引力波数据处理与人工智能技术应用

He Wang (王赫)

hewang@ucas.ac.cn

International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), UCAS

Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), UCAS

on behave of LVK collaboration

July 3, 2025 @南开大学

Interpretable Gravitational Wave Data Analysis with Deep Learning and Large Language Models

01

GW

GW astronomy
GW data analysis
AI for science
(Pros & Cons of AI)

02

AI for GW

GW Search
Parameter inference
(SBI method)

03

LLM for GW

Algorithm Heuristic Design

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

What is Gravitational wave?

GW Characteristics

引力波是时空的涟漪。
大物体的引力扭曲空间和时间，或称为“时空”，就像保龄球在弹跳床上滚动时改变其形状一样。较小的物体因此会以不同的方式移动——就像弹跳床上朝向保龄球大小的凹陷螺旋而去的弹珠，而不是坐在平坦的表面上。

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Gravitational waves (GW) are a strong field effect in General Relativity, ripples in the fabric of spacetime caused by accelerating massive objects.

Gravitational Wave Astronomy

双星并合系统产生的引力波波源

引力波振幅的测量

地面引力波探测器网络

Multi-messenger Astronomy

GW Detection

引力波探测打开了探索宇宙的新窗口
不同波源，频率跨越 20 个数量级，不同探测器

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

The Scientific Significance

基础物理学

引力子是否有质量
引力波的传播速度
...

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

天体物理学

大质量恒星演化模型
恒星级双黑洞的形成机制
...

宇宙学

哈勃常数的测量
暗能量
...

引力波暂现源星表 (GWTC-3)

hewang@ucas.ac.cn

首次探测双黑洞并合引力波事件 GW150914

人类成功观测到引力波的五条关键要素：

良好的探测器技术

良好的波形模板

良好的数据分析方法和技术

多个独立探测器间的一致性观测

引力波天文学和电磁波天文学的一致性观测

DOI:10.1063/1.1629411

– 伯纳德·舒尔茨

Challenge and Methodology: Detecting Signals in GW Data

GW Data Characteristics

LIGO-VIRGO-KAGRA

LISA Project

Noise: non-Gaussian and non-stationary
Signal challenges:
- (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.: 10⁴ of GBs, 10~10² of SMBHs, and 10~10³ 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).

Statistical Approaches

Frequentist Testing:

Make assumptions about signal and noise
Write down the likelihood function
Maximize parameters
Define detection statistic
→ recover MF

Bayesian Testing:

Start from same likelihood
Define parameter priors
Marginalize over parameters
Often treated as Frequentist statistic
→ recover MF (for certain priors)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Challenge and Methodology: Detecting Signals in GW Data

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).

Statistical Approaches

Frequentist Testing:

Make assumptions about signal and noise
Write down the likelihood function
Maximize parameters
Define detection statistic
→ recover MF

Bayesian Testing:

Start from same likelihood
Define parameter priors
Marginalize over parameters
Often treated as Frequentist statistic
→ recover MF (for certain priors)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

h_w[t]

d_w[t]

\rho[t]

线性滤波器

输入序列

输出序列

h_w[t]

脉冲响应函数：

hewang@ucas.ac.cn

Digital Signal Processing

Challenge and Methodology: Detecting Signals in GW Data

地基引力波探测科学数据的特点

噪声特点：非高斯 + 非稳态
信号特点：信噪比低 (约噪声幅度的1/100，约 -60dB )

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

波形模板库的局限性

需要大量的精确波形模板以确保无遗漏，至少百万数量级
受限于已知引力理论预言的波形模板，难以搜寻超越经典广相引力理论 的引力波信号

多信使天文学的兴起 + 引力波探测技术的进步

低(负)延迟的引力波信号搜寻
海量的 累积数据和 成批的 引力波事件，有待高效的仔细分析

真实引力波数据的非高斯性

O1 观测运行时用的波形模板库

在 GW170817 事件后 1.74\(\pm\)0.05s 的伽玛暴 GRB 170817A

hewang@ucas.ac.cn

科学智能：AI for Science

2016年，AlphaGo 第一版发表在了 Nature 杂志上
2021年，AIphaFold 预测蛋白质结构登上 Science、Nature 年度技术突破
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
2023年3月，为贯彻落实国家《新一代人工智能发展规划》，科技部会同自然科学基金委启动“人工智能驱动的科学研究”（AI for Science）专项部署工作，布局“人工智能驱动的科学研究”前沿科技研发体系。
2024.4：美国总统科学技术顾问委员会（PCAST）发布《赋能研究：利用人工智能应对全球挑战》报告
2024.5: 《Science in the age of AI: How artificial intelligence is changing the nature and method of scientific research》 (Royal Soc.)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

AlphaGo
围棋机器人

AlphaTensor
发现矩阵算法

AlphaFold
蛋白质结构预测

验证数学猜想

hewang@ucas.ac.cn

科学智能：AI for Science

2016年，AlphaGo 第一版发表在了 Nature 杂志上
2021年，AIphaFold 预测蛋白质结构登上 Science、Nature 年度技术突破
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
2023年3月，为贯彻落实国家《新一代人工智能发展规划》，科技部会同自然科学基金委启动“人工智能驱动的科学研究”（AI for Science）专项部署工作，布局“人工智能驱动的科学研究”前沿科技研发体系。
2024.4：美国总统科学技术顾问委员会（PCAST）发布《赋能研究：利用人工智能应对全球挑战》报告
2024.5: 《Science in the age of AI: How artificial intelligence is changing the nature and method of scientific research》 (Royal Soc.)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

AlphaGo
围棋机器人

AlphaTensor
发现矩阵算法

AlphaFold
蛋白质结构预测

验证数学猜想

hewang@ucas.ac.cn

传统机器学习

深度学习

输入

特征提取

输入

特征

传统机器学习算法

输出

输入

自动特征提取 + 分类

输出

人工智能 > 机器学习 > 深度学习

人工智能

机器学习

深度学习

人工智能的一个分支。机器学习是用数据或以往的经验，以此优化计算机程序的性能标准

机器学习的一个分支。基于神经网络结构实现端到端的一种建模方法

任何能实现以人类智能相似的方式做出反应的技术

机器学习：
- 线性回归模型、决策树模型、支撑向量机、马尔科夫链-蒙特卡洛方法 (MCMC) ...
深度学习：
- 用神经网络实现自动特征提取的模型
- 深度神经网络是一个万能的函数拟合器，可以表征任意复杂度的非线性函数映射
- 特点：端到端、数据驱动、过参数化 ...
传统引力波数据分析方法 ~ 传统机器学习方法

He Wang | ICTP-AP, UCAS

Towards Transparent AI in Gravitational Wave Data Analysis

The Rise of Machine Learning

AI is taking over the world... literally everywhere

Why should you consider applying ML to gravitational wave astrophysics?

