Using deep learning to localize gravitational wave sources
In this paper, we report on the construction of a deep Artificial Neural Network (ANN) to localize simulated gravitational wave signals in the sky with high accuracy. We have modelled the sky as a sphere and have considered cases where the sphere is divided into 18, 50, 128, 1024, 2048 and 4096 sectors. The sky direction of the gravitational wave source is estimated by classifying the signal into one of these sectors based on it's right ascension and declination values for each of these cases. In order to do this, we have injected simulated binary black hole gravitational wave signals of component masses sampled uniformly between 30-80 solar mass into Gaussian noise and used the whitened strain values to obtain the input features for training our ANN. We input features such as the delays in arrival times, phase differences and amplitude ratios at each of the three detectors Hanford, Livingston and Virgo, from the raw time-domain strain values as well as from analytical versions of these signals, obtained through Hilbert transformation. We show that our model is able to classify gravitational wave samples, not used in the training process, into their correct sectors with very high accuracy (>90%) for coarse angular resolution using 18, 50 and 128 sectors. We also test our localization on test samples with injection parameters of the published LIGO binary black hole merger events GW150914, GW170818 and GW170823 for 1024, 2048 and 4096 sectors and compare the result with that from BAYESTAR and Parameter Estimation (PE). In addition, we report that the time taken by our model to localize one GW signal is around 0.018 secs on 14 Intel Xeon CPU cores.