Deep Learning Networks & Gravitational Wave Signal Recognization

He Wang (王赫)  

[hewang@mail.bnu.edu.cn]

Department of Physics, Beijing Normal University

In collaboration with Zhou-Jian Cao

Aug 23rd, 2019

The 23rd KAGRA face-to-face meeting @Toyama

• Problems
  • Current matched filtering techniques are computationally expensive.
  • Non-Gaussian noise limits the optimality of searches.
  • Un-modelled signals?

A trigger generator \(\rightarrow\) Efficiency+ Completeness + Informative

Background

• Solution:
  • Machine learning (deep learning)
  • ...

Introduction

• Existing CNN-based approaches:
  • Daniel George & E. A. Huerta (2018)
  • Hunter Gabbard et al. (2018)
  • X. Li et al. (2018)
  • Timothy D. Gebhard et al. (2019)​​

Related works

Introduction

• Our main contributions:
  • A brand new CNN-based architecture (MF-CNN)
  • Efficient training process (no bandpass and explicit whitening)
  • Effective search methodology (only 4~5 days on O1)
  • Fully recognized and predicted precisely (<1s) for all GW events in O1/O2

Motivation

MF-ConvNet Model

Convolutional neural network (ConvNet or CNN)

Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012)

Matched-filtering (cross-correlation with the templates) can be regarded as a convolutional layer with a set of predefined kernels.

Is it matched-filtering?

Motivation

MF-ConvNet Model

Matched-filtering (cross-correlation with the templates) can be regarded as a convolutional layer with a set of predefined kernels.

• In practice, we use matched filters as an essential component in the first part of CNN for GW detection.

Convolutional neural network (ConvNet or CNN)

Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2012)

Architechture

\(\bar{S_n}(t)\)

MF-ConvNet Model

\(\bar{S_n}(t)\)

In the meanwhile, we can obtain the optimal time \(N_0\) (relative to the input) of feature response of matching by recording the location of the maxima value corresponding to the optimal template \(C_0\)

Architechture

MF-ConvNet Model

Experiments & Results

Dataset & Templates

• We use SEOBNRE model [Cao et al. (2017)] to generate waveform, we only consider circular, spinless binary black holes.

(In preprint)

• The background noises for training/testing are sampled from a closed set (33x4096s) in the first observation run (O1) in the absence of the segments (4096s) containing the first 3 GW events.

62.50M⊙ + 57.50M⊙ (\(\rho_{amp}=0.5\))

• A sample as input

Experiments & Results

Dataset & Templates

(In preprint)

• We use SEOBNRE model [Cao et al. (2017)] to generate waveform, we only consider circular, spinless binary black holes.

• The background noises for training/testing are sampled from a closed set (33x4096s) in the first observation run (O1) in the absence of the segments (4096s) containing the first 3 GW events.

• Mass distribution of dataset / templates / events

Search methodology

Experiments & Results

(In preprint)

• Every 5 seconds segment as input of our MF-CNN with a step size of 1 second.
• The model can scan the whole range of the input segment and output a probability score.
• In the ideal case, with a GW signal hiding in somewhere, there should be 5 adjacent predictions for it with respect to a threshold.

Search methodology

Experiments & Results

(In preprint)

Input

• Every 5 seconds segment as input of our MF-CNN with a step size of 1 second.
• The model can scan the whole range of the input segment and output a probability score.
• In the ideal case, with a GW signal hiding in somewhere, there should be 5 adjacent predictions for it with respect to a threshold.

Experiments & Results

(In progress)

Population property on O1

• Sensitivity estimation
  • Background: using time-shifting on the closed set from real LIGO recordings in O1
  • Injection: random simulated waveforms

• Statistical significance on O1
  • Count a group of adjacent predictions as one "trigger block".
  • For pure background (non-Gaussian), monotone trend should be observed.
  • In the ideal case, with a GW signal hiding in somewhere, there should be 5 adjacent predictions for it with respect to a threshold.

Number of Adjacent prediction

Experiments & Results

(In progress)

Population property on O1

• Sensitivity estimation
  • Background: using time-shifting on the closed set from real LIGO recordings in O1
  • Injection: random simulated waveforms

• Statistical significance on O1
  • Count a group of adjacent predictions as one "trigger block".
  • For pure background (non-Gaussian), monotone trend should be observed.
  • In the ideal case, with a GW signal hiding in somewhere, there should be 5 adjacent predictions for it with respect to a threshold.

Number of Adjacent prediction

a bump at 5 adjacent predictions

Experiments & Results

(In preprint)

• Recovering all GW events in both O1 and O2

Experiments & Results

(In preprint)

• Recovering all GW events in both O1 and O2

Summary

• Some benefits from MF-CNN architechure

  • Simple configuration for GW data generation

  • Almost no data pre-processing

  • Works on non-stationary background

  • Easy parallel deployments, multiple detectors can be benefit a lot from this design

  • More templates / smaller steps for searching can improve further
• Main understanding of the algorithms:
  • GW templates are used as likely features for matching
  • Generalization of both matched-filtering and neural networks
  • Matched-filtering can be rewritten as convolutional neural layers

Summary

• Some benefits from MF-CNN architechure

  • Simple configuration for GW data generation

  • Almost no data pre-processing

  • Works on non-stationary background

  • Easy parallel deployments, multiple detectors can be benefit a lot from this design

  • More templates / smaller steps for searching can improve further
• Main understanding of the algorithms:
  • GW templates are used as likely features for matching
  • Generalization of both matched-filtering and neural networks
  • Matched-filtering can be rewritten as convolutional neural layers

Thank you for your attention!