Detecting and Denoising Gravitational Wave Signals from Binary Black Holes using Deep Learning Chinthak Murali

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Detecting and Denoising Gravitational Wave Signals from Binary Black Holes using

Deep Learning

Chinthak Murali 1and David Lumley 1, 2

1Department of Physics, The University of Texas at Dallas, Richardson, TX 75080, USA

2Department of Geosciences, The University of Texas at Dallas, Richardson, TX 75080, USA

We present a convolutional neural network, designed in the auto-encoder conﬁguration that can

detect and denoise astrophysical gravitational waves from merging black hole binaries, orders of mag-

nitude faster than the conventional matched-ﬁltering based detection that is currently employed at

advanced LIGO (aLIGO). The Neural-Net architecture is such that it learns from the sparse repre-

sentation of data in the time-frequency domain and constructs a non-linear mapping function that

maps this representation into two separate masks for signal and noise, facilitating the separation of

the two, from raw data. This approach is the ﬁrst of its kind to apply machine learning based grav-

itational wave detection/denoising in the 2D representation of gravitational wave data. We applied

our formalism to the ﬁrst gravitational wave event detected, GW150914, successfully recovering

the signal at all three phases of coalescence at both detectors. This method is further tested on

the gravitational wave data from the second observing run (O2) of aLIGO, reproducing all binary

black hole mergers detected in O2 at both the aLIGO detectors. The Neural-Net seems to have

uncovered a pattern of ’ringing’ after the ringdown phase of the coalescence, which is not a feature

that is present in the conventional binary merger templates. This method can also interpolate and

extrapolate between modeled templates and explore gravitational waves that are unmodeled and

hence not present in the template bank of signals used in the matched-ﬁltering detection pipelines.

Faster and eﬃcient detection schemes, such as this method, will be instrumental as ground based

detectors reach their design sensitivity, likely to result in several hundreds of potential detections in

a few months of observing runs.

Keywords: Gravitational Waves, Black Holes, Machine Learning, Neural Networks

I. INTRODUCTION

The ﬁrst direct detection of a gravitational wave (GW),

GW150914 in 2015 has opened a new window into ob-

serving the universe [1,2]. In the ﬁrst three observing

runs (O1, O2 and O3) of aLIGO [3] and the European

VIRGO detector [4] over the span of 27 months, a total

of 90 CBC (Compact Binary Coalescence) events with an

astrophysical origin probability pastro >0.5 have been de-

tected, as reported in the Gravitational Wave Transient

Catalogues, GWTC-1 [5], GWTC-2 [6] and GWTC-3 [7].

This includes 85 binary black hole (BBH) mergers, four

neutron star black hole (NSBH) mergers and one binary

neutron star (BNS) merger [8]. Hundreds of more de-

tections are expected in the scheduled O4 run of aLIGO

with an enhanced sensitivity [9] and being joined by the

Japanese underground detector KAGRA [10,11]. With

a number of ground based GW detectors under construc-

tion [12,13], the demand for more eﬃcient and reliable

data processing techniques are only getting higher.

aLIGO uses matched-ﬁltering based search to identify

the presence of a GW in the data stream [14]. In this

process, an enormous template bank of signals are cross-

correlated with several months of detector data output,

creating an alert when the matched-ﬁlter signal to noise

ratio (SNR) exceeds the detection threshold of the de-

tection pipeline. Once the presence of a GW is identiﬁed

in the time segment, traditional signal processing tech-

niques are applied to enhance the signal and suppress the

noise, to retrieve the signal from the data stream. The

template with the highest SNR is then used to character-

ize the merger event. A merging BBH system is charac-

terized by eight intrinsic parameters, the two masses and

the two spins (magnitudes and directions) and the ex-

trinsic parameters: the luminosity distance, right ascen-

sion, declination, polarization, inclination, coalescence

time, coalescence phase and two parameters of eccentric-

ity. Sampling a ﬁfteen dimensional parameter space to

characterize each individual GW waveform and perform-

ing matched-ﬁlter analysis with each data segment is not

a trivial computational task [15].

The recent advances in machine learning (ML), namely

Deep Learning (DL), can help us navigate this intense

computational problem. DL is an extremely powerful

machine learning technique that can learn very complex

features and functions through neural networks [16,17].

Convolutional Neural Networks (CNN) is a special class

of neural networks that performs convolution operations

by means of kernel ﬁlters to the input data. During the

training process, the CNN assigns weights to the ﬁlters

that optimally extracts various features from the input

data. As opposed to matched-ﬁltering based search, in

a DL based search, all the intensive computations are

performed only during the training stage of the network,

which is a one time process [18]. This procedure can

also interpolate and in some cases extrapolate between

waveform templates, making it more robust in detecting

GW signals without necessarily training the network on a

15D parameter space. DL based search also opens up the

possibility of detecting GW signals that are outside the

realm of theoretical template banks currently modeled

using Numerical Relativity (NR). Because of the abil-

arXiv:2210.01718v1 [gr-qc] 4 Oct 2022

ity of the neural networks to process data and detect

the GWs orders of magnitude faster, it can be eﬀectively

combined with the matched-ﬁltering based detections to

enhance the conﬁdence of a given detection and also to

eﬃciently target data segments with positive detections

for a subsequent matched-ﬁlter based analysis.

