王赫

2026/05/09 @内蒙古大学

国际理论物理中心（亚太地区）

中国科学院大学

hewang@ucas.ac.cn

机器学习如何改变引力波天文学？

Abstract

Upcoming challenges such as MLGWSC2, currently at the proposal stage, provide a new testbed for exploring machine-learning–based approaches to gravitational-wave analysis. In this flash talk, I briefly introduce my core ideas and experience using evolutionary algorithms, Evo-MCTS, and reinforcement learning as adaptive search and optimization tools. I outline key methodological insights and discuss how these ideas may inform future GW analysis tasks, including potential applications to LISA.

才翻到上面看到有人现场拍照 [破涕为笑]，随手分享一下

我最近常用的PPT英语字体是 Economica，是一个风格比较现代的无衬线字体：https://fonts.google.com/specimen/Economica
但用这个字体显得好看，牺牲了一点儿清晰度，有需要的时候还是会回归Helvetica Neue
衬线字体我喜欢用 Arno Pro: https://fonts.adobe.com/fonts/arno
中文字体已经锁死了喜鹊宋或者木叶（收费字体）
颜色一般从MetBrewer里面挑，但并没有特别注意配色：https://github.com/BlakeRMills/MetBrewer
今天刚和邵老师说，可能是中年危机的一种表现，就现在越来越喜欢五颜六色的东西。。。也体现在了PPT上。这个完全见仁见智。
如果有人对这种PPT感兴趣，我把一个7月份会议的短PPT分享在这供参考：https://www.dropbox.com/scl/fi/duez2bpbcck4ogtn98sw6/songhuang_sesto_20250707.key?rlkey=g18rnjym1hpzke3jxcj5y6ezh&st=ot5xu2w8&dl=0
我自己现在习惯的PPT排版的风格只适合分steps展示，不能一次都show全。我自己开始使用这个风格是上课以后，需要满足PPT好看，能吸引注意力，但同时信息量够足，学生可以拿来复习。暂时觉得还好，但过两年可能还是会学着做简单一点儿。
用字体大小和颜色来highlight关键词是最简单粗暴、最俗的引导视线的方法，属于广告里早就用烂了的。其实有更好的设计语言，但不会。。。
PPT风格纯属个人审美兴趣，和报告水平，更和报告内容好坏无关。

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。

Gravitational Wave

Gravitational Wave Astronomy

爱因斯坦于1916年提出广义相对论，并预言了引力波的存在
引力波是广义相对论中的一种强场效应
- 2015年：首次实验探测到双黑洞并合引力波
- 2017年：首次双中子星多信使探测，开启多信使天文学时代
- 2017年：引力波探测成果被授予诺贝尔物理学奖
- 至今：发现了超过 90 个引力波事件
2024年：中国科学院大学加入地面引力波实验LIGO科学合作组织，成为LIGO目前在中国大陆地区的第二家成员单位。
未来规划：
- 2024-2025年：有希望探测到更多不同类型的引力波事件
- 空间引力波探测计划 (LISA/Taiji/Tianqin) + XG (CE/ET)
- ...

LIGO-VIRGO-KAGRA network

Gravitational waves generated by binary black holes system

GW detector

Multi-messenger astronomy

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
四种系外信使包括：电磁辐射、引力波、中微子，以及宇宙射线。

多信使天文学

“电磁波天文学”

GW's Scientific Objectives

基础理论的检验与修正
- 基础物理学
  - 引力子是否有质量, 引力波的传播速度 ...
- 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 ...

The current clouds over fundamental physics:
- 量子力学与广义相对论的统一
- 星系旋转曲线（暗物质）、宇宙加速膨胀（暗能量）
- 哈勃常数H0
- 中微子震荡和质量问题
- ...

GW & Data Analysis

伯纳德·舒尔茨曾列出成功观测引力波的五条关键要素：
1. 良好的探测器技术
2. 良好的波形模板
3. 良好的数据分析方法和技术
4. 多个独立探测器间的一致性观测
5. 引力波天文学和电磁波天文学的一致性观测

DOI:10.1063/1.1629411

The first GW event of GW150914

LISA / Taiji project

LIGO-VIRGO-KAGRA

GW & Data Analysis

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)

GW & Data Analysis

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)

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：

Digital Signal Processing

Challenge: 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 )

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

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.)

