2024年5月13日, 15:00 | 辽宁 · 沈阳 · 东北大学

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

https://twitter.com/chipro/status/1768388213008445837?s=46&t=JmDXWgIucgr_FlsBFTvuRQ

DINGO+SEOBNRv4EHM找了3个ebbh

Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA
https://dcc.ligo.org/LIGO-G2400750

• 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

• 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

The first GW event of 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 

GWTC-3

• 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

• 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 

GWTC-3

©Floor Broekgaarden (repo)

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).

LISA / Taiji project

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

• 2016年，AlphaGo 第一版发表在了 Nature 杂志上

• 2021年，AI预测蛋白质结构登上 Science、Nature 年度技术突破，潜力无穷

• 2022年，DeepMind团队通过游戏训练AI发现矩阵乘法算法问题​

• 《达摩院2022十大科技趋势》将 AI for Science 列为重要趋势

  • “人工智能成为科学家的新生产工具，催生科研新范式”

• 2023年，DeepMind发布AI工具GNoME (Nature)，成功预测220万种晶体结构

• AI for Science：为科学带来了模型与数据双驱动的新的研究范式

  • AI + 数学、AI + 化学、AI + 医药、AI + 量子、AI + 物理、AI + 天文 ...

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.

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

Matched-filtering Convolutional Neural Network (MFCNN)

• GW templates can be utilized as recognizable features for signal detection.
• It is feasible to generalize both matched-filtering and neural networks.
• Linear filters (i.e., matched-filtering) in signal processing can be reformulated as neural layers (i.e., CNNs).

MLGWSC-1

• The majority of AI algorithms used for testing are highly sensitive to non-Gaussian real noise backgrounds, resulting in high false positive rates.

CL.M., W.W., H.W., et al. PRD (2022)

Ensemble learning

• Leverages statistical approaches to utilize more information for making informed decisions by combining multiple models.

Expanding the dimension of the output

• is to call more information to make decisions in improving AI models.

 Introduction to Speed and Efficiency

• Machine Learning (ML) offers unparalleled speed in GW detection.
• The increasing sensitivity to noise and the growing number of GW events demand faster analysis capabilities.
   

The Need for Integration (an AI pipeline!)

• Numerous AI algorithms exist for signal detection (see more: https://wiki.ligo.org/MLA/ML_at_LIGO_and_VIRGO), highlighting the need for a streamlined pipeline.
• However, none are operational in O4 due to infrastructure challenges and the lack of standardized sensitivity measures against non-stationary noise.

Case study:                   Pipeline

• The Aframe online pipeline (arXiv:2403.18661) represents a significant step forward.
• Utilizes GPU acceleration for signal preprocessing, model inference, and real-time false alarm rate calculation.

Aframe

S.S. Chaudhary, et al. arXiv:2308.04545

Challenges and Future Directions

• A comprehensive online pipeline should consider various signal types, including BNS and NSBH, and all detectors, including Virgo and KAGRA.
• Beyond false alarm rates, additional real-time information is crucial for a holistic analysis.

Case study:                   Pipeline
 

• The Aframe online pipeline (arXiv:2403.18661) represents a significant step forward.

• Despite its advancements, it primarily focuses on BBH signals, with decreased performance on longer signals like BNS, a point also highlighted in MLGWSC1(PRD, 2209.11146).

Aframe

Beyond Speed: Generalization and Discovery in GW Detection

• Our primary goal is not speed but the model's ability to generalize and discover new GW signals, including those beyond the reach of matched filtering techniques and General Relativity (GR).
• Leveraging our experience in  signal modeling  (MFCNN) and noise modeling (WaveFormer), we are gradually building an offline pipeline capable of searching for signals in complete GW observation data and calculating FARs.

Real-time GW searches for GW150914

He Wang, et al. PRD 101, 10 (2020): 104003

He Wang, et al. MLST. 5, 1 (2024): 015046.

Beyond Speed: Generalization and Discovery in GW Detection

• Our primary goal is not speed but the model's ability to generalize and discover new GW signals, including those beyond the reach of matched filtering techniques and General Relativity (GR).
• Leveraging our experience in  signal modeling  (MFCNN) and noise modeling (WaveFormer), we are gradually building an offline pipeline capable of searching for signals in complete GW observation data and calculating FARs.

