2024年5月13日, 15:00 | 辽宁 · 沈阳 · 东北大学

Frontiers of AI in Gravitational Wave Astronomy

王赫 (He Wang)

hewang@ucas.ac.cn

中国科学院大学 · 国际理论物理中心（亚太地区）

中国科学院大学 · 引力波宇宙太极实验室（北京/杭州）

On behalf of the LIGO-VIRGO-KAGRA collaborations

From Data Processing to Scientific Discovery

Content

GW Astronomy
AI for Science · GW Data Analysis
GW search · Pipeline
Parameter estimation · Scientific discovery
Key Takeaways
(Space-based GW Detection)

In 1916, A. Einstein proposed the GR and predicted the existence of GW.
Gravitational waves (GW) are a strong field effect in the GR.
- 2015: the first experimental detection of GW from the merger of two black holes was achieved.
- 2017: the first multi-messenger detection of a BNS signal was achieved, marking the beginning of multi-messenger astronomy.
- 2017: the Nobel Prize in Physics was awarded for the detection of GW.
- As of now: more than 90 gravitational wave events have been discovered.
- O4, which began on May 24th 2023, is currently in progress.

Gravitational waves generated by binary black holes system

GW detector

LIGO-VIRGO-KAGRA network

2017 Nobel Prize in Physics

Gravitational Wave Astronomy

Technical Challenges: Data Processing for GW

GW Data characteristics

Noise: non-Gaussian and non-stationary
Signal:
- (Earth-based) A low signal-to-noise ratio (SNR) which is typically about 1/100 of the noise amplitude (-60 dB).
- (Space-based) A superposition of all GW signals (e.g.: $10^4$ of GBs, $10\sim10^2$ of SMBHs, and $10\sim10^3$ of EMRIs, etc.) received during the mission's observational run.

Matched filtering techniques (匹配滤波方法)

In Gaussian and stationary noise environments, the optimal linear algorithm for extracting weak signals
Works by correlating a known signal model $h(t)$ (template) with the data.
Starting with data: $d(t) = h(t) + n(t)$ .
Defining the matched-filtering SNR $\rho(t)$ :
$\rho^2(t)\equiv\frac{1}{\langle h|h \rangle}|\langle d|h \rangle(t)|^2$ , where $\langle d|h \rangle (t) = 4\int^\infty_0\frac{\tilde{d}(f)\tilde{h}^*(f)}{S_n(f)}e^{2\pi ift}df$ ,
$\langle h|h \rangle = 4\int^\infty_0\frac{\tilde{h}(f)\tilde{h}^*(f)}{S_n(f)}df$ , $S_n(f)$ is noise power spectral density (one-sided).

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LIGO-VIRGO-KAGRA

LISA / Taiji project

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Pioneering works utilizing CNN

The most common and direct approach, from Computer Vision (CV) to GW signal processing: pixel point $\Rightarrow$ sampling point.

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

AI for Science $\rightarrow$ AI for GW Astronomy

Artificial Intelligence (AI) has great potential to revolutionize gravitational wave astronomy by improving data analysis, modeling, and detector development.
Representation and supervised learning crucially extract features from GW signals, autonomously identifying informative features and leveraging labeled data for accuracy.

Text

Exported: Oct, 2023 (in preparation)

PRL, 2018, 120(14): 141103.

PRD, 2018, 97(4): 044039.

引力波数据处理：人工智能技术应用

Data Preprocessing and Training Strategy

\frac{d-mean}{std} = \frac{h}{std}+\frac{n-mean}{std}

\frac{d-mean}{std} = \frac{h}{std}+\frac{n-mean}{std}

Strain

Whiten

Normalized

∼ $10^{−19}$

∼ $10^{2}$

∼ $10^{0}$

32 s

merger

$t_c$ (around GW150914)

\oplus

\oplus

(Cal network SNR)

Band-pass: [20, 2048] Hz

Patching (tokenized) with size 0.125 s and overlap 50%

[1, 128, 256]

(Standard normalization)

dynamic masking

[1, 16512]

[1, 128, 256]

(PSD $_i$ from noise)

Band-pass: [20, 2048] Hz

WaveFormer

MSE-Loss $_i$

$std$

[1, 128, 256]

Noise $_i$ :

Signal $_i$ :

Input $_i$ :

Label $_i$ :

Output $_i$ :

8.0625 s

Given $d = h + n$ , we can normalize $d$ as follows:

Implementations:
- PSD sampling from real noise.
- input size: 8.0625 sec
- fs = 2048Hz
- Band-pass: 20~2048Hz
- Masked loss

Search Strategy Overview

Firstly, we obtain the denoised output by utilizing Waveformer. Then, triggers are defined and identified by three steps including,
- Find Peaks. Locate triggers on a single detector by finding its maximum all local-maximum (0.2s away from neighboring maximum/local-maximum).
- By constraining triggers that exist on both two detectors, we get VALID triggers. (consist 3~4 segments)
- Calculate the correlation of the to-be-evaluated trigger across channels or within a single channel, between its noisy and corresponding denoised segments, as well as between denoised segments themselves.

L^2(\text{Corr}^{\text{ab}}(n))

L^2(\text{Corr}^{\text{ab}}(n))

\text{Corr}^{{{H}\bar{H}}}(n)

\text{Corr}^{{{H}\bar{H}}}(n)

\text{Corr}^{{{L}\bar{L}}}(n)

\text{Corr}^{{{L}\bar{L}}}(n)

\text{Corr}^{\text{ab}}(n) = \max^{i\in[-2,2],i\in\mathbb{Z}}_{t\in[i\Delta t-\epsilon,i\Delta t+\epsilon]} \langle \bar{h}^a_{(n)}(t)|\bar{h}^b_{(n+i)}(t)\rangle\,, a,b\in(H,L,\bar{H}, \bar{L})