Several ML based analysis of GW data have appeared

in the literature over the past few years, beginning with

glitch classiﬁcation and subtraction [19–24]. DL methods

are ﬁrst applied to direct detection of GWs by George

and Huerta using simulated aLIGO noise [18] and fur-

ther extended to real aLIGO noise, resulted in detect-

ing the presence of the ﬁrst GW, GW150914 [25] in the

data stream. This work has inspired several attempts

to identify and locate GWs in real aLIGO data [26–31]

and many other ML based studies focused on parame-

ter estimation of real GWs [32–35] followed. Denoising

GWs using DL was applied in [36], and the proposed

denoising scheme was able to extract four GW events

(three from Hanford, one from Livingston) with high sig-

nal overlaps. In [37,38] the authors proposed a denois-

ing auto-encoder, based on Recurrent Neural Networks

(RNN) to denoise GWs. Most recently, [39] used 1D

CNN in an auto-encoder conﬁguration to denoise many

of the GWs (three events from O1 and three events from

O2), using whitened data from both the detectors.

Although George and Huerta [18] in the foundational

article suggested that using 2D data in the context of

GW detection is sub-optimal because of the extremely

weak signal strength characteristic of GWs, we are using

2D representation of the data in order to separate signal

from the noise. In our denoising scheme, we use 2D CNN

architecture on raw detector data, with un-whitened sig-

nal templates and noise. This approach, to the best of

our knowledge is the ﬁrst attempt to detect and denoise

GWs from raw data in 2D representation.

In this paper we present a DL framework to detect and

denoise GWs from raw strain data from the aLIGO de-

tectors. The detector noise at both aLIGO detectors are

highly non stationary and non-Gaussian, with very high

noise dominating both ends of the frequency spectrum

[40]. While ambient seismic noise (from ocean, traﬃc,

earthquakes, etc.) dominate the low frequency end of the

noise [41], photon shot noise dominate the high frequency

regime. The real GW signals are extremely weak and are

deeply buried inside the detector noises and occupy the

same frequency band as the detector noise, making it

impossible to separate from the noise using traditional

ﬁltering methods.

In this method, we implement a time-frequency denois-

ing technique used in seismic denoising, which success-

fully separated earthquake signals from ambient noise in

2019 [42] using DL. The noisy strain data is ﬁrst trans-

formed into time-frequency domain using Short Time

Fourier Transform (STFT), rendering the one dimen-

sional time series data into two dimensions, represented

by Fourier coeﬃcients. In the Fourier domain, the coef-

ﬁcients associated with noise are attenuated to enhance

the signal coeﬃcients. These modiﬁed Fourier coeﬃcients

are then transformed back in to the time domain using

inverse Fourier transform and thereby reconstructing the

GW chirp signal in the time domain. The underlying

idea is to promote a sparse representation of the sig-

nal in the time-frequency domain where the signal can

be represented by a sparse set of features which makes

the separation of the signal from the noise easier in the

Fourier domain. This method is especially useful when

the GW signal and the detector noise occupy the same

frequency band, making the ﬁltering techniques virtually

impractical.

II. METHOD

The key here is to ﬁnd a mapping function that can

appropriately ﬁnd a threshold to suppress the coeﬃ-

cients corresponding to the noise in the time-frequency

domain, hence enhance signal separation. These func-

tions are highly non-linear and are hence diﬃcult to con-

struct mathematically for the the GW problem. That is

where DL techniques can be incredibly eﬀective, which

learns to build a high dimensional, non-linear mapping

function from the data alone during the training process.

This Neural-Net learns the sparse representation of the

data in the time-frequency domain, and builds a high-

dimensional, non-linear mapping function which maps

these representations into two masks, one for the GW

signal and another one for all the noises.

The raw GW data from the detector d(t) undergoes

STFT and is represented in the time-frequency domain as

D(t, f), which is a combination of the GW signal S(t, f)

and all the noises N(t, f),

D(t, f) = S(t, f) + N(t, f).(1)

The idea is to construct the mapping functions that can

successfully map the detector data into a representation

of the signal and a representation of the noise separately.

This mapping can be accomplished through a soft thresh-

olding in the sparse representation where the threshold is

estimated by assuming a Gaussian distribution of noise

[43].

From here we construct two individual masks MS(t, f )

and MN(t, s) which act as the mapping functions for the

signal and noise respectively, and are given by,

MS(t, f) = 1

1 + |N(t,f)|

|S(t,f)|

,(2)

MN(t, f) =

|N(t,f)|

|S(t,f)|

1 + |N(t,f)|

|S(t,f)|

.(3)

These masks are the targets for the supervised learning

problem, and they are constructed during the training

process from the training data. The Neural-Net is trained

to construct these masks at the output layer, for every

single data segment that is fed into the network as part

of the training data. Once these masks are constructed,

they can be multiplied with the 2D detector data D(t, f)

to reconstruct the signal and noise as follows.

