Monte Carlo Variance Reduction

Weight windows, importance biasing, and splitting that let Kronos resolve deep-shield and rare-channel quantities without brute force.

Why brute force is not enough

Monte Carlo error falls as one over the square root of the history count, so halving the error costs four times the compute. For deep-shield fluxes and rare reaction channels, the burner's 5.44 percent neutron fraction or the flux behind thick breeder shielding, analog sampling almost never reaches the region of interest. Variance reduction is what makes these quantities affordable.

Importance and weight windows

Kronos assigns spatial and energy-dependent importance so particles heading toward the tally region are split into more, lower-weight particles, while those heading away are played roulette. Weight windows bound particle weights in each cell, keeping the population productive where it matters and thin where it does not, without biasing the expected result.

• Geometry splitting and Russian roulette by cell importance
• Weight windows over space and energy
• Source biasing toward rare neutron-producing channels
• Adjoint-informed importance maps for deep penetration

Adjoint-informed importance

The most powerful maps come from an adjoint (importance) calculation: a cheap deterministic solve of the adjoint transport equation estimates how much each region contributes to the target tally, and that field becomes the importance function for the forward Monte Carlo. This couples a deterministic pre-pass to the stochastic run, a hybrid method Kronos uses for the hardest shielding problems.

Variance reduction is unbiased in expectation but must be validated. A badly tuned importance map can produce a confident-looking answer that is wrong, so Kronos checks the figure-of-merit, error times compute time, and the tally's statistical health across batches before trusting a reduced-variance result.

The payoff is decisive for both machines. It lets the breeder shielding and burner DEC-train shielding be resolved to useful precision on tractable compute, and it is what keeps the burner's small-but-real neutron load from requiring an impossible number of analog histories.