QMC methods often use a matrix to enforce antisymmetry conditions on a fermionic wavefunction. The determinant is needed for the wavefunction itself, and the inverse matrix is used for the local energy.
I wonder if a stochastic matrix algorithm would be useful in the QMC calculations. My guess is that it would not be (and if there is an efficiency gain, it might be offset by the added complexity), but it would be interesting to try, if for no other reason than ideological purity (if you're going to use a stochastic method, might as well make it as stochastic as possible!)
Other interesting questions arise. The locations of the all-important wavefunction nodes will now be fuzzy. What consequences does this have for a fixed-node algorithm?
Inverse matrices also appear in Sorella's Stochastic Reconfiguration method for optimization. Another use?
On a side note, I tried looking for background on Google, but searching for "stochastic matrix inversion" returned results relevant to inverting a stochastic matrix rather than stochastic methods for inverting a matrix.
2 comments:
After reading the paper, a possibly more interesting question is can we use stochastic inversion to obtain ultra-efficient DMC propagators? Presumably, if we knew the exact Green's function for an infinite DMC population we could construct the "perfect" propagator, delivering the stationary distribution in a single propagation. With more realistic populations and a rough guess for the inverse, we might be able to construct a propagator that would converge to the stationary distribution after only a small number of steps.
Interesting idea. I suppose this is similar to an implicit time-stepping method , which allows for longer time steps.
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