STROOPWAFEL: an algorithm to efficiently sample rare astrophysical events.

Gravitational-wave observations of double compact object mergers are rapidly providing new insights into the physics of massive stars and the evolution of binary systems [1,2,3].  The distributions of the inferred masses and spins of the black holes and neutron stars contain valuable information about their origin. Distinguishing different theories for their formation and learning about the complex physical processes that govern the lives of their possible massive-star progenitors requires comparing observed populations with theoretical predictions.

However, theoretical simulations of the population of merging double compact objects are challenging because gravitational-wave events represent an extremely rare outcome of binary evolution. From a thousand massive binary systems typically only of order one, or less, yields a double compact object [4]. A meaningful comparison with population observations requires simulating a statistically significant sample of events.  Modeling binaries over cosmological volumes whilst exploring the uncertain physics requires running computationally expensive binary population synthesis simulations with billions of binaries that cost millions of CPU hours.

To make it feasible to simulate such large numbers of systems, all present-day simulations pay a high price. In many studies computational speed is ensured by using highly approximate algorithms that treat the physical processes in a simplified way. Another way to keep the computational costs reasonable is to limit the total number of simulations, restricting the exploration of the impact of the uncertain physical input assumptions beyond a few variations ​

To overcome this issue we developed the algorithm STROOPWAFEL: Sampling The Rare Outcome Of Populations With AIS* For Efficient Learning. We have designed STROOPWAFEL to improve the efficiency of simulations of rare astrophysical events, and so to enable accurate simulations of populations of extremely rare events at reasonable computational cost.

*AIS: Adaptive Importance Sampling

We find that STROOPWAFEL can increase the number of binaries of a target population that are found in a simulation by factors of about 25 – 200 when using our STROOPWAFEL sampling algorithm compared to simulations with traditional sampling. The  figure on the left showcases this for the black hole-neutron star simulation. The figure presents the number of systems formed from the target population as a function of total number of sampled binaries, for both our sampling method and traditional birth distribution Monte Carlo sampling. For this simulation the gain is a factor 53.  

The increase in computational efficiency from STROOPWAFEL leads to finding substantially more events of the target population which naturally enables a much higher resolution mapping of both the input and output parameter spaces. An example is shown above, which demonstrates how the parameter space is explored in far greater detail using our sampling method compared to traditional birth distribution Monte Carlo sampling. The figure shows the location of the target population in the initial parameter space of primary mass m_1,i and separation  a_i at birth. With our  STROOPWAFEL sampling method we obtain more detailed contours and more contour levels that map the initial parameter space with higher resolution. This leads to better knowledge of the initial conditions of a binary system that yield a binary of the target population. Physically the structures seen in the input parameter space correspond to the assumed physics of the different formation channels leading to compact-object mergers. More details are discussed in  [5,6,7].

The STROOPWAFEL code is publicly available. The algorithm is described and published in Broekgaarden et al., 2019. All data used in this study is publicly available, as well as jupyter notebooks to reproduce all figures and the code to reproduce the paper and tables.   

STROOPWAFEL is currently implemented in COMPAS and has already been used in studies including in work on population predictions for common-envelope events in the formation of double neutron stars by Vigna-Gómez et al., 2019 and for a study in forming binary black hole mergers in the upper black hole mass gap with super-Eddington accretion by van Son et al, 2020. Several other studies using STROOPWAFEL are in prep.