He Wang | ICTP-AP, UCAS

Towards Transparent AI in Gravitational Wave Data Analysis

He Wang | ICTP-AP, UCAS

Towards Transparent AI in Gravitational Wave Data Analysis

The "Real" Reasons We Apply ML to GW Astrophysics

Let's be honest about our motivations... 😉

The perfectly valid "scientific" reasons:

✓ It sounded like a cool project
✓ My supervisor said it was a good thing to work on
✓ I will learn some really useful ML skills
✓ I'm already good at ML
✓ I want to get better at ML
✓ I want to get a high-paying job after this PhD/postdoc
✓ I want to be spared when the machines take over

Credit: Chris Messenger (MLA meeting,, Jan 2025)

He Wang | ICTP-AP, UCAS

Towards Transparent AI in Gravitational Wave Data Analysis

Why is AI/ML Everywhere in GW Research?

The core motivations behind nearly all AI+GW research

1

ML is FAST

So much data, so little time!

• Bayesian parameter estimation
• Replaces computationally intensive components

2

ML is ACCURATE*

Consistently outperforms traditional approaches

• Unmodelled burst searches
• Continuous GW searches

3

ML is FLEXIBLE

Provides deeper insights into complex problems

• Reveals patterns through interpretability
• Enables previously impractical approaches

* When properly trained and validated on appropriate datasets

Credit: Chris Messenger (MLA meeting,, Jan 2025)

01

GW

GW astronomy
AI for science
(Pros & Cons of AI)

02

AI for GW

GW Search
Parameter inference
(SBI method)

03

LLM for GW

Algorithm Heuristic Design

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

How do we understand AI's inner workings in GW data analysis?

Uncovering the "black box" to reveal
how AI actually processes GW strain data

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Core Insight from Computer Vision

Direct approach from Computer Vision (CV) to GW signal processing: pixel point \(\Rightarrow\) sampling point.
The CNN framework treats time series data similar to images, where each sampling point represents a feature to learn.

Performance Analysis

Convolutional neural networks (CNN) can achieve comparable performance to Matched Filtering under Gaussian stationary noise.
CNNs significantly outperform traditional methods in terms of execution speed (with GPU support).
Modern architectures show improved robustness against non-Gaussian noise transients (glitches).

Pioneering Research Publications

PRL, 2018, 120(14): 141103.

PRD, 2018, 97(4): 044039.

He Wang | ICTP-AP, UCAS

CNN for GW Detection: Pioneering Approaches

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Matched-filtering Convolutional Neural Network (MFCNN)

HW, SC Wu, ZJ CAO, et al. PRD 101, 10 (2020): 104003

He Wang | ICTP-AP, UCAS

CNN for GW Detection: Feature Extraction

Convolutional Neural Network (ConvNet or CNN)

feature extraction

classifier

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

>> Is it matched-filtering ?
>> Wait, It can be matched-filtering!

Matched-filtering (cross-correlation with templates) can be interpreted as a convolutional layer with predefined kernels.

GW150914

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Transform matched-filtering method from frequency domain to time domain.
The square of matched-filtering SNR for a given data \(d(t) = n(t)+h(t)\):

\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)

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

where

\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.

Deep Learning Framework

\rho^2(t)\equiv\frac{1}{\langle h|h \rangle}|\langle d|h \rangle(t)|^2

Time Domain

(matched-filtering)

(normalizing)

(whitening)

\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

Frequency Domain

\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)\star x_2(t)

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

CNN for GW Detection: Feature Extraction

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

CNN for GW Detection: Feature Extraction

Transform matched-filtering method from frequency domain to time domain.
The square of matched-filtering SNR for a given data \(d(t) = n(t)+h(t)\):

\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)

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

where

\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.

Deep Learning Framework

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

output[n, i, :] = \sum^{channel}_{j=0} input[n,j,:] \ast weight[i,j,:]

FYI: \(N_\ast = \lfloor(N-K+2P)/S\rfloor+1\)

（A schematic illustration for a unit of convolution layer)

\rho^2(t)\equiv\frac{1}{\langle h|h \rangle}|\langle d|h \rangle(t)|^2

Time Domain

(matched-filtering)

(normalizing)

(whitening)

\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

Frequency Domain

\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)\star x_2(t)

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

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

import mxnet as mx
from mxnet import nd, gluon
from loguru import logger

def MFCNN(fs, T, C, ctx, template_block, margin, learning_rate=0.003):
    logger.success('Loading MFCNN network!')
    net = gluon.nn.Sequential()         
    with net.name_scope():
        net.add(MatchedFilteringLayer(mod=fs*T, fs=fs,
                                      template_H1=template_block[:,:1],
                                      template_L1=template_block[:,-1:]))
        net.add(CutHybridLayer(margin = margin))
        net.add(Conv2D(channels=16, kernel_size=(1, 3), activation='relu'))
        net.add(MaxPool2D(pool_size=(1, 4), strides=2))
        net.add(Conv2D(channels=32, kernel_size=(1, 3), activation='relu'))    
        net.add(MaxPool2D(pool_size=(1, 4), strides=2))
        net.add(Flatten())
        net.add(Dense(32))
        net.add(Activation('relu'))
        net.add(Dense(2))
	# Initialize parameters of all layers
    net.initialize(mx.init.Xavier(magnitude=2.24), ctx=ctx, force_reinit=True)
    return net

1 sec duration

35 templates used

Explainable AI Approach

Implements matched filtering operations through custom convolutional layers
Makes the network more interpretable by embedding domain knowledge
Connects traditional signal processing with deep learning
Outperforms standard CNNs in both accuracy and efficiency

Matched-filtering Convolutional Neural Network (MFCNN)

The available codes (2019): https://gist.github.com/iphysresearch/a00009c1eede565090dbd29b18ae982c

CNN for GW Detection: Feature Extraction

HW, SC Wu, ZJ CAO, et al. PRD 101, 10 (2020): 104003

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Gravitational wave signal search algorithm benchmark (MLGWSC-1)
Dataset-4: Sampled from O3a real gravitational wave observation data

First Benchmark for GW Detection Algorithms

Benchmark Results

Publications

Key Findings

On simulated noise data, machine learning algorithms are highly competitive compared to LIGO's most sensitive signal search pipelines
Most tested machine learning algorithms are overly sensitive to non-Gaussian real noise backgrounds, resulting in high false alarm rates

Traditional signal search algorithms can identify gravitational wave signals at low false alarm rates with assured confidence
Tested machine learning algorithms have very limited ability to identify long-duration signals

Note on Benchmark Limitations:

Outperforming PyCBC doesn't conclusively prove that matched filtering is inferior to AI methods. This is both because the dataset represents a specific distribution and because PyCBC settings could be further optimized for this particular benchmark.

He Wang | ICTP-AP, UCAS

arXiv:2501.13846 [gr-qc]

Phys. Rev. D 110, 024024 (2024)

Phys. Rev. D 107, 023021 (2023)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Interpretability Challenges: Comparing Detection Statistics

Challenges in Model Interpretability:
- The black-box nature of AI models complicates interpretability, challenging the comparison of AI-generated detection statistics with traditional matched filtering chi-square distributions.
- Convincing the scientific community of the pipeline's validity and the statistical significance of new discoveries remains difficult despite the model's ability to identify potential gravitational wave signals.

