nuclear physics is a very difficult task
         | given current algorithms, so this opens potential doors for
         | learning "faster" approximations which allow simulating more
         | complex systems. Of course, defining the error in this
         | approximation becomes quite difficult. They claim the following
         | in their paper.
         | 
         | 1. A theoretical proof that the new operation can approximate
         | the relevant equations.
         | 
         | 2. An evaluation of the model trained against a traditional
         | simulation on both equal sized and "larger sized" problems.
         | Unfortunately they only summarize this as a "High degree of
         | accuracy" and present charts. I'd love to see a summary table
         | of results with a final numeric accuracy evaluation.
        
         | savant_penguin wrote:
         | They summarize it in the abstract
         | 
         | "At the heart of this network structure is a novel
         | convolutional layer that preserves gauge equivariance while
         | forming arbitrarily shaped Wilson loops in successive bilinear
         | layers."
         | 
         | Much simpler
        
         | tempay wrote:
         | I've found a surprising lack of accessible content about
         | lattice QCD however it's about simulating the smallest scales
         | in the universe. The calculations are computationally
         | infeasible however you can get useful results from
         | approximiting them in a grid of cells and seeing how it evolves
         | over time. This is still incredibly complex and typically needs
         | the largest supercomputers they can find. Personally I'm a
         | little sceptical that it will be possible to use neural network
         | based approximations to produce physically meaningful results
         | with well understood errors but time will tell.
         | 
         | If you're so inclined, I think this video gives a nice
         | description of lattice QCD:
         | 
         | https://www.youtube.com/watch?v=J3xLuZNKhlY
        
           | evanb wrote:
           | When my collaborators and I published our LQCD computation of
           | the nucleon axial coupling I wrote this
           | http://evanberkowitz.com/2018/05/30/gA.html though I did not
           | get into the technical details of gauge invariance.
           | 
           | We can use neural networks in some steps but not in others.
           | The main use seems to be in the generation of gauge
           | configurations (states of the Markov chains we use). We can
           | use neural networks there because we alway do our Metropolis-
           | Hastings accept/reject step according to the 'true' action,
           | which corrects any numerical errors introduced by the ML
           | approximation.
           | 
           | There are different approaches for this. I've been working on
           | incorporating ML into HMC; see eg.
           | https://arxiv.org/abs/2006.11221. For an approach based on
           | normalizing flows, search for Shanahan eg al.
           | 
           | Happy to answer questions, but it's late and I'm about to go
           | to sleep. Feel free to ask away and I will do my best in the
           | morning. Or email me.
        
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