Low-discrepancy sequences for gravitational-wave template banks
Paper: T. Kumar and A. S. Sengupta, Stochastic template banks for GW searches using low-discrepancy sequences
arXiv:2607.18633
Template-bank construction is usually formulated as a covering problem: we want a set of waveforms such that every physically relevant signal lies sufficiently close to at least one template.
A common approach is stochastic placement. Candidate points are drawn randomly from the parameter space and retained only when they are sufficiently far from the templates already accepted.
Random sampling is simple, but it is not particularly uniform. It naturally produces both clusters and gaps, and many proposals are wasted in regions that have already been well covered.
Low-discrepancy sequences provide an alternative. Sequences such as Sobol and Halton are constructed to fill a multidimensional domain more uniformly than independent random points.
The idea we explore is therefore straightforward: retain the usual stochastic acceptance criterion, but replace the random proposal sequence by a low-discrepancy sequence.
The final number of templates need not change dramatically. The more interesting quantity is the number of candidate points required to reach a given level of coverage. In our tests, low-discrepancy proposals reduce this initial sampling cost, with the improvement depending on dimension and on how the physical parameter space is mapped into the sampling coordinates.
This is useful because the proposal stage becomes increasingly expensive as the dimension of the intrinsic parameter space grows. The method is also easy to combine with geometric pruning and parallel template-bank construction.