AI Model Denoising

Our Model's Detection Statistics

LVK Official Detection Statistics

Signal denoising visualization using our deep learning model (Transformer-based)

Detection statistics from our AI model showing O1 events

HW et al 2024 MLST 5 015046

GW151226

GW151012

Official detection statistics from LVK collaboration

LVK. PRD (2016). arXiv:1602.03839

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Exploring Beyond General Relativity

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

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

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

\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}

Yu-Xin Wang, Xiaotong Wei, Chun-Yue Li, Tian-Yang Sun, Shang-Jie Jin, He Wang*, Jing-Lei Cui, Jing-Fei Zhang, and Xin Zhang*. arXiv:2410.20129
PRD (2025)

He Wang | ICTP-AP, UCAS

arXiv:2407.07820 [gr-qc]

Recent AI Discoveries & Validation Hurdles:

A recent study (arXiv:2407.07820) demonstrates how a ResNet-based (CNN) architecture with careful signal search strategy and post-processing can identify 8 new potential gravitational wave events from LIGO O3 data.
The absence of these events in traditional PyCBC results raises questions: could adjustments to rate priors and p_astro parameters in signal models help traditional pipelines detect these candidates (if they are real GW events)?
The ideal approach combines multiple diverse pipelines working in parallel to ensure comprehensive detection (requiring interpretable models) and using evidence-based detection statistics while simultaneously optimizing both real signal population (p_astro) and noise model (likelihood) fits.

Search

PE

Rate

Key Insight:

Interpretability Challenges: Discoveries vs. Validation (part 1/2)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Interpretability Challenges: Discoveries vs. Validation (part 1/2)

Recent AI Discoveries & Validation Hurdles:

A recent study (arXiv:2407.07820) demonstrates how a ResNet-based (CNN) architecture with careful signal search strategy and post-processing can identify 8 new potential gravitational wave events from LIGO O3 data.
The absence of these events in traditional PyCBC results raises questions: could adjustments to rate priors and p_astro parameters in signal models help traditional pipelines detect these candidates (if they are real GW events)?
The ideal approach combines multiple diverse pipelines working in parallel to ensure comprehensive detection (requiring interpretable models) and using evidence-based detection statistics while simultaneously optimizing both real signal population (p_astro) and noise model (likelihood) fits.

Search

PE

Rate

Key Insight:

Credit: DCC-XXXXXXXX

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

01

GW

GW astronomy
AI for science
(Pros & Cons of AI)

02

AI for GW

GW Search
Parameter inference
(SBI method)

03

LLM for GW

Algorithm Heuristic Design

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Parameter Estimation: Holy Grail of GW data analysis

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Bayesian inference, the Holy Grail of gravitational-wave data analysis, enables astrophysical interpretation and scientific discoveries.
Traditional parameter estimation (PE) techniques rely on Bayesian analysis methods (posteriors + evidence).
Computing the full 15-dimensional posterior distribution estimate is very time-consuming:
- Template generation time-consuming
- Calculating likelihood function

Bayesian statistics

Data quality improvement

Credit: Marco Cavaglià

LIGO-Virgo data processing

GW searches

Astrophsical interpretation of GW sources

CQG. 37 (2020) 055002

Parameter Estimation: Holy Grail of GW data analysis

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

Nature Physics 18, 1 (2022) 112–17

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

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.

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

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

Parameter Estimation: AI application

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

ABC of Normalizing Flow Model (1/4)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

ABC of Normalizing Flow Model (2/4)

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

ABC of Normalizing Flow Model (3/4)

Train

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

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

nflow

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

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

ABC of Normalizing Flow Model (4/4)

Train

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

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

nflow

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

归一化流模型示意图

Test

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

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

nflow

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

He Wang | ICTP-AP, UCAS

Parameter Estimation Challenges with AI Models:

In parameter estimation, AI models' lack of interpretability requires substantial additional scientific validation to ensure credibility and acceptance of results.
Parameter distributions from AI models often lack robustness across different noise realizations and are difficult to calibrate against established methods.
Scientific papers using AI methods must dedicate significant space to validation procedures, comparing against traditional methods and demonstrating reliability across multiple test cases.

arXiv:2404.14286

Phys. Rev. D 109, 123547 (2024)

Interpretability Challenges: Discoveries vs. Validation (part 2/2)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

PRD 108, 4 (2023): 044029.

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

He Wang | ICTP-AP, UCAS

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.

Interpretability Challenges: Discoveries vs. Validation (part 2/2)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

PRD 108, 4 (2023): 044029.

He Wang | ICTP-AP, UCAS

对超分辨率初值面的哈密顿约束和动量约束修正（系统误差）

Numerical Relativity using AI

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

evolve

Thomas Helfer, et al. Super-Resolution without High-Resolution Labels for Black Hole Simulations. arXiv:2411.02453

He Wang | ICTP-AP, UCAS

Why Do We Trust Traditional Models?

Key Trust Factors:

✓ Interpretable: Parameters have physical meaning
✓ Built-in uncertainties: Input uncertainties propagate to outputs
✓ Model selection: Balance simplicity with accuracy
✓ Scientific insight: Reduces complexity, reveals principles

Traditional Physics Approach

Input

Human-Designed Algorithm

(Based on human insight)

Output

Example: Matched Filtering,
Linear Regression

Black-Box AI Approach

Input

AI Model

(Low interpretability)

Output

Examples: CNN, AlphaGo, DINGO

Key Challenge: How can we maintain the interpretability advantages of traditional models while leveraging the power of AI approaches?

Data/
Experience

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Bridging Trust & Performance in GW Analysis

Combining the interpretability of physics with the power of AI

Our Mission: To create transparent AI systems that combine physics-based interpretability with deep learning capabilities

Interpretable AI Approach

The best of both worlds

Input

Physics-Informed
Algorithm

(High interpretability)

Output

Example: Our Approach
(In Preparation)

AI Model

Physics
Knowledge

Traditional Physics Approach

Input

Human-Designed Algorithm

(Based on human insight)

Output

Example: Matched Filtering, linear regression

Black-Box AI Approach

Input

AI Model

(Low interpretability)

Output

Examples: CNN, AlphaGo, DINGO

Data/
Experience

Interpretable Gravitational Wave Data Analysis with DL and LLMs

🎯 OUR WORK

hewang@ucas.ac.cn

LLMs for Gravitational Wave Data Analysis

From applied mathematics and fundamental physics to gravitational wave astronomy and complex systems analysis, scientific discovery relies on decisions driven by prior experience and data assumptions - yet faces persistent challenges in gravitational-wave signal identification.
While existing approaches like matched filtering (MF) and deep neural networks (DNNs) have achieved partial success, their limitations emerge through MF's excessive computational demands and dependence on theoretical assumptions requiring predefined waveform templates, and DNNs' black-box architectures that obscure decision logic while introducing hidden biases and overfitting tendencies.
We propose a synergistic framework where Monte Carlo Tree Search (MCTS) enables stepwise decision-making through strategic exploration, self-evolving (SelfEvo) optimization dynamically adjusts search policies via continuous performance feedback, and large language model (LLM)- generated heuristics inject domain-aware constraints - creating a closed-loop system that combines structured reasoning with adaptive learning.