\text{Corr}^{\text{ab}}(n) = \max^{i\in[-2,2],i\in\mathbb{Z}}_{t\in[i\Delta t-\epsilon,i\Delta t+\epsilon]} \langle \bar{h}^a_{(n)}(t)|\bar{h}^b_{(n+i)}(t)\rangle\,, a,b\in(H,L,\bar{H}, \bar{L})

\bar{t}_{a}(n) =\text{argmax}_t \,h^a_{(n)}(t)

\bar{t}_{a}(n) =\text{argmax}_t \,h^a_{(n)}(t)

\text{Valid}_{\bar{t}_{a}(n)}(n, n+1) = \begin{cases} 1 & \text{ if } |\bar{t}_{a}(n) - \bar{t}_{a}(n+1)| < 0.1 \text{ ms}\\ 0 & \text{ if } \text{otherwise} \end{cases}

\text{Valid}_{\bar{t}_{a}(n)}(n, n+1) = \begin{cases} 1 & \text{ if } |\bar{t}_{a}(n) - \bar{t}_{a}(n+1)| < 0.1 \text{ ms}\\ 0 & \text{ if } \text{otherwise} \end{cases}

\text{Corr}^{{\bar{H}\bar{H}}}(n),\text{Corr}^{{\bar{L}\bar{L}}}(n),\text{Corr}^{{\bar{H}\bar{L}}}(n),\text{Corr}^{{H\bar{H}}}(n),\text{Corr}^{{L\bar{L}}}(n),\text{Corr}^{{H\bar{L}}}(n),\text{Corr}^{{L\bar{H}}}(n)

\text{Corr}^{{\bar{H}\bar{H}}}(n),\text{Corr}^{{\bar{L}\bar{L}}}(n),\text{Corr}^{{\bar{H}\bar{L}}}(n),\text{Corr}^{{H\bar{H}}}(n),\text{Corr}^{{L\bar{L}}}(n),\text{Corr}^{{H\bar{L}}}(n),\text{Corr}^{{L\bar{H}}}(n)

noisy input segments

denoised output segments

$\bar{H}$

$\bar{L}$

${H}$

${L}$

\rho_\text{ranking}

\rho_\text{ranking}

Significance Estimates

Assessed denoising workflow performance by comparing with GWTC-1, GWTC-2, GWTC2.1, and GWTC-3 catalogs and associated data releases.
Noted significant divergence in IFAR distribution between our results and those from GWTC and OGC catalogs.
Achieved significant IFAR improvement across all 75 reported BBH events, indicating effective suppression of loud terrestrial noise.
- Example: For low SNR ( $10.8_{-0.4}^{+0.3}$ ) event GW200208_130117, obtained an IFAR of 8916 years, surpassing maximum IFAR of <4000 years in other catalogs.
Variability in IFAR improvement linked to the original data's noise nature, including its non-Gaussian, non-stationary characteristics, and different signal recognition strategies by pipelines.
IFAR performance significantly depends on the reduction of non-Gaussian noise near each event.
- Events with substantial IFAR improvement had misleading non-Gaussian noise effectively eliminated.
- Events where IFAR underperforms retained non-Gaussian characteristics, possibly due to WaveFormer's inherent systematic errors.

GW search · Pipeline

Exploring Beyond General Relativity

Much of the discussion on model generalization has been within the GR framework. Our collaboration with 东北大学 on beyond General Relativity (bGR) aims to demonstrate AI's potential advantages in detecting signals that surpass GR's limitations.

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Harsh Narola, et al. “Beyond General Relativity: Designing a Template-Based Search for Exotic Gravitational Wave Signals.” PRD 107, 2 (2023): 024017.

Yu-Xin Wang, et al. "Draft in Progress"

iFAR [years]

Sensitivity dfistance [Mpc]

\begin{aligned} \psi & \sim \frac{3}{128 \eta}(\pi f M)^{-5 / 3} \sum_{i=0}^n \textcolor{red}{\varphi_i^{\mathrm{GR}}}(\pi f M)^{i / 3} \\ \varphi_i & \rightarrow\left(1+\delta \varphi_i\right) \textcolor{red}{\varphi_i^{\mathrm{GR}}} \end{aligned}

\begin{aligned} \psi & \sim \frac{3}{128 \eta}(\pi f M)^{-5 / 3} \sum_{i=0}^n \textcolor{red}{\varphi_i^{\mathrm{GR}}}(\pi f M)^{i / 3} \\ \varphi_i & \rightarrow\left(1+\delta \varphi_i\right) \textcolor{red}{\varphi_i^{\mathrm{GR}}} \end{aligned}

B. P. Abbott et al. (LIGO-Virgo), PRD 100, 104036 (2019).

AI for Gravitational Wave: Parameter Estimation

A complete 15-dimensional posterior probability distribution, taking about 1 s (<< $10^4$ s).

Prior Sampling: 50,000 Posterior samples in approximately 8 Seconds.

Capable of calculating evidence
Processing time: (using 64 CPU cores)
- less than 1 hour with IMRPhenomXPHM,
- approximately 10 hours with SEOBNRv4PHM

PRL 127, 24 (2021) 241103.

PRL 130, 17 (2023) 171403.

Nature Physics 18, 1 (2022) 112–17

Big Data Mining and Analytics 5, 1 (2021) 53–63.

A diagram of prior sampling between feature space and physical parameter space

（Based on 1912.02762）

【【机器学习】白板推导系列(三十三) ～流模型(Flow based Model)】

Normalizing Flow Model (1/4)

The main idea of flow-based modeling is to express $\mathbf{y}\in\mathbb{R}^D$ as a transformation $T$ of a real vector $\mathbf{z}\in\mathbb{R}^D$ sampled from $p_{\mathrm{z}}(\mathbf{z})$ :

\mathbf{y}=T(\mathbf{z}) \quad \text { where } \quad \mathbf{z} \sim p_{\mathrm{y}}(\mathbf{z})

\mathbf{y}=T(\mathbf{z}) \quad \text { where } \quad \mathbf{z} \sim p_{\mathrm{y}}(\mathbf{z})

Note: The invertible and differentiable transformation $T$ and the base distribution $p_{\mathrm{z}}(\mathbf{z})$ can have parameters $\{\boldsymbol{\phi}, \boldsymbol{\psi}\}$ of their own, i.e. $T_{\phi}$ and $p_{\mathrm{z},\boldsymbol{\psi}}(\mathbf{z})$ .

