Deep Learning Helps Detect Gravitational Waves

In 1915, Albert Einstein helped build a geometric description of gravity through his general theory of relativity.​​​​ “But any new theory that aims to replace an existing (Newtonian) theory should provide experimentally verifiable predictions that are unique to it,” says Dr. Nikhil Mukund, a scientist at the Max Planck Institute for Gravitational Physics.

​​​Albert Einstein’s theory of relativity predicted gravitational waves as ripples in space-time. These waves can help us measure properties such as distance, mass, and the spin of astronomical objects, including neutron stars and black holes.

In 1916, the instruments did not exist to measure the gravitational waves resulting from astrophysical events such as the collision of two stars. In the following decades, scientists and engineers gradually developed the technology​​ required to measure these elusive​​ waves.

“In the late ’60s and early ’70s, interferometric techniques were investigated and were found to be a viable solution,” Mukund says. “If you push the right technology and suppress the different noises, you can effectively detect perturbations the size of around ​​one ten-thousandth the diameter of a proton. And that will be​​ sufficient to detect events such as two merging black holes or two merging neutron stars at a few hundred megaparsecs.”

Laser interferometers are devices that extract information from disturbances in the trajectory of laser beams. An interferometer splits a beam into two components. These beams will travel several kilometers and reflect off two mirrors and recombine​​ at the beam splitter, leading to constructive or destructive interference. Propagating gravitational waves will introduce a relative phase shift between these beams, changing the final interference pattern. These very minuscule perturbations indicate gravitational waves caused by phenomena such as black holes or neutron star collisions.

“This detection opened a new window to the universe. Until then, we had an electromagnetic way of looking at the universe with telescopes in multiple wavelengths ranging from radio waves to gamma rays,” Mukund says. “We found a new way to observe these exotic objects such as black holes, which have ​​no electromagnetic signature. I would say ​​it’s just as exciting as the invention of the optical telescope in the 1600s. We now have almost 100 confirmed detections of these sources, with many more to come.”

Detecting Black Holes with Neural Networks

“Although the aim was to detect very sensitive astrophysical signals, in the last 50 years or so, the R&D efforts have led to the development of​​ highly accurate sensors and actuators,” Mukund says.

Some of the developed technologies include active and passive seismic vibration isolation systems to keep optics unperturbed, low-noise laser systems, and interferometry-based optical alignment sensors.

“Although we have astrophysics and cosmology as the primary ​​aim, many of the developed technologies​​ are useful to the general community,” Mukund says.

​​​“The gravitational wave community and data analysis community has developed models to solve Einstein’s equation,” Mukund says. “We have analytical post-Newtonian, phenomenological, and numerical relativity–based methods to generate the signals from two colliding binary black holes or neutron stars.”

The researchers applied these​​ mathematical models to synthesize the data needed to train their machine learning models. To make the data realistic, they added the kind of noise picked up by LIGO-like detectors.

Mukund used Deep Learning Toolbox™ to select and fine-tune a neural network for his application. In this case, he found that the Inception convolutional neural network was a suitable architecture for gravitational wave detection. With Deep Learning Toolbox, his team​​ configured and retrained the Inception-v3 network on his data set to classify interferometer signals.

“We had started this work during the final year of my Ph.D. and had to experiment with different network architectures in a limited amount of time,” Mukund said. “Support for different architectures and GPU computing helped reduce the time it took to search across all these different models.”

“It was truly fascinating,” Mukund says​​. “Not only did the trained network recover all the previously reported GW events, but it also helped us to claim the detection of a previously missed binary blackhole event.”

​​Tackling the Control Problem

“There are multiple degrees of freedom, and we need to minimize the jitter even before we start the experiments,” Mukund says.

To adjust the mirrors, scientists establish hundreds of control loops that run in parallel, with extra care taken to minimize the cross-couplings between all the optics.

“We are trying to assess if we can build a data-driven control strategy that can perform at the level of human-engineered filters and maybe even go beyond,” Mukund says.

Reinforcement learning differs from other machine learning methods because it is based on actions, states, and rewards. A reinforcement learning agent is presented with an environment and a set of actions. It must learn to take sequences of actions that result in the optimal state and maximize its reward.

“The first step in designing the reinforcement learning control strategy is to sense the misalignments,” Mukund says. “The traditional way to measure this is to use wavefront sensors. Instead, we used a neural sensor​​ composed of convolutional and LSTM layers, which measures misalignments by analyzing the video from cameras placed in the optomechanical layout.”

The sensing neural network, created using Deep Learning Toolbox, became the component that determines the state of the environment. The action space was the adjustments made to the optics. And the reward function was designed based on the principles of classic control theory to optimize for actions that improve mirror alignment.

“The nice thing about this reward function was that I could automatically generate part of it using Simulink Design Optimization™,” Mukund says. “We gave it our model specifications, such as bandwidth, design performance, robustness, and speed. Simulink Design Optimization is nicely integrated with Reinforcement Learning Toolbox™, and it was able to generate a template reward to which we added our physics knowledge.”

“One of the benefits of MATLAB^® was that I could iterate across different reinforcement learning algorithms quickly, which greatly reduced the time it took to reach the final choice,” Mukund says. “I determined the soft actor-critic algorithm was the optimal solution for the control problem.”

Modeling the ​Environment

“AI is a very interesting and fast-growing field, and people in the gravitational waves community are excited about it,” Mukund says. “In the past five years, we have used deep learning extensively for data analysis. We are now at the stage where we want to use reinforcement learning in the control part of our work. The technology still must stand up to the hype that surrounds it. But I see a lot of promise here. The next generation of gravitational wave detectors, like the Einstein Telescope and the Cosmic Explorer, will be much more sophisticated. Artificial intelligence and reinforcement learning, in particular, will be indispensable tools to tackling these challenges.​​”