He Wang | ICTP-AP, UCAS

Deep Learning Applications in Gravitational Wave Data Analysis

hewang@ucas.ac.cn

Automated Heuristic Design: Problem Definition

He Wang | ICTP-AP, UCAS

For any complex task \(P\) (especially NP-hard problems), Automated Heuristic Design (AHD) searches for the optimal heuristic \(h^*\) within a heuristic space \(H\):

\(h^*=\underset{h \in H}{\arg \max } g(h) \)

The heuristic space \(H\) contains all feasible algorithmic solutions for task \(P\). Each heuristic \(h \in H\) maps from the set of task inputs \(I_P\) to corresponding solutions \(S_P\):

\(h: I_P \rightarrow S_P\)

Performance measure \(g(\cdot)\) evaluates each heuristic's effectiveness, \(g: H \rightarrow \mathbb{R}\). For minimization problems with objective function \(f: S_P \rightarrow \mathbb{R}\), we estimate performance by evaluating the heuristic instances \({ins}\in D \subseteq I_P\) on dataset \(D\) as follows:

\(g(h)=\mathbb{E}_{\boldsymbol{ins} \in D}[-f(h(\boldsymbol{ins}))]\)

arXiv.2410.14716

P

H

S_p

\mathbb{R}

f

I_p

h

external_knowledge
(constraint)

h

g(h)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

import numpy as np
import scipy.signal as signal
def pipeline_v1(strain_h1: np.ndarray, strain_l1: np.ndarray, times: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    def data_conditioning(strain_h1: np.ndarray, strain_l1: np.ndarray, times: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
        window_length = 4096
        dt = times[1] - times[0]
        fs = 1.0 / dt
        
        def whiten_strain(strain):
            strain_zeromean = strain - np.mean(strain)
            freqs, psd = signal.welch(strain_zeromean, fs=fs, nperseg=window_length,
                                       window='hann', noverlap=window_length//2)
            smoothed_psd = np.convolve(psd, np.ones(32) / 32, mode='same')
            smoothed_psd = np.maximum(smoothed_psd, np.finfo(float).tiny)
            white_fft = np.fft.rfft(strain_zeromean) / np.sqrt(np.interp(np.fft.rfftfreq(len(strain_zeromean), d=dt), freqs, smoothed_psd))
            return np.fft.irfft(white_fft)

        whitened_h1 = whiten_strain(strain_h1)
        whitened_l1 = whiten_strain(strain_l1)
        
        return whitened_h1, whitened_l1, times
    
    def compute_metric_series(h1_data: np.ndarray, l1_data: np.ndarray, time_series: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
        fs = 1 / (time_series[1] - time_series[0])
        f_h1, t_h1, Sxx_h1 = signal.spectrogram(h1_data, fs=fs, nperseg=256, noverlap=128, mode='magnitude', detrend=False)
        f_l1, t_l1, Sxx_l1 = signal.spectrogram(l1_data, fs=fs, nperseg=256, noverlap=128, mode='magnitude', detrend=False)
        tf_metric = np.mean((Sxx_h1**2 + Sxx_l1**2) / 2, axis=0)
        gps_mid_time = time_series[0] + (time_series[-1] - time_series[0]) / 2
        metric_times = gps_mid_time + (t_h1 - t_h1[-1] / 2)
        
        return tf_metric, metric_times

    def calculate_statistics(tf_metric, t_h1):
        background_level = np.median(tf_metric)
        peaks, _ = signal.find_peaks(tf_metric, height=background_level * 1.0, distance=2, prominence=background_level * 0.3)
        peak_times = t_h1[peaks]
        peak_heights = tf_metric[peaks]
        peak_deltat = np.full(len(peak_times), 10.0)  # Fixed uncertainty value
        return peak_times, peak_heights, peak_deltat

    whitened_h1, whitened_l1, data_times = data_conditioning(strain_h1, strain_l1, times)
    tf_metric, metric_times = compute_metric_series(whitened_h1, whitened_l1, data_times)
    peak_times, peak_heights, peak_deltat = calculate_statistics(tf_metric, metric_times)
    
    return peak_times, peak_heights, peak_deltat

Input: H1 and L1 detector strains, time array | Output: Event times, significance values, and time uncertainties

P

H

S_p

\mathbb{R}

f

I_p

h

external_knowledge
(constraint)

h

g(h)

Problem: Pipeline Workflow

Conditions raw detector data (whitening)
Computes time-frequency metrics
Identifies peaks above background
Returns event candidates with timestamps

Optimization Target: Maximizing Area Under Curve (AUC) in the 1-1000Hz false alarms per-year range, balancing detection sensitivity and false alarm rates across algorithm generations

Automated Heuristic Design: Problem Definition

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

He Wang | ICTP-AP, UCAS

Algorithmic Exploration：LLM Prompt Engineering

external_knowledge
(constraint)

h

g(h)

Prompt Structure for Algorithm Evolution

This template guides the LLM to generate optimized gravitational wave detection algorithms by learning from comparative examples.

Key Components:

Expert role establishment
Example pair analysis (worse/better algorithm)
Reflection on improvements
Targeted new algorithm generation
Strict output format enforcement

You are an expert in gravitational wave signal detection algorithms. Your task is to design heuristics that can effectively solve optimization problems.

{prompt_task}

I have analyzed two algorithms and provided a reflection on their differences. 

[Worse code]
{worse_code}

[Better code]
{better_code}

[Reflection]
{reflection}

Based on this reflection, please write an improved algorithm according to the reflection. 
First, describe the design idea and main steps of your algorithm in one sentence. The description must be inside a brace outside the code implementation. Next, implement it in Python as a function named '{func_name}'.
This function should accept {input_count} input(s): {joined_inputs}. The function should return {output_count} output(s): {joined_outputs}. 
{inout_inf} {other_inf}

Do not give additional explanations.

One Prompt Template for MLGWSC1 Algorithm Synthesis

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

hewang@ucas.ac.cn

Algorithmic Synergy: MCTS, Evolution & LLM Agents

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Within each evolutionary iteration, MCTS decomposes complex signal detection problems into manageable decision sequences, enabling depth-wise and path-wise exploration of algorithmic possibilities.
We propose four evolutionary operations for MCTS expansion: Parent Crossover (PC) combines information from nodes at the parent level, Sibling Crossover (SC) exchanges features between nodes sharing the same parent, Point Mutation (PM) introduces random perturbations to individual nodes, and Path-wise Crossover (PWC) synthesizes information along complete trajectories from root to leaf.

hewang@ucas.ac.cn

deepseek-R1 for reflection generation
o3-mini-medium for code generation

Algorithmic Synergy: MCTS, Evolution & LLM Agents

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

deepseek-R1 for reflection generation
o3-mini-medium for code generation

MLGWSC1 Benchmark: Optimization Performance Results

Optimization Progress & Algorithm Diversity

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

Pipeline Workflow

Conditions raw detector data (whitening)
Computes time-frequency metrics
Identifies peaks above background
Returns event candidates with timestamps

Diversity in Evolutionary Computation

Population encoding:

Removing comments and docstrings using abstract-syntax tree,
standardizing code snippets into a common coding style (e.g., PEP81),
Convert code snippets to vector representations using a code embedding model.