Change of Variables:

p_{\mathrm{y}}(\mathbf{y})=p_{\mathrm{z}}(\mathbf{z})\left|\operatorname{det} J_{T}(\mathbf{z})\right|^{-1} \quad \text { where } \quad \mathbf{u}=T^{-1}(\mathbf{x}) .

p_{\mathrm{y}}(\mathbf{y})=p_{\mathrm{z}}(\mathbf{z})\left|\operatorname{det} J_{T}(\mathbf{z})\right|^{-1} \quad \text { where } \quad \mathbf{u}=T^{-1}(\mathbf{x}) .

J_{T}(\mathbf{z})=\left[\begin{array}{ccc} \frac{\partial T_{1}}{\partial \mathrm{z}_{1}} & \cdots & \frac{\partial T_{1}}{\partial \mathrm{z}_{D}} \\ \vdots & \ddots & \vdots \\ \frac{\partial T_{D}}{\partial \mathrm{z}_{1}} & \cdots & \frac{\partial T_{D}}{\partial \mathrm{z}_{D}} \end{array}\right]

J_{T}(\mathbf{z})=\left[\begin{array}{ccc} \frac{\partial T_{1}}{\partial \mathrm{z}_{1}} & \cdots & \frac{\partial T_{1}}{\partial \mathrm{z}_{D}} \\ \vdots & \ddots & \vdots \\ \frac{\partial T_{D}}{\partial \mathrm{z}_{1}} & \cdots & \frac{\partial T_{D}}{\partial \mathrm{z}_{D}} \end{array}\right]

Equivalently,

The Jacobia $J_{T}(\mathbf{u})$ is the $D \times D$ matrix of all partial derivatives of $T$ given by:

p_{\mathrm{y}}(\mathbf{y})=p_{\mathrm{z}}\left(T^{-1}(\mathbf{y})\right)\left|\operatorname{det} J_{T^{-1}}(\mathbf{y})\right|

p_{\mathrm{y}}(\mathbf{y})=p_{\mathrm{z}}\left(T^{-1}(\mathbf{y})\right)\left|\operatorname{det} J_{T^{-1}}(\mathbf{y})\right|

p_{\mathrm{y}}(\mathbf{y})

p_{\mathrm{y}}(\mathbf{y})

p_{\mathrm{z}}(\mathbf{z})

p_{\mathrm{z}}(\mathbf{z})

\mathbf{z}

\mathbf{z}

\mathbf{y}

\mathbf{y}

T

T

T^{-1}

T^{-1}

base density

target density

（Based on 1912.02762）

Normalizing Flow Model (2/4)

Data: target data $\mathbf{y}\in\mathbb{R}^{15}$ (with condition data $\mathbf{x}$ ).
Task:
- Fitting a flow-based model $p_{\mathrm{y}}(\mathbf{y} ; \boldsymbol{\theta})$ to a target distribution $p_{\mathrm{y}}^{*}(\mathbf{y})$
- by minimizing KL divergence with respect to the model’s parameters $\boldsymbol{\theta}=\{\boldsymbol{\phi}, \boldsymbol{\psi}\}$ ,
- where $\boldsymbol{\phi}$ are the parameters of $T$ and $\boldsymbol{\psi}$ are the parameters of $p_{\mathrm{z}}(\mathbf{z})=\mathcal{N}(0,\mathbb{I})$ .
Loss function:
Assuming we have a set of samples $\left\{\mathbf{y}_{n}\right\}_{n=1}^{N}\sim p_{\mathrm{y}}^{*}(\mathbf{y})$ ,

Minimizing the above Monte Carlo approximation of the KL divergence is equivalent to fitting the flow-based model to the samples $\left\{\mathbf{y}_{n}\right\}_{n=1}^{N}$ by maximum likelihood estimation.

\mathcal{L}(\boldsymbol{\theta}) \approx-\frac{1}{N} \sum_{n=1}^{N} \log p_{\mathrm{z}}\left(T^{-1}\left(\mathbf{y}_{n} ; \boldsymbol{\phi}\right) ; \boldsymbol{\psi}\right)+\log \left|\operatorname{det} J_{T^{-1}}\left(\mathbf{y}_{n} ; \boldsymbol{\phi}\right)\right|+\mathrm{const.}

\mathcal{L}(\boldsymbol{\theta}) \approx-\frac{1}{N} \sum_{n=1}^{N} \log p_{\mathrm{z}}\left(T^{-1}\left(\mathbf{y}_{n} ; \boldsymbol{\phi}\right) ; \boldsymbol{\psi}\right)+\log \left|\operatorname{det} J_{T^{-1}}\left(\mathbf{y}_{n} ; \boldsymbol{\phi}\right)\right|+\mathrm{const.}

p_{\mathrm{y}}(\mathbf{y})

p_{\mathrm{y}}(\mathbf{y})

p_{\mathrm{z}}(\mathbf{z})

p_{\mathrm{z}}(\mathbf{z})

