臺灣博碩士論文加值系統

As the improvement of gravitational wave detectors, gravitational
wave events become more and more popular which opens a new win-
dow of astronomy. In 2017, a binary neutron star event, GW170817,
has been detected through the gravitational wave and also the electro-
magnetic signal. After that, people start to consider an efficient way
to detect the GW and extract its dynamics parameters. In this thesis,
we construct a Bayesian inference based on deep learning machine,
CVAE, for the parameter estimation of binary black hole coalescence.
This machine can obtain the inference of 5-dimensional parameters of
the GW event within one second, where the parameters are two com-
ponent mass m1 , m2 , luminosity distance dL , and time and phase of
coalescence (tc , φ0 ). Since the noise of real detectors varies from time
to time, in contract to previous CVAE envelopments, we train our
machine not only by strain data but also the corresponding amplitude
spectrum density, which is used to characterize the noise background.
We find our machine can obtain the compatible result in comparison
to traditional PE algorithm even with the noise drift, which means
the noise background varies event by event. Finally, we apply our
machine to the LIGO/Virgo third observing run (O3) events to test
the performance of our machine against real data.

Contents
1 Introduction 1
1.1 Background of gravitational wave observation 1
1.1.1 background 1
1.1.2 Basic data analysis for gravitational wave 4
1.1.3 Parameters Estimation 5
1.1.4 Introduction to Markov Chain Monte Carlo and nested sampling 7
1.2 Background of deep learning and autoencoder 9
1.2.1 Basic concept of deep learning 9
1.2.2 Conditional variational autoencoder 10
1.2.3 Normalizing flow 13
1.2.4 MNIST as an example 16
1.3 Applications of deep learning to GW data analysis 19
1.3.1 Application to low latency detection 20
1.3.2 Application to parameter estimation 21
2 Review of Parameter estimation by CVAE 23
2.1 Parameter estimation by CVAE 23
2.1.1 The cost function 23
2.1.2 The training procedure 25
2.1.3 Observation 27
2.2 Parameter estimation with autoregressive neural network 31
2.2.1 Autoregressive flow 33
2.2.2 Combined models 35
2.2.3 Observation 36
3 Universal CVAE model with PSD condition 39
3.1 Motivation 39
3.2 Preparation of training data 40
3.3 The detailed structure of CVAE model 42
3.4 Training the CVAE Model and the Performance 44
3.5 Application to O3 events 53
3.6 Summary of chapter 3 56
4 Conclusion 58
Glossaries and Acronyms 60
Bibliography 62

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