Pipeline Workflow

Conditions raw detector data (whitening)
Computes time-frequency metrics
Identifies peaks above background
Returns event candidates with timestamps

hewang@ucas.ac.cn

MLGWSC1 Benchmark: Optimization Performance Results

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

Refs of Benchmark Models

Sage: 2501.13846 [gr-qc]
Virgo-AUTh / TPI FSU Jena: PRD 110, 024024 (2024)
Others: PRD 107, 023021 (2023)

hewang@ucas.ac.cn

Interpretability Analysis: PT Level 5

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

import numpy as np
import scipy.signal as signal
from scipy.signal.windows import tukey
from scipy.signal import savgol_filter

def pipeline_v2(strain_h1: np.ndarray, strain_l1: np.ndarray, times: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    The pipeline function processes gravitational wave data from the H1 and L1 detectors to identify potential gravitational wave signals.
    It takes strain_h1 and strain_l1 numpy arrays containing detector data, and times array with corresponding time points.
    The function returns a tuple of three numpy arrays: peak_times containing GPS times of identified events,
    peak_heights with significance values of each peak, and peak_deltat showing time window uncertainty for each peak.
    """
    eps = np.finfo(float).tiny
    dt = times[1] - times[0]
    fs = 1.0 / dt
    # Base spectrogram parameters
    base_nperseg = 256
    base_noverlap = base_nperseg // 2
    medfilt_kernel = 101       # odd kernel size for robust detrending
    uncertainty_window = 5     # half-window for local timing uncertainty

    # -------------------- Stage 1: Robust Baseline Detrending --------------------
    # Remove long-term trends using a median filter for each channel.
    detrended_h1 = strain_h1 - signal.medfilt(strain_h1, kernel_size=medfilt_kernel)
    detrended_l1 = strain_l1 - signal.medfilt(strain_l1, kernel_size=medfilt_kernel)

    # -------------------- Stage 2: Adaptive Whitening with Enhanced PSD Smoothing --------------------
    def adaptive_whitening(strain: np.ndarray) -> np.ndarray:
        # Center the signal.
        centered = strain - np.mean(strain)
        n_samples = len(centered)
        # Adaptive window length: between 5 and 30 seconds
        win_length_sec = np.clip(n_samples / fs / 20, 5, 30)
        nperseg_adapt = int(win_length_sec * fs)
        nperseg_adapt = max(10, min(nperseg_adapt, n_samples))
        
        # Create a Tukey window with 75% overlap.
        tukey_alpha = 0.25
        win = tukey(nperseg_adapt, alpha=tukey_alpha)
        noverlap_adapt = int(nperseg_adapt * 0.75)
        if noverlap_adapt >= nperseg_adapt:
            noverlap_adapt = nperseg_adapt - 1
        
        # Estimate the power spectral density (PSD) using Welch's method.
        freqs, psd = signal.welch(centered, fs=fs, nperseg=nperseg_adapt,
                                  noverlap=noverlap_adapt, window=win, detrend='constant')
        psd = np.maximum(psd, eps)
        
        # Compute relative differences for PSD stationarity measure.
        diff_arr = np.abs(np.diff(psd)) / (psd[:-1] + eps)
        # Smooth the derivative with a moving average.
        if len(diff_arr) >= 3:
            smooth_diff = np.convolve(diff_arr, np.ones(3)/3, mode='same')
        else:
            smooth_diff = diff_arr
        
        # Exponential smoothing (Kalman-like) with adaptive alpha using PSD stationarity.
        smoothed_psd = np.copy(psd)
        for i in range(1, len(psd)):
            # Adaptive smoothing coefficient: base 0.8 modified by local stationarity (±0.05)
            local_alpha = np.clip(0.8 - 0.05 * smooth_diff[min(i-1, len(smooth_diff)-1)], 0.75, 0.85)
            smoothed_psd[i] = local_alpha * smoothed_psd[i-1] + (1 - local_alpha) * psd[i]
            
        # Compute Tikhonov regularization gain based on deviation from median PSD.
        noise_baseline = np.median(smoothed_psd)
        raw_gain = (smoothed_psd / (noise_baseline + eps)) - 1.0
        
        # Compute a causal-like gradient using the Savitzky-Golay filter.
        win_len = 11 if len(smoothed_psd) >= 11 else ((len(smoothed_psd)//2)*2+1)
        polyorder = 2 if win_len > 2 else 1
        delta_freq = np.mean(np.diff(freqs))
        grad_psd = savgol_filter(smoothed_psd, win_len, polyorder, deriv=1, delta=delta_freq, mode='interp')
        
        # Nonlinear scaling via sigmoid to enhance gradient differences.
        sigmoid = lambda x: 1.0 / (1.0 + np.exp(-x))
        scaling_factor = 1.0 + 2.0 * sigmoid(np.abs(grad_psd) / (np.median(smoothed_psd) + eps))
        
        # Compute adaptive gain factors with nonlinear scaling.
        gain = 1.0 - np.exp(-0.5 * scaling_factor * raw_gain)
        gain = np.clip(gain, -8.0, 8.0)
        
        # FFT-based whitening: interpolate gain and PSD onto FFT frequency bins.
        signal_fft = np.fft.rfft(centered)
        freq_bins = np.fft.rfftfreq(n_samples, d=dt)
        interp_gain = np.interp(freq_bins, freqs, gain, left=gain[0], right=gain[-1])
        interp_psd = np.interp(freq_bins, freqs, smoothed_psd, left=smoothed_psd[0], right=smoothed_psd[-1])
        denom = np.sqrt(interp_psd) * (np.abs(interp_gain) + eps)
        denom = np.maximum(denom, eps)
        white_fft = signal_fft / denom
        whitened = np.fft.irfft(white_fft, n=n_samples)
        return whitened

    # Whiten H1 and L1 channels using the adapted method.
    white_h1 = adaptive_whitening(detrended_h1)
    white_l1 = adaptive_whitening(detrended_l1)

    # -------------------- Stage 3: Coherent Time-Frequency Metric with Frequency-Conditioned Regularization --------------------
    def compute_coherent_metric(w1: np.ndarray, w2: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
        # Compute complex spectrograms preserving phase information.
        f1, t_spec, Sxx1 = signal.spectrogram(w1, fs=fs, nperseg=base_nperseg,
                                              noverlap=base_noverlap, mode='complex', detrend=False)
        f2, t_spec2, Sxx2 = signal.spectrogram(w2, fs=fs, nperseg=base_nperseg,
                                               noverlap=base_noverlap, mode='complex', detrend=False)
        # Ensure common time axis length.
        common_len = min(len(t_spec), len(t_spec2))
        t_spec = t_spec[:common_len]
        Sxx1 = Sxx1[:, :common_len]
        Sxx2 = Sxx2[:, :common_len]
        
        # Compute phase differences and coherence between detectors.
        phase_diff = np.angle(Sxx1) - np.angle(Sxx2)
        phase_coherence = np.abs(np.cos(phase_diff))
        
        # Estimate median PSD per frequency bin from the spectrograms.
        psd1 = np.median(np.abs(Sxx1)**2, axis=1)
        psd2 = np.median(np.abs(Sxx2)**2, axis=1)
        
        # Frequency-conditioned regularization gain (reflection-guided).
        lambda_f = 0.5 * ((np.median(psd1) / (psd1 + eps)) + (np.median(psd2) / (psd2 + eps)))
        lambda_f = np.clip(lambda_f, 1e-4, 1e-2)
        # Regularization denominator integrating detector PSDs and lambda.
        reg_denom = (psd1[:, None] + psd2[:, None] + lambda_f[:, None] + eps)
        
