Detecting Gravitational Waves using Deep Learning

What is a Gravitational Wave?

Albert Einstein in his theory of relativity predicted the existence of gravitational waves. The general theory of relativity stated that the mass bends space-time curvature, creating gravity and space-time tells mass how to move. Space-time fabric is a four-dimensional quantity including the three normal dimensions and a fourth dimension of time! 

Consider Earth as a ball with a specific mass and space-time as an elastic sheet of rubber (or a trampoline). If we place Earth at the center of this sheet, then it will obviously bend the sheet creating a curvature. Now, place a smaller ball with less mass, and call it the Moon. If we place the moon on the sheet, then will not directly collide with the Earth, rather it will travel in rotational motion around the Earth, before colliding. This simple movement of the smaller ball (Moon) revolving around the larger ball (Earth) explains the formation of gravity. 

We all know, for any binary system in the universe, gravity is the main reason for their circular motions. But, Einstein also stated that this movement also creates ripples in space-time creating gravitational waves. Like a ripple in a pond, the gravitational wave also spreads out through the universe. These waves usually possess a fraction of energy from the source. 

How to detect these waves?

As stated above, these waves carry energy, they stretch and squeeze space, causing objects to move closer and then farther. Detecting such waves is a challenging task. However, special instruments called gravitational wave detectors are used for this purpose. These instruments are highly sensitive, developed especially for the purpose of detecting low-energy waves like the gravitational wave. When a GW travels through these detectors, it causes the distance between mirrors within the detector to change. Scientists precisely measure this distance to identify a gravitational wave.

Some famous and widely regarded GW detectors are listed below:

1. Laser Interferometer Gravitational-Wave Observatory (LIGO): LIGO is a ground-based gravitational wave observatory consisting of two identical detectors located in Livingston, Louisiana, and Hanford, Washington, in the United States. LIGO made the first direct detection of gravitational waves in 2015.
2. Virgo: Virgo is a gravitational wave detector located in Cascina, Italy. It is part of the global network of detectors and collaborates closely with LIGO.
3. KAGRA: KAGRA (Kamioka Gravitational Wave Detector) is a gravitational wave detector located in the Kamioka Observatory in Japan. It is an underground interferometer, making it less susceptible to environmental noise.
4. LISA (Laser Interferometer Space Antenna): LISA is a space-based gravitational wave observatory currently under development by the ESA. It will consist of three spacecraft flying in formation, using laser interferometry to detect gravitational waves in space.

It is interesting to note that the source of gravitational waves is usually a massive object like a black hole or a neutron star. However, the stretching and squeezing created by these waves are usually at the atomic scale. Also, GW travels at the speed of light.  

Background

In 2015 LIGO detected the first GW from the merger of a binary black hole. Since the addition of the advanced VIRGO (AdVirgo) detector, there have been numerous detections of GWs from similar systems. Recently, GWs from a binary neutron star merger were observed, along with an associated gamma-ray burst, and subsequent follow-up observations across the electromagnetic spectrum. In the near future, with the KAGRA interferometer joining LIGO and VIRGO in joint observations, we can expect many more detections of GWs from similar compact binary coalescence (CBC) systems.  

Apart from CBCs, another type of astrophysical event that holds potential as sources for aLIGO, AdVirgo, and KAGRA interferometers are massive stars in the range of 10-100 M⊙. These stars, during their zero-age main sequence, undergo core-collapse supernovae (CCSNe) as they reach the end of their lives. These CCSNe events are also considered potential targets for the aforementioned gravitational wave detectors.

The reason behind the formation of such supernovae is still a subject of intense research. However, two main mechanisms are considered as a reason for such events. These are the neutrino-driven mechanism and the magnetorotational mechanism. The majority of the observed CCSNe can be explained by the neutrino mechanism. 

Accurately categorizing the GW signals from a CCSN is crucial for gaining insights into the explosion mechanism. Since GWs are generated in the central core of a CCSN, they have the potential to directly convey information about the CCSN itself. Therefore, GWs serve as a valuable tool for investigating the explosion mechanism responsible for their production.

Researchers have devised methods and algorithms to detect and classify signals originating from CCSNe. One such technique is principle component analysis, which involves creating a set of component basis vectors derived from a larger collection of CCSN waveforms associated with a specific mechanism. These basis vectors capture the common features shared by those waveforms, allowing for efficient identification and classification of CCSN signals.

Implementing Deep Learning

Researchers have used this set of data (signals) to create and train a CNN for the efficient detection of gravitational waves. One advantage of employing a CNN for GW signal detection is its relatively low computational cost compared to traditional methods. The computational burden is mainly concentrated during the training phase of the CNN, where extensive calculations are performed beforehand to optimize the network's performance. As a result, when the CNN is applied for actual GW signal detection, it tends to be computationally efficient.

The CNN model developed by Chan, Heng, and Chris Messenger used input data as waveforms from the magnetorotational and neutrino-driven mechanisms. They develop a CNN with the objective of classifying detector time series into three distinct categories: magneto-rotational signals with background noise, neutrino-driven signals with background noise, and pure background noise. The CNN is designed to accurately distinguish between these classes based on the input time series data.

Using both mechanisms as an input source created a huge set of data. When incorporating waveforms from various studies, the distribution of waveforms becomes more diverse, covering a broader parameter space. This increased variability in the data poses a challenge for CNN's learning process. Consequently, the performance of the trained CNN on testing samples appeared inferior compared to using a dataset generated from a subset of waveforms.

However, the advantage of including a larger parameter space is that it compels the CNN to learn the common features present across different waveforms, rather than relying solely on a subset. Consequently, the trained network becomes more adept at recognizing and handling waveforms with unexpected characteristics, which are more likely to occur in real-world scenarios. In essence, the broader range of waveforms encountered during training allows the CNN to generalize better and perform more effectively when confronted with novel waveform patterns.

The CNN architecture developed consists of 8 convolutional layers, three max-pooling layers, and three fully-connected layers. The identification of waveform is a multiclass classification problem. Hence they used categorical cross entropy as a loss function while training the model.

Conclusion

In the training, validation, and testing of the CNN, a dataset consisting of 1.26 × 10^6 samples of simulated time series was utilized. These allowed the model to train efficiently. The final simulations and results showed that the CNN can be used efficiently for the detection of gravitational waves from different sources. Further research might prove that not only from CCSNe but GWs from black hole collision, binary neutron star mergers, or gamma-ray bursts can also be detected using CNNs.