Deep Learning for Gravitational-Wave Data Analysis: A Resampling White-Box Approach

• Main Authors: Manuel D. Morales, Javier M. Antelis, Claudia Moreno, Alexander I. Nesterov
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Sensors
• Subjects: gravitational waves; Deep Learning; convolutional neural networks; binary black holes; LIGO detectors; probabilistic binary classification
• Online Access: https://www.mdpi.com/1424-8220/21/9/3174

In this work, we apply Convolutional Neural Networks (CNNs) to detect gravitational wave (GW) signals of compact binary coalescences, using single-interferometer data from real LIGO detectors. Here, we adopted a resampling white-box approach to advance towards a statistical understanding of uncertainties intrinsic to CNNs in GW data analysis. We used Morlet wavelets to convert strain time series to time-frequency images. Moreover, we only worked with data of non-Gaussian noise and hardware injections, removing freedom to set signal-to-noise ratio (SNR) values in GW templates by hand, in order to reproduce more realistic experimental conditions. After hyperparameter adjustments, we found that resampling through repeated <i>k</i>-fold cross-validation smooths the stochasticity of mini-batch stochastic gradient descent present in accuracy perturbations by a factor of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3.6</mn></mrow></semantics></math></inline-formula>. CNNs are quite precise to detect noise, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.952</mn></mrow></semantics></math></inline-formula> for H1 data and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.932</mn></mrow></semantics></math></inline-formula> for L1 data; but, not sensitive enough to recall GW signals, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.858</mn></mrow></semantics></math></inline-formula> for H1 data and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0.768</mn></mrow></semantics></math></inline-formula> for L1 data—although recall values are dependent on expected SNR. Our predictions are transparently understood by exploring tthe distribution of probabilistic scores outputted by the softmax layer, and they are strengthened by a receiving operating characteristic analysis and a paired-sample t-test to compare with a random classifier.