        # Weighted phase coherence that balances phase alignment with noise levels.
        weighted_comp = phase_coherence / reg_denom
        
        # Compute axial (frequency) second derivatives as curvature estimates.
        d2_coh = np.gradient(np.gradient(phase_coherence, axis=0), axis=0)
        avg_curvature = np.mean(np.abs(d2_coh), axis=0)
        
        # Nonlinear activation boost using tanh for regions of high curvature.
        nonlinear_boost = np.tanh(5 * avg_curvature)
        linear_boost = 1.0 + 0.1 * avg_curvature
        
        # Cross-detector synergy: weight derived from global median consistency.
        novel_weight = np.mean((np.median(psd1) + np.median(psd2)) / (psd1[:, None] + psd2[:, None] + eps), axis=0)
        
        # Integrated time-frequency metric combining all enhancements.
        tf_metric = np.sum(weighted_comp * linear_boost * (1.0 + nonlinear_boost), axis=0) * novel_weight
        
        # Adjust the spectrogram time axis to account for window delay.
        metric_times = t_spec + times[0] + (base_nperseg / 2) / fs
        return tf_metric, metric_times

    tf_metric, metric_times = compute_coherent_metric(white_h1, white_l1)

    # -------------------- Stage 4: Multi-Resolution Thresholding with Octave-Spaced Dyadic Wavelet Validation --------------------
    def multi_resolution_thresholding(metric: np.ndarray, times_arr: np.ndarray) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
        # Robust background estimation with median and MAD.
        bg_level = np.median(metric)
        mad_val = np.median(np.abs(metric - bg_level))
        robust_std = 1.4826 * mad_val
        threshold = bg_level + 1.5 * robust_std

        # Identify candidate peaks using prominence and minimum distance criteria.
        peaks, _ = signal.find_peaks(metric, height=threshold, distance=2, prominence=0.8 * robust_std)
        if peaks.size == 0:
            return np.array([]), np.array([]), np.array([])

        # Local uncertainty estimation using a Gaussian-weighted convolution.
        win_range = np.arange(-uncertainty_window, uncertainty_window + 1)
        sigma = uncertainty_window / 2.5
        gauss_kernel = np.exp(-0.5 * (win_range / sigma) ** 2)
        gauss_kernel /= np.sum(gauss_kernel)
        weighted_mean = np.convolve(metric, gauss_kernel, mode='same')
        weighted_sq = np.convolve(metric ** 2, gauss_kernel, mode='same')
        variances = np.maximum(weighted_sq - weighted_mean ** 2, 0.0)
        uncertainties = np.sqrt(variances)
        uncertainties = np.maximum(uncertainties, 0.01)

        valid_times = []
        valid_heights = []
        valid_uncerts = []
        n_metric = len(metric)

        # Compute a simple second derivative for local curvature checking.
        if n_metric > 2:
            second_deriv = np.diff(metric, n=2)
            second_deriv = np.pad(second_deriv, (1, 1), mode='edge')
        else:
            second_deriv = np.zeros_like(metric)

        # Use octave-spaced scales (dyadic wavelet validation) to validate peak significance.
        widths = np.arange(1, 9)  # approximate scales 1 to 8
        for peak in peaks:
            # Skip peaks lacking sufficient negative curvature.
            if second_deriv[peak] > -0.1 * robust_std:
                continue
            local_start = max(0, peak - uncertainty_window)
            local_end = min(n_metric, peak + uncertainty_window + 1)
            local_segment = metric[local_start:local_end]
            if len(local_segment) < 3:
                continue
            try:
                cwt_coeff = signal.cwt(local_segment, signal.ricker, widths)
            except Exception:
                continue
            max_coeff = np.max(np.abs(cwt_coeff))
            # Threshold for validating the candidate using local MAD.
            cwt_thresh = mad_val * np.sqrt(2 * np.log(len(local_segment) + eps))
            if max_coeff >= cwt_thresh:
                valid_times.append(times_arr[peak])
                valid_heights.append(metric[peak])
                valid_uncerts.append(uncertainties[peak])

        if len(valid_times) == 0:
            return np.array([]), np.array([]), np.array([])
        return np.array(valid_times), np.array(valid_heights), np.array(valid_uncerts)

    peak_times, peak_heights, peak_deltat = multi_resolution_thresholding(tf_metric, metric_times)
    return peak_times, peak_heights, peak_deltat

hewang@ucas.ac.cn

Interpretability Analysis

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

Out-of-distribution (OOD) detection

Generalization capability and robustness of the optimized algorithms

MCTS Depth-Stratified Performance Analysis.

Analyzed the relationship between MCTS tree depth and algorithm fitness across different optimization phases. The 10-layer MCTS structure was stratified into three depth groups: Depth I (depths 1-4), Depth II (depths 5-7), and Depth III (depths 8-10), representing shallow, intermediate, and deep exploration levels, respectively.

hewang@ucas.ac.cn

Algorithmic Component Impact Analysis.

A comprehensive technique impact analysis using controlled comparative methodology

GW150914

Framework Mechanism Analysis

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

HW et al., In preparation

Effect of scale

Ablation study of various LLM contributions (code generator) and their robustness (Each curve is averaged over at least 5 runs)

Contributions of knowledge synthesis

Compare to w/o external knowledge (linear only; no content used)

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Bridging Trust & Performance in GW Analysis

Combining the interpretability of physics with the power of AI

Our Mission: To create transparent AI systems that combine physics-based interpretability with deep learning capabilities

Interpretable AI Approach

The best of both worlds

Input

Physics-Informed
AI Algorithm

(High interpretability)

Output

Example: Our Approach
(In Preparation)

AI Model

Physics
Knowledge

Traditional Physics Approach

Input

Human-Designed Algorithm

(Based on human insight)

Output

Example: Matched Filtering, linear regression

Black-Box AI Approach

Input

AI Model

(Low interpretability)

Output

Examples: CNN, AlphaGo, DINGO

Data/
Experience

Interpretable Gravitational Wave Data Analysis with DL and LLMs

🎯 OUR WORK

hewang@ucas.ac.cn

引力波数据分析：知识框架

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

理论基础：
- 引力波物理
- 数字信号处理
- 数理统计
编程基础：
硬件基础：

Miller, M.C., Yunes, N. The new frontier of gravitational waves. Nature 568, 469–476 (2019).