\mathbf{z}

\mathbf{z}

\mathbf{y}

\mathbf{y}

T

T

T^{-1}

T^{-1}

base density

target density

\begin{aligned} \mathcal{L}(\boldsymbol{\theta}) &=D_{\mathrm{KL}}\left[p_{\mathrm{y}}^{*}(\mathbf{y}) \| p_{\mathrm{y}}(\mathbf{y} ; \boldsymbol{\theta})\right] \\ &=-\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathbf{y}}(\mathbf{y} ; \boldsymbol{\theta})\right]+\text { const. } \\ &=-\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathrm{z}}\left(T^{-1}(\mathbf{y} ; \boldsymbol{\phi}) ; \boldsymbol{\psi}\right)+\log \left|\operatorname{det} J_{T^{-1}}(\mathbf{y} ; \boldsymbol{\phi})\right|\right]+\mathrm{const} . \end{aligned}

\begin{aligned} \mathcal{L}(\boldsymbol{\theta}) &=D_{\mathrm{KL}}\left[p_{\mathrm{y}}^{*}(\mathbf{y}) \| p_{\mathrm{y}}(\mathbf{y} ; \boldsymbol{\theta})\right] \\ &=-\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathbf{y}}(\mathbf{y} ; \boldsymbol{\theta})\right]+\text { const. } \\ &=-\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathrm{z}}\left(T^{-1}(\mathbf{y} ; \boldsymbol{\phi}) ; \boldsymbol{\psi}\right)+\log \left|\operatorname{det} J_{T^{-1}}(\mathbf{y} ; \boldsymbol{\phi})\right|\right]+\mathrm{const} . \end{aligned}

\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathbf{y}}^{*}(\mathbf{y} ; \boldsymbol{\theta})\right]

\mathbb{E}_{p_{\mathbf{y}}^{*}(\mathbf{y})}\left[\log p_{\mathbf{y}}^{*}(\mathbf{y} ; \boldsymbol{\theta})\right]

Rational Quadratic Neural Spline Flows
(RQ-NSF)

Train

\vec\theta = (m_1,m_2,d_L, ...) \in P_{prior}

\vec\theta = (m_1,m_2,d_L, ...) \in P_{prior}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

nflow

\vec{z} \Rightarrow \mathbb{N}(0,\mathbb{I})

\vec{z} \Rightarrow \mathbb{N}(0,\mathbb{I})

Normalizing Flow Model (3/4)

归一化流模型示意图

Test

\vec\theta = (m_1,m_2,d_L, ...) \in P_{posterior}

\vec\theta = (m_1,m_2,d_L, ...) \in P_{posterior}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

nflow

\vec{z} \in \mathbb{N}(0,\mathbb{I})

\vec{z} \in \mathbb{N}(0,\mathbb{I})

Train

\vec\theta = (m_1,m_2,d_L, ...) \in P_{prior}

\vec\theta = (m_1,m_2,d_L, ...) \in P_{prior}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

\vec{x}=\vec{h}_{\vec{\theta}} + \vec{n}

nflow

\vec{z} \Rightarrow \mathbb{N}(0,\mathbb{I})

\vec{z} \Rightarrow \mathbb{N}(0,\mathbb{I})

Normalizing Flow Model (4/4)

Bayesian inference, the Holy Grail of gravitational-wave data analysis,
enables astrophysical interpretation and scientific discoveries.

Simulation-Based Inference (SBI)

SBI $\Rightarrow$ Fast and precise parameter estimation.
SBI $\Rightarrow$ TGR / Cosmology / PTA ...

Text

PRL 127, 24 (2021) 241103.

PRL 130, 17 (2023) 171403.

Real-time gravitational wave science with neural posterior estimation

Sampling with prior knowledge for high-dimensional gravitational wave data analysis

He Wang, et al. Big Data Min. Anal. (2021)

PRD 108, 4 (2023): 044029.

Neural Posterior Estimation with Guaranteed Exact Coverage: The Ringdown of GW150914

arXiv:2310.13405, LIGO-P2300306

Cosmological Inference using Gravitational Waves and Normalising Flows

Parameter estimation · Scientific discovery

Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows

arXiv:2310.12209

He Wang, et al. (2024)

Normalizing Flows as an Avenue to Studying Overlapping Gravitational Wave Signals

DOI: 10.1103/PhysRevLett.130.171402

PRL 131, 17 (2023): 171403.

Angular Power Spectrum of Gravitational-Wave Transient Sources as a Probe of the Large-Scale Structure

Parameter estimation · Scientific discovery

PRD 108, 4 (2023): 044029.

Text

Appreciating the Ringdown Overtone Test of GW150914

A notable work involves ringdown overtone testing, which, acknowledging the difficulty in achieving DINGO-like precision for complex waveforms, leverages the speed advantage of AI.
By simulating the signal and $10^3$ realizations of LIGO noise for each pixel, it accomplishes what is impossible for MCMC methods, prioritizing speed over precision in a strategic trade-off.

Parameter estimation · Scientific discovery

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Exploring Stochastic Gravitational Wave Background with AI

Utilizing AI for parameter estimation in the stochastic gravitational wave background (SGWB) presents a fascinating blend of rich theoretical content and the potential for optimizing current data processing methods.
While still preliminary and ongoing, our work shows promising results for high SNR SGWB scenarios, where AI-based posterior probabilities are notably more precise and narrower compared to traditional cross-correlation methods used in PyGWB.

\Omega_{\mathrm{GW}}(f)=\Omega_{\mathrm{ref}}\left(\frac{f}{f_{\mathrm{ref}}}\right)^\alpha

\Omega_{\mathrm{GW}}(f)=\Omega_{\mathrm{ref}}\left(\frac{f}{f_{\mathrm{ref}}}\right)^\alpha

\Omega_{\mathrm{ref}}=10^{-6.1}

\Omega_{\mathrm{ref}}=10^{-6.1}

Our result (preliminary)

Parameter estimation · Scientific discovery

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Exploring Stochastic Gravitational Wave Background with AI

Performance saturation is observed between SNR levels of $10^{-6}$ to $10^{-7}$ , indicating a plateau in model effectiveness in low SNR conditions.
Unlike PyGWB, which can accumulate cross-correlation data from SGWB to further constrain the power spectrum, AI model outputs do not readily provide statistically meaningful information for aggregation. Multiplying posterior probabilities from multiple segments leads to ambiguous, and potentially biased, results due to the lack of statistically significant fluctuations across different posterior distributions.

Abbott R, et al. PRD 104, 2 (2021): 022004.