He Wang, et al. PRD 101, 10 (2020): 104003

He Wang, et al. MLST. 5, 1 (2024): 015046.

Real-time GW searches for GW150914

数据增益 -> GWToolkit （缺一个好看的高吞吐性能图和loss/acc性能图）+ Data Protal (缺一个可视化和性能表现CKAN?)

Pipeline -> MFCNN + WaveFormer（缺雪藏event的corner图）; bGR（缺结果图）

信号探测（缺各种文章中的探测统计量图像）-> 引出新的理论缺失： machine learning GW statistics

• The WaveFormer, a billion-scale transformer-based model, excels in suppressing realistic noise and recovering injections or GW events, thereby significantly improving data quality.
• In its application, it treats each overlapping time-domain data subsequence as an individual token, akin to tokenization in natural language processing (NLP).

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

• Noise level percentile amplitude is significantly reduced, by approximately two orders.
• Further ASD analysis shows that WaveFormer effectively eliminates both narrowband and broadband spectral information, substantially lowering frequency contributions.
• Using the Gravity Spy database for glitches with SNR > 10 and confidence > 0.95, results show significant suppression of glitches in real advanced LIGO-Virgo noise.

• Overlap and matched-filtering signal-to-noise are calculated to represent phase and amplitude recovery performance.
• Among the intermediate frequency range (20–200 Hz) that covers rich BBH signal information, the ASD distribution of denoised waveform is evidently consistent with that of target signal.

(Upper panels: Signal amplitude recovery performance

(Bottom panels: Signal phase recovery performance​)

• These results show that our denoising algorithm outperformed others by capturing the characteristic chirping morphology of BBH evolution, and can denoise signals in realistic detection scenarios without affecting signal characteristics such as phase and amplitude.
• For the event GW191204_171526, classified as either an NSBH or a low-mass BBH candidate in GWTC-3, the overlap with IMRPhenomXPHM achieved 0.93 and 0.95 on H1 and L1, respectively, which are marked improvements over those achieved by BayesWave and cWB (with overlaps between 0.82–0.86).

GW191204_171526

• 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).

• An search algorithm for GW require that: [cite: 2010.07244]

  1. the same signal is seen in the detectors; (the same signal is seen by time-shifting in single detector)

  2. the same waveform must be present both detectors;

  3. and the signal’s time of arrival must be consistent with the GW travel time between the observatories.

• 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)

• 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.

• 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.

• Through time shift, background analysis is done on other triggers around the target trigger. (time-shift interval 0.1 sec)
• Finally, by counting the number of false alarm trigger pairs, we obtain the IFAR value of the target trigger, which represents the reported or candidate BBH event in this experiment.

(PyCBC) Davies​, et al. PRD 2020

Ours

• 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.

Challenges in Model Interpretability

• The black-box nature of AI models poses significant challenges in interpretability, making it difficult to compare AI-generated detection statistics with those derived from matched filtering chi-square distributions.
• Despite being able to identify potential gravitational wave signals, convincing the scientific community of the pipeline's validity and the statistical significance of new discoveries remains a hurdle.

He Wang, et al. MLST. 5, 1 (2024): 015046.

The negative log-likelihood cost function always strongly penalizes the most active incorrect prediction. And the correctly classified examples will contribute little to the overall training cost."
—— I. Goodfellow, Y. Bengio, A. Courville. Deep Learning. 2016. (book)

LVK.  arXiv:1602.03839

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.

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"

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

Credit: LIGO Magazine.

• Traditional parameter estimation (PE) techniques rely on Bayesian analysis methods (posteriors + evidence)

• Computing the full 15-dimensional posterior distribution estimate is very time-consuming:
  • Calculating likelihood function
  • Template generation time-consuming
• Machine learning algorithms are expected to speed up! 

• 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

Nature Physics 18, 1 (2022) 112–17

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

（Based on 1912.02762）

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

（Based on 1912.02762）

• 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.

归一化流模型示意图

DINGO  要特别快，要足够准

（缺DINGO技术相关的前沿动态）

Enrico 只要够快就足够了，可以做引力检验

（调研所有和最新的AI+引力检验文章）

（缺PyGWB的引入、数据描述、结果）-> 同样遇到如何做statistics的问题

• 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 ...