引力波物理与引力波天文学

数字信号处理

R.C. Cofer, Benjamin F. Harding, in Rapid System Prototyping with FPGAs, 2006

Dieter Rasch, Dieter Schott. Mathematical Statistics, (2018)

数理统计

引力波数据分析：知识框架

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

理论基础：
- 引力波物理 (pycbc, lalsuite, lisacode, bilby, ... )
- 数字信号处理 (scipy, stat, ...)
- 数理统计 (bilby, emcee, ptemcee, ptmcmc, …)
编程基础：
- Python (numpy, pandas; matplotlib; ...),
- AI (scikit-learn, XGBoost, PyTorch, TensorFlow, JAX, ...)
- Linux (docker, github, bash, vim, emacs …)
硬件基础：
- 主板、内存，GPUs，显存 ...
- AI时代程序员都应该了解的GPU基础知识

Summary: AI for (Gravitational Wave) Science

Key Insights from Our Journey

Deep learning methods have transformed GW data analysis, enabling detection capabilities that complement traditional approaches
Evolution from simple CNN architectures to sophisticated frameworks that leverage domain knowledge
LLM-guided algorithmic optimization demonstrates potential for creating high-performance, interpretable methods
Balancing sensitivity and false alarm rates remains a key challenge
Benchmark results validate the potential of AI-driven approaches in scientific discovery

The Critical Role of Interpretability

Algorithm interpretability provides multiple essential benefits:

Scientific Understanding: Reveals unique characteristics of different model architectures and their decision processes
Algorithm Interpolation: Enables meaningful combination of different approaches by understanding their complementary strengths
Result Controllability: Provides confidence in outcomes and minimizes unexplained behaviors
Model Calibration: Allows fine-tuning of algorithms based on physical understanding rather than black-box optimization

The future of (gravitational wave) science lies at the intersection of traditional physics-inspired methods and interpretable AI approaches, creating a new paradigm for reliable scientific discovery.

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Summary: AI for Gravitational Wave Science

Key Insights from Our Journey

Deep learning methods have transformed GW data analysis, enabling detection capabilities that complement traditional approaches
Evolution from simple CNN architectures to sophisticated frameworks that leverage domain knowledge
LLM-guided algorithmic optimization demonstrates potential for creating high-performance, interpretable methods
Balancing sensitivity and false alarm rates remains a key challenge
Benchmark results validate the potential of AI-driven approaches in scientific discovery

The Critical Role of Interpretability

Algorithm interpretability provides multiple essential benefits:

Scientific Understanding: Reveals unique characteristics of different model architectures and their decision processes
Algorithm Interpolation: Enables meaningful combination of different approaches by understanding their complementary strengths
Result Controllability: Provides confidence in outcomes and minimizes unexplained behaviors
Model Calibration: Allows fine-tuning of algorithms based on physical understanding rather than black-box optimization

The future of gravitational wave science lies at the intersection of traditional physics-inspired methods and interpretable AI approaches, creating a new paradigm for reliable scientific discovery.

hewang@ucas.ac.cn

Interpretable Gravitational Wave Data Analysis with DL and LLMs

引力波物理和引力波天文学
引力波数据分析
人工智能时代下的科学研究
- 乐观？悲观？
- 探索物理的新途径 + 理解问题的新视角

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

Key Questions

Q1: Can LLMs truly generate novel content beyond their training data?

Q2: Why can LLMs perform reasoning in ways that remain imperceptible to us?

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

The Rise of LLMs: How Code Training Transformed AI Capabilities

Evolution of GPT Capabilities

A careful examination of GPT-3.5's capabilities reveals the origins of its emergent abilities:

Original GPT-3 gained generative abilities, world knowledge, and in-context learning through pretraining
Instruction-tuned models developed the ability to follow directions and generalize to unseen tasks
Code-trained models (code-davinci-002) acquired code comprehension
The ability to perform complex reasoning likely emerged as a byproduct of code training

GPT-3.5 series [Source: University of Edinburgh, Allen Institute for AI]

He Wang | ICTP-AP, UCAS

GPT-3 (2020)

ChatGPT (2022)

Magic: Code + Text

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Recent research demonstrates that LLMs can solve complex optimization problems through carefully engineered prompts. DeepMind's OPRO (Optimization by PROmpting) approach showcases how LLMs can generate increasingly refined solutions through iterative prompting techniques.

OPRO: Optimization by PROmpting

Example: Least squares optimization through prompt engineering

arXiv:2309.03409 [cs.NE]

Two Directions of LLM-based Optimization

arXiv:2405.10098 [cs.NE]

He Wang | ICTP-AP, UCAS

The Optimization Potential of Large Language Models

LLMs can generate high-quality solutions to optimization problems without specialized training

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Theoretical Understanding of LLMs' Emergent Abilities

The Interpolation Theory

LLMs' ability to generate novel responses from few examples is increasingly understood as manifold interpolation rather than mere memorization:

LLMs learn a continuous semantic manifold of language during pre-training
Few-shot examples serve as anchor points in this high-dimensional space
The model interpolates between examples to generate responses for novel inputs
This enables coherent generalization beyond the training distribution
The quality of interpolation improves with model scale and training data breadth

The theory suggests that in-context learning is not "learning" in the traditional sense, but rather a form of implicit conditioning on the manifold of learned representations.

Representation Space Interpolation

Real-world Case: FunSearch (Nature, 2023)

Google DeepMind's FunSearch system pairs LLMs with evaluators in an evolutionary process
Discovered new mathematical knowledge for the cap set problem in combinatorics, improving on best known bounds
Also created novel algorithms for online bin packing that outperform traditional methods
Demonstrates LLMs can make verifiable scientific discoveries beyond their training data

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Key Questions

Q1: Can LLMs truly generate novel content beyond their training data?

Q2: Why can LLMs perform reasoning in ways that remain imperceptible to us?

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Iterative Inference: The New Frontier of LLM Scaling

He Wang | ICTP-AP, UCAS

📄 Google DeepMind: "Scaling LLM Test-Time Compute Optimally" (arXiv:2408.03314)

🔗 OpenAI: Learning to Reason with LLMs

Iterative refinement during inference dramatically improves reasoning capabilities without increasing model size or retraining

Performance improvements with test-time compute scaling

From pre-training to test-time:
Three scaling regimes

Different search methods for iterative reasoning

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Key Questions

Q1: Can LLMs truly generate novel content beyond their training data?

Q2: Why can LLMs perform reasoning in ways that remain imperceptible to us?

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Q3: Why should you consider applying ML to gravitational wave astrophysics?

Why should you consider applying ML to gravitational wave astrophysics?

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

我们为什么要考虑用 AI tool 来替换传统方法做研究呢？

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

The Rise of Machine Learning

AI is taking over the world... literally everywhere

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply ML to GW Astrophysics

Let's be honest about our motivations... 😉

The perfectly valid "scientific" reasons:

✓ It sounded like a cool project
✓ My supervisor said it was a good thing to work on
✓ I will learn some really useful ML skills
✓ I'm already good at ML
✓ I want to get better at ML
✓ I want to get a high-paying job after this PhD/postdoc
✓ I want to be spared when the machines take over

Credit: Chris Messenger (MLA meeting,, Jan 2025)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

严肃的讲，上述 motivation 并不应该是成为从事科学研究的思路和方向。

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Why is AI/ML Everywhere in GW Research?

The core motivations behind nearly all AI+GW research

1

ML is FAST

So much data, so little time!

• Bayesian parameter estimation
• Replaces computationally intensive components

2

ML is ACCURATE*

Consistently outperforms traditional approaches

• Unmodelled burst searches
• Continuous GW searches

3

ML is FLEXIBLE

Provides deeper insights into complex problems

• Reveals patterns through interpretability
• Enables previously impractical approaches

* When properly trained and validated on appropriate datasets

Credit: Chris Messenger (MLA meeting,, Jan 2025)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

He Wang | ICTP-AP, UCAS

Why is AI/ML Everywhere in GW Research?

