2023.04.23 11:10-11:30 | 中国·重庆

Clearing the Path to Discovery: Detecting and Denoising Gravitational Waves with Deep Learning

王赫

hewang@ucas.ac.cn

中国科学院大学 · 国际理论物理中心（亚太地区）

Reference:

PRD 107.2 (2023): 023021
PRD 107.6 (2023): 063029
PLB (2023): 137904.
arXiv:2212.14283

Gravitational Wave Astronomy

Fundamental physics
- Existence of gravitational waves
- To put constraints on the properties of gravitons
Astrophysics
- Refine our understanding of stellar evolution
- and the behavior of matter under extreme conditions.
Cosmology
- The measurement of the Hubble constant
- Dark energy

GWTC-3

The First GW Event: GW150914

Detecting gravitational waves require a mix of FIVE key ingredients:
1. good detector technology
2. good waveform predictions
3. good data analysis methodology and technology
4. coincident observations in several independent detectors
5. coincident observations in electromagnetic astronomy

—— Bernard F. Schutz

DOI:10.1063/1.1629411

Gravitational Wave Detection

PRL, 2018, 120(14): 141103.

Matched filtering techniques (匹配滤波方法)
- In Gaussian and stationary noise environments, the optimal linear algorithm for extracting weak signals

Convolutional neural networks (CNN) can achieve comparable performance to MF, and outperform them in terms of execution speed (with GPU support).
... under Gaussian stationary noise.

PRD, 2018, 97(4): 044039.

GW Data characteristics:
- Noise: non-Gaussian and non-stationary
- Signal: A low signal-to-noise ratio (SNR) which is typically about 1/100 of the noise amplitude (-60 dB)

Gravitational Wave Detection

改进并开发神经网络模型，以适应真实的引力波观测数据的任务
匹配滤波算法当中的波形模板 $\rightarrow$ 卷积层中的卷积核权重参数
Matched-filtering layer (匹配滤波感知层)
可以准确探测到 GWTC-1 中的 11 个真实引力波事件，甚至包括 GW170817
可以直接应用于空间引力波数据场景，探测 MBHBs

GW170817

GW190412

GW190814

mass distribution

Ruan WH, Wang H, et al. PLB (2023)

Matched-filtering Convolutional Neural Network (MFCNN)

Wang H, et al. PRD (2020)

Gravitational Wave Detection

改进并开发神经网络模型，以适应真实的引力波观测数据的任务
匹配滤波算法当中的波形模板 $\rightarrow$ 卷积层中的卷积核权重参数
Matched-filtering layer (匹配滤波感知层)
“神经网络化”的探测统计量 (匹配滤波信噪比)

Frequency domain

\langle h|h \rangle = 4\int^\infty_0\frac{\tilde{h}(f)\tilde{h}^*(f)}{S_n(f)}df

\langle h|h \rangle = 4\int^\infty_0\frac{\tilde{h}(f)\tilde{h}^*(f)}{S_n(f)}df

\langle d|h \rangle (t) = 4\int^\infty_0\frac{\tilde{d}(f)\tilde{h}^*(f)}{S_n(f)}e^{2\pi ift}df

\langle d|h \rangle (t) = 4\int^\infty_0\frac{\tilde{d}(f)\tilde{h}^*(f)}{S_n(f)}e^{2\pi ift}df

(whitening)

Time domain

(normalizing)

(matched-filtering)

\langle h|h \rangle \sim [\bar{h}(t) \ast \bar{h}(-t)]|_{t=0}

\langle h|h \rangle \sim [\bar{h}(t) \ast \bar{h}(-t)]|_{t=0}

\langle d|h \rangle (t) \sim \,\bar{d}(t)\ast\bar{h}(-t)

\langle d|h \rangle (t) \sim \,\bar{d}(t)\ast\bar{h}(-t)

where $S_n(|f|)$ is the one-sided average PSD of $d(t)$

\bar{S_n}(t)=\int^{+\infty}_{-\infty}S_n^{-1/2}(f)e^{2\pi ift}df

\bar{S_n}(t)=\int^{+\infty}_{-\infty}S_n^{-1/2}(f)e^{2\pi ift}df

\left\{\begin{matrix} \bar{d}(t) = d(t) * \bar{S}_n(t) \\ \bar{h}(t) = h(t) * \bar{S}_n(t) \end{matrix}\right.

\left\{\begin{matrix} \bar{d}(t) = d(t) * \bar{S}_n(t) \\ \bar{h}(t) = h(t) * \bar{S}_n(t) \end{matrix}\right.

In the 1-D convolution ( $*$ ), given input data with shape [batch size, channel, length] :

（A schematic illustration for a unit of convolution layer)

\int\tilde{x}_1(f) \cdot \tilde{x}_2(f) e^{2\pi ift}df= x_1(t)*x_2(t)

\int\tilde{x}_1(f) \cdot \tilde{x}_2(f) e^{2\pi ift}df= x_1(t)*x_2(t)

x_1(t)*x_2^*(-t) = x_1(t)\star x_2(t)

x_1(t)*x_2^*(-t) = x_1(t)\star x_2(t)

\int\tilde{x}_1(f) \cdot \tilde{x}^*_2(f) e^{2\pi ift}df= x_1(t)\star x_2(t)

\int\tilde{x}_1(f) \cdot \tilde{x}^*_2(f) e^{2\pi ift}df= x_1(t)\star x_2(t)

Matched-filtering Convolutional Neural Network (MFCNN)

Wang H, et al. PRD (2020)

Gravitational Wave Detection

改进并开发神经网络模型，以适应真实的引力波观测数据的任务
匹配滤波算法当中的波形模板 $\rightarrow$ 卷积层中的卷积核权重参数
Matched-filtering layer (匹配滤波感知层)
“神经网络化”的探测统计量 (匹配滤波信噪比)
Insight: 引力波信号处理 $\rightarrow$ 智能引力波信号处理

Matched-filtering Convolutional Neural Network (MFCNN)

Wang H, et al. PRD (2020)

An example of transfer function:

CNN

RNN

Gravitational Wave Detection

改进并开发神经网络模型，以适应真实的引力波观测数据的任务
匹配滤波算法当中的波形模板 $\rightarrow$ 卷积层中的卷积核权重参数
Matched-filtering layer (匹配滤波感知层)
“神经网络化”的探测统计量 (匹配滤波信噪比)
The first machine learning gravitational wave signal search challenge (MLGWSC1) https://github.com/gwastro/ml-mock-data-challenge-1