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

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.)

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

科学智能：AI for Science

CNN for GW Detection

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.

Pioneering Approaches

MFCNN for GW Detection

Matched-filtering Convolutional Neural Network (MFCNN)

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

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

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

\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)

MFCNN for GW Detection

First Benchmark for GW Detection

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

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.

arXiv:2501.13846 [gr-qc]

Phys. Rev. D 110, 024024 (2024)

Phys. Rev. D 107, 023021 (2023)

Exploring Beyond General Relativity

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)

Parameter Estimation:
Holy Grail of GW data analysis

Parameter Estimation

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: AI application

Credit: Marco Cavaglià

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

DINGO

進撃の DINGO 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] (ICLR 2022)
- 2210.05686: +Importance sampling [2] (PRL)
- 2211.08801: Noise forecasting [2] (PRD)
- 2311.12093: Population studies [2] (PRD)
- 2404.14286: Find evidence for eccentric binaries. [2] (PRD)
- 2407.09602: BNS inference [2] (Nature)
- 2512.02968: +Transformer, (Dingo-T1) [3] (?)
- 2603.20431: For LISA [4] (?)

https://github.com/stephengreen/lfi-gw (2020)
https://github.com/dingo-gw/dingo (2023.03)
https://github.com/dingo-gw/dingo-T1 (2025.11)
https://github.com/AliSword/dingo-lisa (2026.04)
https://github.com/stephengreen/gw-school-corfu-2023 (Tutorial)
https://github.com/annalena-k/tutorial-dingo-introduction (Tutorial)

Interpretability Challenges:
Discoveries vs. Validation

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.

Phys. Rev. D 112 (2025) 104045

Phys. Rev. D 109, 123547 (2024)

PRD 108, 4 (2023): 044029.

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

ABC of Normalizing Flow Model (1/4)

ABC of Normalizing Flow Model (2/4)

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})

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})

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})

ABC of Normalizing Flow Model (4/4)

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

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

\mathbf{z}

\mathbf{y}

T

T^{-1}

base density

target density

左图展示了归一化流（Normalizing Flow）的核心思想：通过一系列可逆变换在数据空间与潜在空间之间建立一一对应关系。
在左侧的数据空间 \(\mathcal{X} \) 中，原始数据分布是复杂的（例如弯曲的双 moons 形流形）；通过学习到的可逆映射，将其逐步“拉直”并变换到右侧的潜在空间 \(\mathcal{Z} \)，使其变为简单的标准分布（如各向同性高斯）。反过来，从简单的潜在分布采样，再通过逆变换映射回数据空间，就可以生成复杂结构的数据。
关键点是：整个变换过程是双射（bijective）且可计算雅可比行列式，从而可以精确地进行概率密度的变换与建模。

Part II: Evo-MCTS, LLM-informed
mutations, and principled discovery
beyond hand-designed GW pipelines

Uncovering the "black box" to reveal how LLM actually works

HW, LZ. arXiv:2508.03661 [cs.AI]

科学智能：AI for Science

2025年的后半年，大家纷纷开始押注 AI for Science!

OpenAI 首席产品官（CPO）Kevin Weil 在社交媒体上正式宣布 OpenAI 将开启一项新计划 ——OpenAI for Science，旨在打造下一代科学工具：一个由人工智能驱动、能加速科学发现的平台。
2025年11月24日，美国白宫，特朗普正式签署，「创世纪计划」（Genesis Mission）正式启动！这是一项被比作「AI曼哈顿计划」的重大行政命令。这项计划的核心目标是：加速利用AI推动科学突破！
DeepMind：把“AI 科学合作者”直接送进国家实验室

