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Research Notes:

Gravitational Waves

Machine Learning Analysis

Specific Focus: Detecting/Estimating Eccentricity

With Dr Elaha Khalouei & Prof Hyung Mok Lee

Center for Gravitational-Wave Universe, SNU

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Inspiral Events

Current templated searches for gravitational waves (GWs) emanated from compact binary coalescences (CBCs) assume that the binaries have circularized by the time they enter the sensitivity band of the LIGO-Virgo-KAGRA (LVK) network.

However, certain formation channels predict that in future observing runs (O4 and beyond), a fraction of detectable binaries could enter the sensitivity band with a measurable eccentricity e.

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Formation mechanisms for eccentric inspiral events

Samsing, MacLeod, & Ramirez-Ruiz

ApJ 784, 2014

In the near future it is expected that a significant number of inspiral events with non-negligible eccentricity will be detected by LIGO-VIRGO

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Machine Learning: Eccentricity

We are attempting to create a fast detection method to determining if a GW event has eccentricity

We generate events with realistic noise for various

  • Masses
  • Distances
  • Eccentricities
  • But Not Spin!

We use Python based code: PyCBC (compact binary coalescence, CBC)

Approximate numerical schemes

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Machine Learning: Eccentricity

e=0.0

e=0.4

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Spectrogram: Distance to Source

GWs are like the luminosity distance

M1 = M2 = 10M☉

D= 100Mpc

D= 500Mpc

D= 1000Mpc

D= 2000Mpc

The more distant the source, the weaker the signal, the more difficult to detect

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Spectrogram: Eccentricity

e=0.0

e=0.1

M1 = M2 = 10M☉

Distance = 100Mpc

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Spectrogram: Eccentricity

e=0.0

e=0.4

M1 = M2 = 10M☉

Distance = 100Mpc

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CNN

We work with 2D spectrograms (256x256) i.e. (time x freq)

Generate 20,000 events with � - Masses in Uniform(10 , 80) Msun� - Distances Uniform(100 , 2000) Mpc� - eccentricities in Uniform(0.0 , 0.4)�

Split into 90%/10% training and testing

Define a 4 layer CNN + ANN as regression for event eccentricity�Other event parameters are essentially marginalised over / ignored.

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CNN: Preliminary result

Don't like these departures from the true values at high and low ecc.

So I will try a custom loss function that gives extra weight to the Mean-Squared-Error (MSE) for high and low ecc

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CNN: Preliminary result

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CNN: Preliminary result

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Test the trained network

ecc=0

ecc=0.1

ecc=0.2

Can we reduce the widths of these distributions

-> lower final errorbar

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Transfer Learning (ImageNET)

Transfer Learning

Fine Tuning

Model = Xception (20M parameters)

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Transfer Learning (ImageNET)

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Transfer Learning (ImageNET)

Transfer Learning

Fine-Turning

  • Previously I was generating events up to 500Mpc, which resulted in too many high SNR events
  • Now changed to 0 < D < 2Gpc

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Transfer Learning (ImageNET)

  • Previously I was generating events up to 500Mpc, which resulted in too many high SNR events
  • Now changed to 0 < D < 2Gpc
  • Looks like ecc detectable for ecc>0.1 (exact calculation later)�Similar to LIGO collaboration estimates.