PyGWB result

Our result (preliminary)

\Omega_{\mathrm{GW}}(f)=\Omega_{\mathrm{ref}}\left(\frac{f}{f_{\mathrm{ref}}}\right)^\alpha

\Omega_{\mathrm{GW}}(f)=\Omega_{\mathrm{ref}}\left(\frac{f}{f_{\mathrm{ref}}}\right)^\alpha

AI Predicting the Universe: Opportunities and Challenges

Exploring the importance of understanding how AI models make predictions in scientific research.
- The critical role of generative models (生成模型是关键)
- Quantifying uncertainty: a key aspect (不确定性量化问题)
- Fostering controllable and reliable models (模型的可控可信问题)

AI or Bayes

Text-to-image

"A running dog"

The most common and direct approach, from Artificial Intelligence Generated Content (AIGC) to GW statistical inference: pixel point $\Rightarrow$ inferred parameter.

AI Predicting the Universe: Opportunities and Challenges

Exploring the importance of understanding how AI models make predictions in scientific research.
- The critical role of generative models (生成模型是关键)
- Quantifying uncertainty: a key aspect (不确定性量化问题)
- Fostering controllable and reliable models (模型的可控可信问题)

AI or Bayes

Text-to-image

"A corgi running on the street"

A picture is worth a thousand words.

A fraction of a thousand words.

Credit: 李宏毅

"A running dog"

The most common and direct approach, from Artificial Intelligence Generated Content (AIGC) to GW statistical inference: pixel point $\Rightarrow$ inferred parameter.

Key Takeaways

Text

On-going

Agentic Reasoning for Inference
...

Text

Insights

AI is not just a tool; it is a revolutionary pathway for scientific discoveries.
Theoretical Advancements in ML for GW Statistics
- There is a pressing need for the theoretical refinement of ML applications in GW statistics, aiming to bridge current gaps and enhance model reliability.
Improve the interpretability of AI models, as it is essential for enhanced and trustworthy discoveries.

~~Statistics~~

\times N

\times N

\times N

\times N

~~Statistics~~

Key Takeaways

Text

On-going

Agentic Reasoning for Inference

Text

Insights

AI is not just a tool; it is a revolutionary pathway for scientific discoveries.
Theoretical Advancements in ML for GW Statistics
- There is a pressing need for the theoretical refinement of ML applications in GW statistics, aiming to bridge current gaps and enhance model reliability.
Improve the interpretability of AI models, as it is essential for enhanced and trustworthy discoveries.

~~Statistics~~

\times N

\times N

\times N

\times N

~~Statistics~~

for _ in range(num_of_audiences):
    print('Thank you for your attention! 🙏')

This silde: https://slides.com/iphysresearch/2024may_neu

空基引力波探测科学数据的分析与地基相比差距很大：

大量的混叠波源 ( $\neq$ 孤立事件)
在不同时间尺度上观测到更大的波形周期 ( $\neq$ 短时信号)
信号主导的探测 ( $\neq$ 噪声主导)
依赖更复杂的技术评估噪声 ( $\neq$ 定期获取无信号数据)

空间引力波观测频段内含有大量的波源和多种波源类型：

$10^4$ 可探测的银河系内致密双星绕转 (UCB, VGB)
$10\sim10^2$ 超大质量黑洞双星合并 (SMBH)
$10\sim10^3$ 极端质量比黑洞双星绕转 (EMRI)
恒星级质量黑洞双星的绕转 (SOBH)
随机引力波背景 (SGWB)
未建模的波源事件 (Burst...)

Text

空间引力波探测科学数据处理：典型波源

天琴计划

Credit: ESA, K. Holley-Bockelmann

Credit: Minghui Du

空间太极计划

(Sec.8.3.1 Red Book)

波源模板

与地面不同，完备的空间引力波探测模板需要涵盖更广泛的波源参数范围和更复杂的波源运动特性。
- 以 MBHB 为代表的波源信噪比通常较高(可达 $O(10^3)$ 以上)，对模板的精度要求也相应提高。
- 一些模板(SEOBNRE、SEOBNRPHM、 IMRPhenomXPHM等)加入了如高阶模、离心率、进动等特性，不仅有助于精细刻画波源的运动和演变，也有助于打破参数之间的简并关系，提高参数的估计精度。
- EMRI 双星的质量比约 $10^3 − 10^6$ ，波形复杂度极高，预期会观测到 $10^4 −10^5$ 个周期 (可观测时间长)。
- EMRI模板的核心挑战是数值相对论基准波形的不足？
- 空间引力波探测对其模板的精度和效率要求较高，兼顾精度和效率的方法仍在探索之中(AK、AAK、NK等)。
- 传播路径中考虑引力透镜效应。(5年任务周期内 $\leq4$ 个)

Text

空间引力波探测科学数据处理：1. 信号建模与计算

MNRAS 488, L94–L98 (2019)

EMRI 波形模板需求量 40 个数量级以上

Marsat et al. PRD 103, 8 (2021)

Our results indicate that the existing numerical relativity waveforms are as accurate as 99% with respect to space-based detectors including LISA, Taiji and Tianqin. Such accuracy level is comparable to the one with respect to LIGO.
(ZW, JJZ, ZJC, arXiv:2401.15331)

p(\vec{\theta} \mid \textcolor{black}{\vec{d}}, \mathcal{M})=\frac{p(\textcolor{black}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\textcolor{black}{\vec{d}} \mid \mathcal{M})}

p(\vec{\theta} \mid \textcolor{black}{\vec{d}}, \mathcal{M})=\frac{p(\textcolor{black}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\textcolor{black}{\vec{d}} \mid \mathcal{M})}

p(\textcolor{black}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\textcolor{black}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\textcolor{black}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

p(\textcolor{black}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\textcolor{black}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\textcolor{black}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

Bayes' theorem:

探测器响应

空间引力波探测响应计算的复杂性：
- 轨道的调制效应：空间引力波探测目标信号的可观测时间可达数月甚至数年，与探测器轨道运动的时间尺度相近。
- TDI 通道的组合：臂长不等、臂长随时间变化以及第二代 TDI 方案有待研究。