MS(t, f)×D(t, f)∼S(t, f),(4)

MN(t, f)×D(t, f)∼N(t, f).(5)

These reconstructed signal and noise are inverse trans-

formed back into the time domain to reproduce the one

dimensional time series of signal and noise,

ST F T −1(S(t, f)) = S(t),(6)

ST F T −1(N(t, f)) = N(t).(7)

The denoising process aims to ﬁnd the true GW signal

Sfrom the data by minimising the mean squared error

between the true signal and the estimated signal, calcu-

lated as,

Error = || ˆ

S−S||2.(8)

The masks MS(t, f) and MN(t, f) have the same di-

mension as the input data D(t, f) and take values be-

tween 0 and 1 and are mutually exclusive (MN= 1−MS).

The entire process of signal and noise separation is pre-

sented as a sequence in Figure 2.

A. Neural-Net Architecture

Auto-encoders are a class of artiﬁcial neural networks

that can learn to code patterns from unlabelled data (un-

supervised learning), typically for dimensionality reduc-

tion [44]. The encoder part of the auto-encoder maps

the representation to a code and the decoder part recon-

structs the coded representation. Because of the ability

of auto-encoders to learn a sparse representation of the

data, our Neural-Net is designed as a series of fully con-

nected 2 dimensional convolutional layers with descend-

ing and then ascending sizes, like an auto-encoder, as

shown in Figure 1. Skip connections are used to improve

convergence during the training process [45], which are

represented as over-head arrows connecting the encoder

and decoder layers of same dimensions. In addition to

improving the convergence, skip connections helped to

minimize the signal leakage into the noise.

The input to the Neural-Net is through two channels

: one takes the real part of the Fourier coeﬃcients and

the other takes the imaginary part of the Fourier coeﬃ-

cients. This enables the Neural-Net to learn from both

the amplitude and phase information of the data. These

inputs go through a series of 2D convolutional layers of

constantly decreasing dimensions, where each layer uses

a Rectiﬁed Linear Unit (ReLU) activation function and

are Batch Normalized. The dimensions of the convolu-

tional layers are reduced using a stride of 2 ×2 and the

kernel size of each layer remains at 3×3. Each of the con-

volutional layers extract features from the data and learn

to represent the data more and more sparsely as they go

along the layers. At the bottleneck layer, we have the

smallest and sparsest representation of the data possible

and then it goes through the deconvolutional layers which

generates a high-dimensional, non-linear mapping of this

sparse representation into output masks. The output la-

bels are the masks created for the signal (MS) and for

the noise (MN). During the training process, the network

learns to generate the masks that optimally separates sig-

nal from noise by minimizing a loss function, which is a

binary cross-entropy loss function. A softmax normalized

exponential function is used at the ﬁnal layer to produce

the output masks. Figure 1shows the Neural-Net archi-

tecture which takes the inputs through two channels and

generates two outputs, one of which is the familiar GW

chirp signal in the time-frequency domain.

B. Training Strategy

The data used for training is the publicly available GW

strain data from the Gravitational Wave Open Science

Center (GWOSC [46]). These are continuous recordings

at both the aLIGO detectors over the course of the ﬁrst

three observing runs. We used the data from O1 to train

the network to detect the event GW150914 and data from

O2 to train the network for the rest of the events. From

a few hours of continuous noise recordings, we generated

diﬀerent realizations of the noise to create a larger noise

set, to make the Neural-Net more adaptive to variations

in noise. Data from GWOSC is sampled at 4096Hz and

are 4096s long data segments. We down-sampled the

data into 2048Hz and divided them into eight second

long data segments in the training phase. These eight

second long data segments are pure noise where there is

no known GW event reported so far, or any hardware

injection, often used for calibration purposes. We ap-

plied a lower frequency cut-oﬀ of 30Hz for this analysis

as all the events detected so far are above this frequency.

This noise is then combined with simulated GW signals,

modeled using the optimised Eﬀective One Body Numer-

ical Relativity waveform SEOBNRv4 opt [47] (an opti-

mized version of SEOBNRv4 [48]) sampled at 2048Hz

with masses ranging from 5Mto 80M. For the analy-

sis we assumed optimal orientation of both detectors with

the event, also spins and eccentricities are assumed to

be zero. This makes the analysis essentially two dimen-

sional, where the signals are characterized by individual

masses of the binary, which to the ﬁrst order, captures

the essence of the GW signal.

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DetectingandDenoisingGravitationalWaveSignalsfromBinaryBlackHolesusingDeepLearningChinthakMurali1andDavidLumley1,21DepartmentofPhysics,TheUniversityofTexasatDallas,Richardson,TX75080,USA2DepartmentofGeosciences,TheUniversityofTexasatDallas,Richardson,TX75080,USAWepresentaconvolutionalneuralnetwork,d...

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Detecting and Denoising Gravitational Wave Signals from Binary Black Holes using Deep Learning Chinthak Murali

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