NVIDIA：把科学问题变成 AI 基建问题。在 NVIDIA 的叙事里，AI for Science 并不局限于“模型”，而是一整套算力平台 + 仿真系统 + 自动化实验 + 工程化工作流，这是 Genesis 能“站得住”的物理基础。
2025 年 8 月，中国国务院发布《关于深入实施“人工智能+”行动的意见》（国发〔2025〕11 号），明确强调加快人工智能驱动的新型科研范式，加速“从 0 到 1”重大科学发现进程。

OpenAI 计划组建一个由顶尖学者组成的小型团队，这些学者需要满足三个条件：

在其研究领域达到世界级水准；
深度认同人工智能理念；
具备卓越的科学传播能力。

这一系列举措表明，AI 驱动的科学发现正从学术探索迈向战略竞争新阶段。

Cap Set Problem

给定一个N，求维度为N的网格里面最大能找到多少个点，这些点中任意三个点都不能连成一条直线。

Bin Packing Problem

如何在线将不同尺寸的物品装入最少数量的箱子中。

The largets cap set in N=2 has size 4.

The largest cap set in N=3 has size 9 > \(2^3\)

For N > 6, the size of the largest cap set is unknown.

Discover new knowledge and efficient algorithms using AI

Illustrative example of bin packing using existing heuristic – Best-fit heuristic (left), and using a heuristic discovered by FunSearch (right).

DeepMind Blog (Source)

LLM guided search in ”program“ space

Discover new knowledge and efficient algorithms using AI

LLM guided search in ”program“ space

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

YouTube (Source)

Discover new knowledge and efficient algorithms using AI

YouTube (Source)

LLM guided search in ”program“ space

Discover new knowledge and efficient algorithms using AI

LLM guided search in ”program“ space

arXiv:2506.13131 [cs.AI]

arXiv:2602.02990 [cs.AI]

Evaluation for MLGWSC-1 benchmark

Concept

Mechanism

problem → algorithm

data → algorithm → reward
↺ LLM-guided algorithm updates

LLM as designer

arXiv:2410.14716 [cs.LG]

external_knowledge
(constraint)

from problem-solving to algorithm discovery

HW, LZ. arXiv:2508.03661 [cs.AI]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

external_knowledge
(constraint)

Evaluation for MLGWSC-1 benchmark

LLM as designer

arXiv:2410.14716 [cs.LG]

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

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

MLGWSC-1 benchmark

HW, LZ. arXiv:2508.03661 [cs.AI]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

external_knowledge
(constraint)

PyCBC (linear-core)

cWB (nonlinear-core)

Simple filters (non-linear)

CNN-like (highly non-linear)

Benchmarking against state-of-the-art methods

Evaluation for MLGWSC-1 benchmark

LLM as designer

arXiv:2410.14716 [cs.LG]

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

HW, LZ. arXiv:2508.03661 [cs.AI]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

external_knowledge
(constraint)

PyCBC (linear-core)

cWB (nonlinear-core)

Simple filters (non-linear)

CNN-like (highly non-linear)

Benchmarking against state-of-the-art methods

Evaluation for MLGWSC-1 benchmark

LLM as designer

arXiv:2410.14716 [cs.LG]

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

HW, LZ. arXiv:2508.03661 [cs.AI]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

He Wang | ICTP-AP, UCAS

AI and Cosmology: From Computational Tools to Scientific Discovery

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}

{external_knowledge}

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

LLM as designer

external_knowledge
(constraint)

arXiv:2410.14716 [cs.LG]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

He Wang | ICTP-AP, UCAS

AI and Cosmology: From Computational Tools to Scientific Discovery

LLM as designer

external_knowledge
(constraint)

arXiv:2410.14716 [cs.LG]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

LLMs act as policies over algorithms, not predictors of data.

Algorithmic Synergy: MCTS, Evolution & LLM Agents

He Wang | ICTP-AP, UCAS

AI and Cosmology: From Computational Tools to Scientific Discovery

h

MCTS

Casse1: Go Game

Case 2: OpenAI Strawberry (o1)

The release of o1 marks the formal deployment of the inference-time scaling paradigm in production. As Richard Sutton pointed out in The Bitter Lesson, only learning and search are methods that can scale indefinitely with compute. From this point on, the focus has increasingly shifted toward search.

