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It is due to computing resources. LQCD calculations consume a large fraction of all the world's supercomputing, and there's never enough to go around. The pro
by evanb 9y ago
It is due to computing resources. LQCD calculations consume a large fraction of all the world's supercomputing, and there's never enough to go around.
The procedure is essentially an evaluation of a millions-of-dimensions-large integral via Markov-chain Monte Carlo. Each step in the Markov chain requires inverting extremely large ill-conditioned matrices, which we can make better-conditioned by moving away from physical parameters (and then trying to extrapolate). People are glad to have only hundreds or thousands of independent samples in an ensemble. You need ensembles for multiple lattice spacings and spatial volumes in order to ensure you can control your discretization and finite-volume artifacts when you extrapolate to the continuum and to infinite volume.
What is generated in the Markov chain is essentially the configurations of the gluons and quark loops. With these configurations in hand we can measure physical observables on each.
Observables with baryons have an exponentially bad signal-to-noise problem in the temporal direction (time on the grid, not Monte Carlo time) and you either need an exponentially large computer, an exponentially long time, or an exponentially wealthy funding agency. There are attempts to circumvent this issue, we'll see how successful they prove...
- effie 9y agoIs it really necessary to invert those matrices? Often that is possible, but not the best way to find the solution of the problem: https://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/ https://www.johndcook.com/blog/2010/01/19/dont-invert-that-m...
- msds 9y agoPresumably, an ensemble of nuclear theorists, particularly those dedicating their lives to making big LQCD calculations, would avoid inverting large ill-conditioned matrices, if that was a clever thing to do. I know a few QFT types - they tend to be decently intelligent and mathematically capable. Ok, they're more like wickedly smart...
- evanb 9y agoIt depends on the computational step. Often we "just" need to compute the determinant, in which case we use a trick. In some other cases, we do only need linear solves. Exact inversion of the whole thing is often prohibitive.