Text

空间引力波探测科学数据处理：1. 信号建模与计算

在时域中计算的挑战性在于，在每个采样点处都需要计算波形和响应，如果考虑到不同的 TDI 组合方式，则计算的时间复杂度将进一步增大。频域中的 TDI 响应形式，可简单概况为：

其中 $\alpha \in\{+, \times\}$ ，如果要考虑高阶模的贡献，则 $\alpha=\ell m$ 。 $t_\alpha(f)$ 描述了时间与引力波瞬时频率的关系，可通过

计算, 其中 $\Psi_\alpha$ 表示 $\alpha$ 模式频域波形的相位。 $\mathcal{T}$ 对时间的依赖关系反映了探测器轨道运动对信号的调制效应，如右图所示。调制效应为响应的建模和计算增加了复杂性，但同时也有助于在参数估计中解除外禀参数之间的简并，提升对波源的定位精度。

\tilde{h}^{A, E, T}(f)=\sum_\alpha \mathcal{T}_\alpha^{A, E, T}\left[f, t_\alpha(f)\right] \tilde{h}_\alpha(f)

\tilde{h}^{A, E, T}(f)=\sum_\alpha \mathcal{T}_\alpha^{A, E, T}\left[f, t_\alpha(f)\right] \tilde{h}_\alpha(f)

t_\alpha(f)=-\frac{1}{2 \pi} \frac{d \Psi_\alpha(f)}{d f}

t_\alpha(f)=-\frac{1}{2 \pi} \frac{d \Psi_\alpha(f)}{d f}

p(\vec{\theta} \mid \textcolor{red}{\vec{d}}, \mathcal{M})=\frac{p(\textcolor{red}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\textcolor{red}{\vec{d}} \mid \mathcal{M})}

p(\vec{\theta} \mid \textcolor{red}{\vec{d}}, \mathcal{M})=\frac{p(\textcolor{red}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\textcolor{red}{\vec{d}} \mid \mathcal{M})}

p(\textcolor{red}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\textcolor{red}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\textcolor{red}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

p(\textcolor{red}{\vec{d}} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\textcolor{red}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\textcolor{red}{\vec{d}}-\sum_{\mathcal{M}} \textcolor{red}{\vec{h}}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

Bayes' theorem:

TDI-A

TDI-A

TDI-E

TDI-T

Credit: Minghui Du

数据噪声

引力波数据分析通常假设噪声是高斯稳态的，数据是连续的，而在实际探测中，噪声的非稳态性、非高斯性及各种可能的数据异常，如环境或设备因素导致的 glitch、数据间断等，都可能导致引力波事件的误警、漏警或参数估计偏差。

Text

空间引力波探测科学数据处理：2. 噪声与数据异常

Addressing Instrumental Imperfections

数据间断（Data gaps）
瞬态噪声事件（glitches）
频谱线（Spectral lines）
非平稳性（Non-stationarities）
不完美校准（imperfect calibration）

Text

(Sec.8.3.3 Red Book)

Sasli et al., Phys. Rev. D (2023)

Baghi et al., Phys. Rev. D (2019)

似然函数建模

针对 glitch 导致的非高斯性，可以考虑用 student-t 分布、广义双曲分布、高阶 Edge worth 展开等方式为似然函数建模。

Text

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{d} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T \textcolor{red}{C}\left(\textcolor{red}{\theta_{\text {noise }}}\right)^{-1}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

p(\vec{d} \mid \vec{\theta}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)^T \textcolor{red}{C}\left(\textcolor{red}{\theta_{\text {noise }}}\right)^{-1}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\vec{\theta}_{\mathrm{GW}}\right)\right)}

Bayes' theorem:

搜索技术

空间引力波探测信号搜索流水线开发的重点是天体物理波源，特别是最明亮的 MBHB 和数量最多的 UCB：
- PyCBC-INFERENCE
  - MBHB
- BILBY
  - MBHB
- Strub et al. PRD 2022/2023
  - UCB
  - GPU-based
- Eryn
  - UCB
- ...

Text

空间引力波探测科学数据处理：3. 参数反演

Karnesis et al. 2303.02164.

Hoy & Nuttall. 2312.13039.

Weaving et al. CQG 41, (2023)

Strub et al., PRD. arXiv:2307.03763

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{d} \mid \textcolor{red}{\vec{\theta}}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)}

p(\vec{d} \mid \textcolor{red}{\vec{\theta}}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)^T C\left(\theta_{\text {noise }}\right)^{-1}\left(\vec{d}-\sum_{\mathcal{M}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)}

Bayes' theorem:

Nat. Astron. 2022, 6(12): 1356-1363.

Nat. Astron. 2022, 6(12): 1334-1338.

背景与挑战

空间引力波探测需识别尽可能多的引力波信号源
数据中引力波信号相互混叠，影响波源参数反演
单独识别单个源或某类特定源类型效率低下
波源在任务生命周期内持续存在，增加识别难度

全局拟合方法 (Global-fit method)

对所有源/噪声的参数同时做引力波信号全局搜索和波源参数反演
随着更多数据的接收，不断更新全局搜索和参数反演的数据

实践应用步骤

全局搜索结合其他波源的数据分析流水线
在全局搜索后处理最新最佳拟合残差
识别到的源反馈至未来的全局搜索方案，以实现持续优化

潜在局限性

收敛速度受限
- 受限于未知的波源数目
- $\mathcal{O}(10^5)$ 高维参数空间
- 波形模板仿真等

全局拟合
Global-fit

Text

空间引力波探测科学数据处理：全局拟合

全局拟合

全局拟合方法（global fit）思想在于对空间引力波数据中存在的所有天体物理和仪器特征同时进行综合建模。
这种方法不仅仅关注单一波源的信号，而是尝试捕捉数据中所有波源的综合影响，对整个数据集进行全面分析，以识别和建模所有潜在的信号和噪声源。