Browne et al. (2012)

arXiv:2305.14078 [cs.RO]

Monte Carlo Tree Search (MCTS), which combines stochastic simulation with tree-based search to optimize decision-making, has long been a core technique in modern game-playing systems such as AlphaGo.

LLM-Informed Evo-MCTS

OpenAI. Learning to reason with LLMs (2024)

OpenAI. Openai o1 system card (2024)

深度推理时代的来临：OpenAI o1开创推理扩展的新范式 (2024)

Algorithmic Synergy: MCTS, Evolution & LLM Agents

He Wang | ICTP-AP, UCAS

AI and Cosmology: From Computational Tools to Scientific Discovery

h

Within each evolutionary iteration, Monte Carlo Tree Search (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.

LLM-Informed Evo-MCTS

EA

Evolutionary Algorithms (EAs) are a class of heuristic search methods that simulate the mechanisms of biological evolution in nature, such as selection, crossover, and mutation. Their main advantages include:

Strong global search capability
No requirement for gradient information (high generality)
Good robustness and adaptability
Inherent parallelism (high computational efficiency)
Well-suited for multi-objective optimization problems

LLM-Driven Algorithmic Evolution Through Reflective Code Synthesis.

Monte Carlo Tree Search (MCTS) Algorithmic Evolution Pathway

What changed?

LLMs propose actions that guide the search
Evaluations (fitness/likelihood/...) become reusable memory

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

HW, LZ. arXiv:2508.03661 [cs.AI]

When LLMs Enter the Algorithmic Loop

The LLM does not predict answers — it reshapes how we search for algorithms.

Search trajectories matter more than isolated optima.

Interpretability Analysis

Algorithmic Component Impact Analysis.

A comprehensive technique impact analysis using controlled comparative methodology

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

Automatically discover and interpret the value of nonlinear algorithms
Facilitating new knowledge production along with experience guidance

PT Level 5

HW, LZ. arXiv:2508.03661 [cs.AI]

Framework Mechanism Analysis

Integrated Architecture Validation

A comprehensive comparison of our integrated
Evo-MCTS framework against its constituent components operating in isolation.
- Evo-MCTS: MCTS + Self-evolve + Reflection mech.
- MCTS-AHD: MCTS framework for CO.
- ReEvo: evolutionary framework for CO.

Contributions of knowledge synthesis

Compare to w/o external knowledge
- non-linear vs linear only

LLM Model Selection and Robustness Analysis

Ablation study of various LLM contributions (code generator) and their robustness.
- ```
o3-mini-medium
o1-2024-12-17
gpt-4o-2024-11-20
```
```
claude-3-7-sonnet-20250219-thinking
```

59.1%

115%

HW, LZ. arXiv:2508.03661 [cs.AI]

Framework Mechanism Analysis

He Wang | ICTP-AP, UCAS

AI and Cosmology: From Computational Tools to Scientific Discovery

Contributions of knowledge synthesis

Compare to w/o external knowledge
- non-linear vs linear only

59.1%

115%

59.1%

### External Knowledge Integration
1. **Non-linear** Processing Core Concepts:
    - Signal Transformation: 
        * Non-linear vs linear decomposition
        * Adaptive threshold mechanisms
        * Multi-scale analysis
    
    - Feature Extraction:
        * Phase space reconstruction
        * Topological data analysis
        * Wavelet-based detection
    
    - Statistical Analysis:
        * Robust estimators
        * Non-Gaussian processes
        * Higher-order statistics

2. Implementation Principles:
    - Prioritize adaptive over fixed parameters
    - Consider local vs global characteristics
    - Balance computational cost with accuracy

HW, LZ. arXiv:2508.03661 [cs.AI]

Interpretable AI Approach

The best of both worlds

Input

Physics-Informed
Algorithm

(High interpretability)

Output

Example: Evo-MCTS, AlphaEvolve

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

🎯 OUR WORK

Scientific discovery requires interpretability, not just performance.

Interpretable AI for Gravitational-Wave Discovery

Scientific discovery requires interpretability — not just performance.

Key Takeaways: ... against Symbolic Regression

vs

The design of any algorithm can be viewed as an optimization problem.