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)

He Wang, et al.  (2024)

PRD 108, 4 (2023): 044029.

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.

arXiv:2404.14286

• 進撃のnflow model in GW inference area.

  • 2002.07656: 5D toy model [1] (PRD)

  • 2008.03312: 15D binary black hole inference [1] (MLST)

  • 2106.12594: Amortized inference and group-equivariant neural posterior estimation [2] (PRL)

  • 2111.13139: Group-equivariant neural posterior estimation [2]

  • 2210.05686: Importance sampling [2] (PRL)

  • 2211.08801: Noise forecasting [2] (PRD)

  • 2305.17161: FMPE

  • 2404.14286: eccentricity of BBHs

1. https://github.com/stephengreen/lfi-gw  (2020)

2. https://github.com/dingo-gw/dingo   (2023.03)

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.

Our result (preliminary)

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)

• 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)

"A running dog"

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

• 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)

"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.

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

On-going

• Agentic Reasoning for Inference
• ...

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.

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

For further reference or to cite the work presented today,
please cite this silde: https://slides.com/iphysresearch/2024mar_bnuz

https://twitter.com/chipro/status/1768388213008445837?s=46&t=JmDXWgIucgr_FlsBFTvuRQ

如何把大模型这个概念在合适的地方讲出来？（开头？最后？）

高维、多模态的inference挑战（是整个引力波相关的科学研究的技术难点）

PTMCMC 的算法描述图

Multi-agent 的概念图，及其相关结果的对比图

DINGO: A Leap Forward

• DINGO and related works represent the cutting edge in this field within the LIGO frequency band.
• Tested on 42 BBH events from GWTC-3
• Being deployed for O4, with the potential to become a new gravitational wave signal search pipeline
• Capable of calculating evidence
• Processing time: (using 64 CPU cores)
  • less than 1 hour with IMRPhenomXPHM,
  • approximately 10 hours with SEOBNRv4PHM
• ​Evidence for eccentricity in the population of BBH observed by LVK. (LIGO-G2400750, 2024 Mar)

• 進撃のnflow model in GW inference area.

  • 2002.07656: 5D toy model [1] (PRD)

  • 2008.03312: 15D binary black hole inference [1] (MLST)

  • 2106.12594: Amortized inference and group-equivariant neural posterior estimation [2] (PRL)

  • 2111.13139: Group-equivariant neural posterior estimation [2]

  • 2210.05686: Importance sampling [2] (PRL)

  • 2211.08801: Noise forecasting [2] (PRD)

[1]. https://github.com/stephengreen/lfi-gw  (published @2020)

[2]. https://github.com/dingo-gw/dingo   (published @2023.03)

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

引力波天文学 & 引力波多信使天文学

• 目前，国内外正在计划进行各种引力波探测项目，包括利用宇宙微波背景辐射的B模极化的CMB-S4、LiteBIRD、BICEP3/Keck Array、AliCPT；利用脉冲星定时阵列的NANOGrav、EPTA、PPTA、CPTA；利用空间引力波星间激光干涉仪的LISA、太极计划、天琴计划等；以及用于地面引力波干涉仪的ET、BBO。最近，NANOGrav、EPTA和CPTA共同宣布了存在纳赫兹级随机引力波背景的强有力证据。

Chinese Journal of Space Science,  2023, 43(4): 589-599.

LIGO-G2300554

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...)

空间太极计划

• 空间引力波探测主要有以下 4 类波源：

  • 恒星级质量的致密双星 (黑洞、中子星、白矮星以及它们的两两组合) 的旋近

  • 双白矮星的并合、​超大质量双黑洞的并合

  • 极端质量比旋进 (通常是一个恒星级致密天体绕着一个超大质量黑洞的旋进）

  • 宇宙中可能存在的中等质量双黑洞以及前面这些源的信号叠加形成的引力波背景

天琴计划

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...)