The core motivations behind nearly all AI+GW research

1

ML is FAST

So much data, so little time!

• Bayesian parameter estimation
• Replaces computationally intensive components

2

ML is ACCURATE*

Consistently outperforms traditional approaches

• Unmodelled burst searches
• Continuous GW searches

3

ML is FLEXIBLE

Provides deeper insights into complex problems

• Reveals patterns through interpretability
• Enables previously impractical approaches

* When properly trained and validated on appropriate datasets

Credit: Chris Messenger (MLA meeting,, Jan 2025)

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

但杀鸡焉用牛刀？！

He Wang | ICTP-AP, UCAS

Is It Really So Simple?

The reality of ML in scientific research is more nuanced

No: We need to think more critically

❓ Are we just trying to predict a function?
❓ Are there any astrophysical constraints?
❓ Do we need to understand how/why it works?
❓ What about errors? Quality flags?
❓ What happens if things go wrong?

Twitter: @DeepLearningAI_

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

本质上，都可以归结为“黑箱”或“可解释性差”的问题

He Wang | ICTP-AP, UCAS

Why Even Use AI?

The mathematical inevitability and the path to understanding

Universal Approximation Theorem

The existence theorem that guarantees solutions

Neural networks with sufficient hidden layers can approximate any continuous function on compact subsets of \(\mathbb{R}^n\)
Ref: Cybenko, G. (1989), Hornik et al. (1989)

The solution is mathematically guaranteed — our challenge is finding the path to it

1

Machine learning will win in the long run

AI models still have vast potential compared to the human brain's efficiency. Beating traditional methods is mathematically inevitable given sufficient resources.

2

The question is not if AI/ML will win, but how

Understanding AI's inner workings is the real challenge, not proving its capabilities.

That's where we can learn something exciting with Foundation Models.

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

尽管种种，还是应该报以理性的期待和足够的乐观

Key Questions

Q1: Can LLMs truly generate novel content beyond their training data?

Q2: Why can LLMs perform reasoning in ways that remain imperceptible to us?

He Wang | ICTP-AP, UCAS

Interpretable Gravitational Wave Data Analysis with DL and LLMs

Q4:In general, how to use AI for science?

Q3: Why should you consider applying ML to gravitational wave astrophysics?

Application of AI

Interpretable Gravitational Wave Data Analysis with DL and LLMs

He Wang | ICTP-AP, UCAS

hewang@ucas.ac.cn

https://github.com/Nikasa1889/HistoryObjectRecognition

Gebru et al. ICCV (2017)

Zhou et al. CVPR (2018)

Shen et al. CVPR (2018)

Image courtesy of Tesla (2020)

从AI应用的原理理解技术相同点

eg: GW search

Representation Space Interpolation

Core Insights: Generative models' ability to perform accurate statistical inference can be understood as manifold learning rather than mere density estimation:

Models learn a continuous latent manifold of data distributions
Statistical parameters act as coordinates in this space
Inference occurs through latent space navigation
Enables robust generalization for complex distributions

He Wang | ICTP-AP, UCAS

Theoretical Understanding of Generative Models

Generative models don't memorize examples, but learn a continuous manifold
where similar concepts lie near each other. Statistical inference becomes
a form of navigation through this learned representation space.

Deep Learning is Not As Impressive As you Think, It's Mere Interpolation.

CVAE

Encodes data into latent space, enabling conditional generation

Flow-based

Transforms simple distributions into complex ones via invertible mappings

Interpretable Gravitational Wave Data Analysis with DL and LLMs

hewang@ucas.ac.cn

AI for Science

The core driving force of AI4Sci largely lies in its “interpolation” generalization capabilities, showcasing its powerful complex modeling abilities.

From 李宏毅

Interpretable Gravitational Wave Data Analysis with DL and LLMs

He Wang | ICTP-AP, UCAS

hewang@ucas.ac.cn

The core driving force of AI4Sci largely lies in its “interpolation” generalization capabilities, showcasing its powerful complex modeling abilities.

AI for Science

Interpretable Gravitational Wave Data Analysis with DL and LLMs

He Wang | ICTP-AP, UCAS

Test of General Relatively

2403.18936

hewang@ucas.ac.cn

2407.07229

2103.01641

引力波数据处理与人工智能技术应用

Contents

01

02

03

What is Gravitational wave?

Gravitational Wave Astronomy

Multi-messenger Astronomy

The Scientific Significance

Challenge and Methodology: Detecting Signals in GW Data

Challenge and Methodology: Detecting Signals in GW Data

Challenge and Methodology: Detecting Signals in GW Data

科学智能：AI for Science

科学智能：AI for Science

人工智能 > 机器学习 > 深度学习

The Rise of Machine Learning

Why should you consider applying ML to gravitational wave astrophysics?

The "Real" Reasons We Apply ML to GW Astrophysics

Why is AI/ML Everywhere in GW Research?

ML is FAST

ML is ACCURATE*

ML is FLEXIBLE

Contents

01

02

03

How do we understand AI's inner workings in GW data analysis?

CNN for GW Detection: Pioneering Approaches

CNN for GW Detection: Feature Extraction

CNN for GW Detection: Feature Extraction

CNN for GW Detection: Feature Extraction

CNN for GW Detection: Feature Extraction

First Benchmark for GW Detection Algorithms

Interpretability Challenges: Comparing Detection Statistics

Exploring Beyond General Relativity

Interpretability Challenges: Discoveries vs. Validation (part 1/2)

Interpretability Challenges: Discoveries vs. Validation (part 1/2)

Contents

01

02

03

Parameter Estimation: Holy Grail of GW data analysis

Parameter Estimation: Holy Grail of GW data analysis

Parameter Estimation: AI application

ABC of Normalizing Flow Model (1/4)

ABC of Normalizing Flow Model (2/4)

ABC of Normalizing Flow Model (3/4)

ABC of Normalizing Flow Model (4/4)

Interpretability Challenges: Discoveries vs. Validation (part 2/2)

Interpretability Challenges: Discoveries vs. Validation (part 2/2)

Numerical Relativity using AI

Why Do We Trust Traditional Models?

Bridging Trust & Performance in GW Analysis

Contents

01

02

03

LLMs for Gravitational Wave Data Analysis

Automated Heuristic Design: Problem Definition

Automated Heuristic Design: Problem Definition

Algorithmic Exploration：LLM Prompt Engineering

Algorithmic Synergy: MCTS, Evolution & LLM Agents

Algorithmic Synergy: MCTS, Evolution & LLM Agents

MLGWSC1 Benchmark: Optimization Performance Results

MLGWSC1 Benchmark: Optimization Performance Results

Interpretability Analysis: PT Level 5

Interpretability Analysis

Framework Mechanism Analysis

Bridging Trust & Performance in GW Analysis

引力波数据分析：知识框架

引力波数据分析：知识框架

Summary: AI for (Gravitational Wave) Science

Summary: AI for Gravitational Wave Science

Key Questions

The Rise of LLMs: How Code Training Transformed AI Capabilities

The Optimization Potential of Large Language Models

Theoretical Understanding of LLMs' Emergent Abilities

Key Questions

Iterative Inference: The New Frontier of LLM Scaling

Key Questions