Many intermediate steps in gravitational wave data analysis can likewise be formulated as “algorithm optimization” problems, such as filter design, noise modeling, and the construction of detection statistics.
Similarly, many approaches in theoretical physics and cosmology—such as analytical modeling and symbolic regression—can also be interpreted within the framework of algorithm optimization.
- Symbolic regression vs. algorithm optimization:

Other Opt. Problem Egs:
- AI-driven design of experiments. [Phys. Rev. X 15, 021012 (2025)]
- RL design for multiple filters in LIGO control system. [Science (2025)]

Key Takeaways

维度重构：从“信号匹配”到“特征提取” (Feature Extraction)

范式转移：机器学习将预设模板的物理匹配转化为高维空间的可学习特征提取。
核心逻辑：突破传统算法对先验物理模型的依赖，通过非线性映射捕捉非稳态噪声中的微弱关联，实现从“按图索骥”到“自主识别”的跨越。

连续推断：从“离散采样”到“隐空间建模” (Latent Space Interpolation)

范式转移：归一化流（Normalizing Flow）将复杂的后验概率分布映射为简单的潜在分布。
核心逻辑：利用隐空间的连续性实现物理参数的即时插值与生成，将耗时数天的蒙特卡洛采样（MCMC）坍缩至毫秒级的确定性推断，定义了计算效率的新边界。

智能涌现：从“实验工具”到“科研合作者” (Nature of AI for Science)

范式转移：大语言模型（LLM）通过语义理解与原理性搜索，引导超越人类经验的科学发现。
核心逻辑：科学发现的本质正在从“基于经验的假设驱动”转向“基于概率的智能驱动”；AI 不再仅仅处理数据，而是在逻辑拓扑中探索物理定律的潜在变体。

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

太极实验室 2026 年度“大学生创新实践训练计划’

(引力波数据分析与 AI for Science 方向)

中国科学院大学引力波宇宙太极实验室(北京)引力波数据分析与机器学习课题组长期面向全国高校学生开放科研训练机会,现面向全国优秀学生招募参加太极实验室2026年度“大学生创新实践训练计划”,本课题组致力于探索引力波天文学、数值模拟与人工智能技术的交叉研究，重点发展新一代 Al for Science 方法，用于解决复杂物理系统建模、信号处理与科学数据分析问题,欢迎对 引力波科学、人工智能算法与科学计算 充满兴趣的同学加入，在真实科研项目中接受系统训练，并参与国际前沿研究。

此外，本实验室长期欢迎对相关研究方向感兴趣的同学联系咨询，本广告长期有效.

https://github.com/iphysresearch/UndergradResearchLab/blob/main/2026科创计划及选拔题目.pdf

How can LLMs be used for scientific discovery?

He Wang | ICTP-AP, UCAS

Towards Transparent AI in Gravitational Wave Data Analysis

Uncovering the "black box" to reveal how LLM actually works

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

arXiv:2507.11810 [cs.DL]

"科学家"

"合作者"

"评估者"

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

AI and Cosmology: From Computational Tools to Scientific Discovery

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

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

直接不行？那就包装回炉再来一遍。

npj Artif. Intell. 1, 14 (2025).

"序列输出"

"序列输入"

Direct fails. Refine and recover.

AI and Cosmology: From Computational Tools to Scientific Discovery

Demo: LLM 验证开普勒行星运动三定律 (2025.3)

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

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

AI and Cosmology: From Computational Tools to Scientific Discovery

Generative agents rely on predefined rules. 🤫

arXiv:2304.03442 [cs.HC]

arXiv:2201.11903 [cs.CL]

arXiv:2305.10601 [cs.CL]

NVIDIA Blog: How Scaling Laws Drive Smarter, More Powerful AI (Source)

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

🔗 OpenAI: Learning to Reason with LLMs

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

GPT能力的演变

对GPT-3.5能力的仔细审查揭示了其新兴能力的起源：

原始的GPT-3通过预训练获得了生成能力、世界知识和上下文学习
经过指令调优的模型发展出了遵循指令和推广到未见任务的能力
代码训练模型（code-davinci-002）获得了代码理解能力
进行复杂推理的能力可能是代码训练的副产品

What are our thoughts on LLMs?

