Variance of a converged model about ferminet HOT 7 CLOSED

from ferminet.

Thanks for the quick response! Could you give an order of magnitude for the variance, as running the experiment is quite costly on GPU time? 10^-3, 10^-4, ...?

from ferminet.

Note that the variance logged is just the variance over the batch. This is sometimes (but rarely) a useful diagnostic and is extremely noisy, especially for relatively small batch sizes and large systems (your H2 calculation is probably in the opposite regime, with a comparatively large batch size for a small system).

From the logged output, you can calculate the mean and variance of the local energy quite easily. In both cases, serial correlation needs to be removed. The CASINO manual is (as ever) excellent on such technical details.

from ferminet.

For a ballpark estimate, our papers report a typical standard error of O(10^{-5}) Ha from O(10^5) Metropolis-Hastings steps. The correlation time is not reported but it's usually not large for VMC. Either way, this gives an upper bound on the variance of these calculations.

from ferminet.

Thanks for the estimate and insights. Does O(10^5) Metropolis-Hastings steps refer to the number of actual steps, the number of samples or the number of batches since these all differ by orders of magnitude?

from ferminet.

The calculations in our papers typically used 10^4-10^5 energy evaluations (averaged over the batch of walkers, usually of O(2^12)), with O(10) Metropolis-Hastings steps between each energy evaluation. The standard error was calculated from the set of energy evaluations.

from ferminet.

Thanks for the details!

from ferminet.