Text

空间引力波探测科学数据处理：3. 参数反演

Pipeline	Targets	Programing Language (sampling method)	Comments
GLASS (Littenberg&Cornish 2023)	Noise, UCB, VGB, MBHB	C / Python (TPMCMC / RJMCMC)	noise_mcmc+gb_mcmc+vb_mcmc+global_fit
Eryn	UCB	Python (TPMCMC / RJMCMC)	No code for UCB case
PyCBC-INFERENCE	MBHB	Python (?)	Unavailable
Bilby in Space / tBilby	MBHB / ?	? / Python? (RJMCMC)	Unavailable
Strub et al.	UCB	? (GP)	Unavailable / GPU-based
Zhang et al. (LZU)	UCB	? (PSO)	MLP

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{\theta} \mid \vec{d}, \mathcal{M})=\frac{p(\vec{d} \mid \vec{\theta}, \mathcal{M}) p(\vec{\theta} \mid \mathcal{M})}{p(\vec{d} \mid \mathcal{M})}

p(\vec{d} \mid \textcolor{red}{\vec{\theta}}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\textcolor{red}{\sum_{\mathcal{M}}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)^T C\left(\textcolor{red}{\theta_{\text {noise }}}\right)^{-1}\left(\vec{d}-\textcolor{red}{\sum_{\mathcal{M}}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)}

p(\vec{d} \mid \textcolor{red}{\vec{\theta}}, \mathcal{M}) \propto e^{-\frac{1}{2}\left(\vec{d}-\textcolor{red}{\sum_{\mathcal{M}}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)^T C\left(\textcolor{red}{\theta_{\text {noise }}}\right)^{-1}\left(\vec{d}-\textcolor{red}{\sum_{\mathcal{M}}} \vec{h}\left(\textcolor{red}{\vec{\theta}_{\mathrm{GW}}}\right)\right)}

Bayes' theorem:

Nat. Astron. 2022, 6(12): 1334-1338.

Nat. Astron. 2022, 6(12): 1356-1363.

(Sec.8.6 Red Book)

超高维度的波源参数空间特性 (编码波形)

随着星座的轨道运动，引力波信号会随时间发生变化 (链路相关)。
星座对特定波源的探测敏感性也会随时间而改变。
我们如何在波形的模式识别中融入星座的轨道运动信息？

科学数据的动态性 (编码数据)

面对科学数据的固有复杂性——尤其是数据的高维度——我们应如何应对？

资源优化挑战 (CPU vs GPU)

总 CPU 需求 (以 CPU 小时计)是 20-30M，其中每年需要进行3次迭代，每次迭代需要2个管道。用转换系数 10 来估计 GPU 的需求，可估算出所有波源类型的 GPU 卡需求可达 $10^3$ 以上。（异步调度+并行计算）
如何在最小化等待时间和最大化计算
节点效率的过程中，进行资源分配和
优化策略。
高频UCB迭代并行计算耗时
...

F(t) over 1 year

h(t) over 10 min

y(t) over 1 year

Text

多类型的大量波源混叠问题

空间引力波探测科学数据处理技术难题

2

Actually, there are more ...

非模板引力波信号(背景)的探测与重构
...

Credit: Maude Le Jeune (2021)

MCMC采样的高效性和收敛性

改进Proposal 以有效采样高维+多模+变维的参数空间
提高接受率 以确保MC链的高效收敛

Text

AI could help ?!
- nflow-assisted? (2402.13701)
- multi-agentic reasoning

超高维度的波源参数空间特性 (编码波形)

随着星座的轨道运动，引力波信号会随时间发生变化 (链路相关)。
星座对特定波源的探测敏感性也会随时间而改变。
我们如何在波形的模式识别中融入星座的轨道运动信息？

科学数据的动态性 (编码数据)

面对科学数据的固有复杂性——尤其是数据的高维度——我们应如何应对？

资源优化挑战 (CPU vs GPU)

总 CPU 需求 (以 CPU 小时计)是 20-30M，其中每年需要进行3次迭代，每次迭代需要2个管道。用转换系数 10 来估计 GPU 的需求，可估算出所有波源类型的 GPU 卡需求可达 $10^3$ 以上。（异步调度+并行计算）
如何在最小化等待时间和最大化计算
节点效率的过程中，进行资源分配和
优化策略。
高频UCB迭代并行计算耗时
...

F(t) over 1 year

h(t) over 10 min

y(t) over 1 year

Text

多类型的大量波源混叠问题

空间引力波探测科学数据处理技术难题

2

Actually, there are more ...

非模板引力波信号(背景)的探测与重构
...

Credit: Maude Le Jeune (2021)

MCMC采样的高效性和收敛性

改进Proposal 以有效采样高维+多模+变维的参数空间
提高接受率 以确保MC链的高效收敛

Text

AI could help ?!
- nflow-assisted? (2402.13701)
- multi-agentic reasoning

for _ in range(num_of_audiences):
    print('Thank you for your attention! 🙏')

This silde: https://slides.com/iphysresearch/2024may_neu

空间引力波探测科学数据处理：人工智能技术

极端质量比黑洞双星的绕旋 (EMRI) 是空间引力波探测的重要信号源。
由于相对论效应的影响，波形复杂度极高，预期会观测到 $10^4 \sim 10^5$ 周期。
深度学习技术的应用：波形建模
- 利用GPU加速EMRI波形的模式识别分析，为毫赫兹空间引力波数据分析提供了强大的计算工具和新的可能性，显著提升了数据处理的效率和精度

Text

$h(\theta):=\sum_i \alpha_i(\theta) e_i \equiv \alpha(\theta) \text {, }$

where $\alpha\in\mathbb{C}^{241}$ and reduced basis $\{e_i\}$ with $\left\langle e_i \mid e_j\right\rangle=\delta_{i j}$ .