天琴计划

空间太极计划

(Sec.8.3.1 Red Book)

空间引力波探测获得的是什么样的 (科学) 数据？

• 来自几十个激光干涉仪的分数频率偏差 (相对多普勒频移)
• 预计天线重新定位 (9天) 和激光重新锁定 (几周) 会导致短时间 (＜小时) 的间隔，而类似LPF的意外长时间间隔 (∼天) 经常被考虑在内，总占空比约80-90%。 (日心轨道)
• 主要受激光噪声的影响
• 经过预处理后，得到3个时间延迟干涉 (TDI) 数据流 (X, Y, Z)
• ...

Analyses cannot treat sources independently and sequentially work through a list of candidate detections.

空间引力波探测获得的是什么样的 (科学) 数据？

• 来自几十个激光干涉仪的分数频率偏差 (相对多普勒频移)
• 预计天线重新定位 (9天) 和激光重新锁定 (几周) 会导致短时间 (＜小时) 的间隔，而类似LPF的意外长时间间隔 (∼天) 经常被考虑在内，总占空比约80-90%。 (日心轨道)
• 主要受激光噪声的影响
• 经过预处理后，得到3个时间延迟干涉 (TDI) 数据流 (X, Y, Z)
• ...

其他重要的科学数据处理的技术挑战：

• 随机噪声（Stochastic noise）

• 仪器瞬变（glitches）

• 频谱线（Spectral lines）

• 数据间断（Data gaps）

• 非平稳性（Non-stationarities）

Baghi et al., Phys. Rev. D (2019)

Analyses cannot treat sources independently and sequentially work through a list of candidate detections.

Mock Data Challenges

http://taiji-tdc.ictp-ap.org/

https://lisa-ldc.lal.in2p3.fr/​

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)

Marsat et al. PRD 103, 8 (2021)

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。

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。

Bayes' theorem:

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。

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）

(Sec.8.3.3 Red Book)

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

  • ...

Bayes' theorem:

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

1. 全局搜索结合其他波源的数据分析流水线
2. 在全局搜索后处理最新最佳拟合残差
3. 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

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。

Bayes' theorem:

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
• ...

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

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

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

局限性

• 收敛速度慢
  • 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

研究现状

• GLASS (The global LISA analysis software suite)
  • Modeling: noise, UCB, VGB, MBHB
  • Blind search
• PyCBC-INFERENCE
  • MBHB
• BILBY
  • MBHB
• Strub et al. PRD 2023

  • UCB

  • GPU-based

• Eryn
  • UCB

• ...

技术痛点/局限性

• 似然函数：计算耗时/先验知识依赖
• 优化收敛：高频UCB迭代并行计算耗时
• 高性能硬件：CPU+GPU异构并行计算
• ...

• 空间引力波探测：全局拟合问题
• 科学智能：引力波数据处理
• 空间引力波探测科学数据处理：人工智能技术

• 2016年，AlphaGo 第一版发表在了 Nature 杂志上

• 2021年，AI预测蛋白质结构登上 Science、Nature 年度技术突破，潜力无穷

• 2022年，DeepMind团队通过游戏训练AI发现矩阵乘法算法问题​

• 《达摩院2022十大科技趋势》将 AI for Science 列为重要趋势

  • “人工智能成为科学家的新生产工具，催生科研新范式”

• 2023年，DeepMind发布AI工具GNoME (Nature)，成功预测220万种晶体结构

• AI for Science：为科学带来了模型与数据双驱动的新的研究范式

  • AI + 数学、AI + 化学、AI + 医药、AI + 量子、AI + 物理、AI + 天文 ...

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.

Matched-filtering Convolutional Neural Network (MFCNN)

• GW templates can be utilized as recognizable features for signal detection.
• It is feasible to generalize both matched-filtering and neural networks.
• Linear filters (i.e., matched-filtering) in signal processing can be reformulated as neural layers (i.e., CNNs).

MLGWSC-1

• The majority of AI algorithms used for testing are highly sensitive to non-Gaussian real noise backgrounds, resulting in high false positive rates.

CL.M., W.W., H.W., et al. PRD (2022)

Ensemble learning

• Leverages statistical approaches to utilize more information for making informed decisions by combining multiple models.

Expanding the dimension of the output

• is to call more information to make decisions in improving AI models.

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

• 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。

• 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。

• 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)

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)

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