Optimizing the placement of numerical relativity simulations using a mismatch predicting neural network

Gravitational wave observations from merging compact objects are becoming commonplace, and as detectors improve and gravitational wave sources become more varied, it is increasingly important to have dense and expansive template banks of predicted gravitational waveforms. Since numerical relativity is the only way to fully solve the nonlinear merger regime of general relativity for comparably massed systems, numerical relativity simulations are critical for gravitational wave detection and analysis. These simulations are computationally expensive, with each simulation placing one point within the high dimensional parameter space of binary black hole coalescences. This makes it important to have a method of placing new simulations in ways that use our computational resources optimally while ensuring sufficient coverage of the parameter space. Accomplishing this requires predicting the impact of a new set of parameters before performing the simulation. To this effect, this paper introduces a neural network to predict the mismatch between the gravitational waves of two binary systems. Using this network, we then show how we can propose new numerical relativity simulations that will provide the most benefit. We also use the network to identify gaps in existing public catalogs and identify degeneracies in the binary black hole parameter space.

Figure 1

Diagram showing the structure of the neural network including the input parameters ($\eta$, $a_{1x}$, $a_{1y}$, $a_{1z}$, $a_{2x}$, $a_{2y}$, $a_{2z}$ for each of the two binary systems) and the output (the mismatch between the gravitational waves emitted from the two systems). The network consists of 15 hidden layers, each with 56 nodes.

Figure 2

Coverage of the parameter space by NR simulations in training (blue), development (orange), and test sets (green).

Figure 3

The error in the predicted mismatch for the waveforms in the test set.

Figure 4

The mean absolute error in the mismatch for the test set binned by the symmetric mass ratio. The blue represents the first system and the orange represents the second system.

Figure 5

The mean absolute error in the mismatch for the test set binned by the difference in the symmetric mass ratio between the two systems.

Figure 6

The mean absolute error in the mismatch for the test set binned by the magnitudes of the spins of the primary (left) and secondary (right) black holes. The blue represents the first system and the orange represents the second system.

Figure 7

The mean absolute error in the mismatch for the test set binned by ${\chi }_{\mathrm{eff}}$ (left) and ${\chi }_p$ (right). The blue represents the first system and the orange represents the second system.

Figure 8

The mean absolute error in the mismatch for the test set binned by the components of the spin. The blue represents the first system and the orange represents the second system.

Figure 9

Suggested simulations, selected so as to maximize their mismatch with existing simulations. Blue points are existing simulations from the maya catalog, and red points are suggested new simulations. The shade denotes a point’s mismatch with its nearest neighbor at the time it is suggested, with darker being a higher mismatch.

Figure 10

Randomly sampled points whose mismatch with their nearest neighbor in existing public NR waveform catalogs is greater than 0.1.

Figure 11

Mismatch between a reference simulation and other simulations throughout the parameter space. All simulations considered here have BH spins aligned with the orbital angular momentum. The black dot in each panel denotes the reference simulation. From left to right, the reference simulations have symmetric mass ratios of $\eta =0.1$, 0.16, 0.25, and from top to bottom, the reference simulations have ${\chi }_{\mathrm{eff}}=-0.5$, 0, 0.5.