深度学习算法的学习目标：

$(\mathcal{M}_c, \eta)\in\Theta\subset\mathbb{R}^2$

$(\alpha_r, \alpha_i) \in\mathbb{R}^{482}$

Neural
Network

AAK - FastEMRIWaveforms (FEW)

Katz et al., Phys. Rev. D (2021)

Chua et al., Phys. Rev. Lett., (2021)

~1s (快 ≳ $10^4$ 倍)

MNRAS 488, L94–L98 (2019)

EMRI 波形模板需求量 40 个数量级以上

Text

极端质量比黑洞双星的绕旋 (EMRI) 是空间引力波探测的重要信号源。
传统的匹配滤波方法需求巨量的高精度波形模板 ( $约10^{40}$ ) ，计算上不切实际。
深度学习技术的应用：信号探测
- 通过基于人工智能模型的 EMRIs 波形的原理验证研究，能够在约 10 毫秒的时间内实现波形信号的有效探测。

张雪婷, C. Messenger, N. Korsakova,
ML Chan, 胡一鸣, 张建东, Phys. Rev. D (2022)

赵天宇, 周阅, 施锐俊, 曹周键, 任智祥, arXiv:2308.16422

恽倩芸, 韩文标, 郭意扬, 王赫, 杜明辉, arXiv:2309.06694

Text

	Zhang et al. PRD (2022)	Zhao et al. (2308.16422)	Yun et al. (2309.06694)
TDI	-	TDI-1.5	TDI-2.0
Duration	3 months	1 year	0.5 year
Waveform Family (train)	AK	AAK	AAK
Waveform Family (test)	AK / AAK	AK / AAK	AAK
GW Project	TianQin	LISA	Taiji
Acceleration Noise [fm/sqrt(Hz)]	1	3	3
OMS Noise [pm/sqrt(Hz)]	1	15	8
Base Model	CNN	CNN	CNN
Input Feature domain	time	frequency	time-frequency
sampling rate	1/30 Hz	1/15 Hz	1/10 Hz

Text

空间引力波探测科学数据处理：人工智能技术

极端质量比黑洞双星的绕旋 (EMRI) 是空间引力波探测的重要信号源。
传统的匹配滤波方法需求巨量的高精度波形模板 ( $约10^{40}$ ) ，计算上不切实际。
深度学习技术的应用：信号探测/参数反演
- 通过基于人工智能模型的 EMRIs 波形的原理验证研究，能够在约 10 毫秒的时间内实现波形信号的有效探测，以及对波源参数的反演。

Text

Yun et al. (2311.18640)
TDI-2.0
0.5 year
AAK
AAK / EOB
Taiji
3
8
Unet / VGG
time-frequency
1/10 Hz

	Zhang et al. PRD (2022)	Zhao et al. (2308.16422)	Yun et al. (2309.06694)
TDI	-	TDI-1.5	TDI-2.0
Duration	3 months	1 year	0.5 year
Waveform Family (train)	AK	AAK	AAK
Waveform Family (test)	AK / AAK	AK / AAK	AAK
GW Project	TianQin	LISA	Taiji
Acceleration Noise [fm/sqrt(Hz)]	1	3	3
OMS Noise [pm/sqrt(Hz)]	1	15	8
Base Model	CNN	CNN	CNN
Input Feature domain	time	frequency	time-frequency
sampling rate	1/30 Hz	1/15 Hz	1/10 Hz

空间引力波探测科学数据处理：人工智能技术

Text

超大质量黑洞双星 (MBHB) 的并合是空间引力波可以探测到的最强瞬态信号源，对于低红移源，信噪比 (SNR) 可超过1000。
预期质量范围是 $10^4\sim10^7$ 太阳质量，可观测到晚期的双星绕旋、并合和振荡衰减阶段，事件率约为每年几个到几百个。
深度学习技术的应用：信号探测
- 通过基于人工智能模型的原理验证研究，可实现多种波源波形信号的实时探测。

赵天宇*, Ruoxi Lyu*, 王赫, 曹周键, 任智祥, Commun. Phys., (2023)

"One Model to Rule Them All"：EMRI / MBHB / GBs / SGWB 的信号提取

王赫, 吴仕超, 曹周键, 刘骁麟, 朱建阳,
Phys. Rev. D, (2020)

阮文洪*, 王赫*, 刘畅, 郭宗宽,
Phys. Lett. B, (2023)

LDC 一年数据上对 MBHB (+GBs) 信号的信号探测

Text

空间引力波探测科学数据处理：人工智能技术

Text

杜明辉*, 梁博*, 王赫†, 徐鹏, 罗子人, 吴岳良†, accepted by SCPMA, arXiv:2308.05510

超大质量黑洞双星 (MBHB) 的并合是空间引力波可以探测到的最强瞬态信号源，对于低红移源，信噪比 (SNR) 可超过1000。
预期质量范围是 $10^4\sim10^7$ 太阳质量，可观测到晚期的双星绕旋、并合和振荡衰减阶段，事件率约为每年几个到几百个。
深度学习技术的应用：参数反演
- 人工智能算法可实现混叠 MBHB 信号的全波源参数反演，比传统估计后验分布算法的采样效率高 3 个数量级。

阮文洪, 王赫, 刘畅, 郭宗宽,
Universe (2023)

Text

亮点：

可以实现完整参数维度的快速参数反演
在AI推断结果中发现额外的多模态
利用投影对称性解放模型的泛化性

空间引力波探测科学数据处理：人工智能技术

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杜明辉*, 梁博*, 王赫†, 徐鹏, 罗子人, 吴岳良†, accepted by SCPMA, arXiv:2308.05510

超大质量黑洞双星 (MBHB) 的并合是空间引力波可以探测到的最强瞬态信号源，对于低红移源，信噪比 (SNR) 可超过1000。
预期质量范围是 $10^4\sim10^7$ 太阳质量，可观测到晚期的双星绕旋、并合和振荡衰减阶段，事件率约为每年几个到几百个。
深度学习技术的应用：参数反演
- 人工智能算法可实现混叠 MBHB 信号的全波源参数反演，比传统估计后验分布算法的采样效率高 3 个数量级。

阮文洪, 王赫, 刘畅, 郭宗宽,
Universe (2023)

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亮点：

可以实现完整参数维度的快速参数反演
在AI推断结果中发现额外的多模态
利用投影对称性解放模型的泛化性

空间引力波探测科学数据处理：人工智能技术

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