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

GPT-3 (2020)

ChatGPT (2022)

Magic: Code + Text

究竟是什么让 LLMs 如此强大？

Code! (1/3)

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

What are our thoughts on LLMs?

究竟是什么让 LLMs 如此颠覆？

MCP

MCP Tool

https://github.com/iphysresearch/gw150914-mcp-signal-search

prompt

"Please generate gw templates first."

模型上下文协议（Model Context Protocol，MCP），是由Anthropic推出的开源协议，旨在实现大语言模型与外部数据源和工具的集成，用来在大模型和数据源之间建立安全双向的连接。

Demo: GW150914 MCP Signal Search

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

What are our thoughts on LLMs?

Nat Mach Intell 7, 592–601 (2025).

Rule-Based Vs. LLMs: (Source)

Natural Language Programming! (2/3)

究竟是什么让 LLMs 如此颠覆？

MCP

RAG

具身智能

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

What are our thoughts on LLMs?

It's Mere Interpolation! (3/3)

究竟如何解释 AI/LLMs 的原理？

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

Deep Learning is Not As Impressive As you Think, It's Mere Interpolation (Source)

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

What are our thoughts on LLMs?

It's Mere Interpolation! (3/3)

究竟如何解释 AI/LLMs 的原理？

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

Deep Learning is Not As Impressive As you Think, It's Mere Interpolation (Source)

Representation Space Interpolation

Representation Space Interpolation

He Wang | ICTP-AP, UCAS

The "Real" Reasons We Apply LLMs to Scientific Discovery

AI and Cosmology: From Computational Tools to Scientific Discovery

What are our thoughts on LLMs?

It's Mere Interpolation! (3/3)

究竟如何解释 AI/LLMs 的原理？

Deep Learning is Not As Impressive As you Think, It's Mere Interpolation (Source)

【信号搜索】通过对超出广相的BGR波形进行测试，框架在不同PN阶和光度距离下均展现出与GR信号检测相媲的通用化能力和鲁棒性。

GR

BGR

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*. “Search for Exotic Gravitational Wave Signals beyond General Relativity Using Deep Learning.” PRD 112 (2), 024030. e-Print: arXiv:2410.20129 [gr-qc]

【宇宙学】CVAE模型能将CMB功率谱谱高效压缩到仅5个潜在维度，并在Planck不确定性内实现了超过99.9%的高保真度重建，即使在参数外推下也能可靠重构。

~ sampling

Tian-Yang Sun, Tian-Nuo Li, He Wang*, Jing-Fei Zhang, Xin Zhang*. Conditional variational autoencoders for cosmological model discrimination and anomaly detection in cosmic microwave background power spectra. e-Print: arxiv:2510.27086 [astro-ph.CO]

通过设计非线性映射，将科学数据表示到多样化的特征空间中，以提升对复杂科学问题的建模与推断能力。

《纽伦堡编年史》上这些圆圈并不是随意涂写，而是某位古代读者试图调和《七十士译本》（希腊旧约）与《希伯来圣经》两种不同年代计算体系所做的笔记。

AI 与考古：

Traditional Physics

✓ Fully interpretable
✗ Performance ceiling

Human-designed pipelines
Fixed heuristics

Examples:
Matched filtering
χ² tests

Black-box AI

✓ High performance
✗ Opaque decisions

End-to-end prediction
Model-centric learning

Examples:
CNNs, DINGO

Interpretable
Algorithmic Discovery

Algorithms as search objects
Physics-informed objectives

Performance:
Competitive with state-of-the-art
(MLGWSC-1 benchmark)

Example:
Evo-MCTS (this work)
AlphaEvolve

Interpretable AI for Gravitational-Wave Discovery

Scientific discovery requires interpretability — not just performance.

AI should help us understand why an algorithm works — not just output an answer.

PyCBC (linear-core)

cWB (nonlinear-core)

Simple filters (non-linear)

CNN-like (highly non-linear)

Benchmarking against state-of-the-art methods
(MLGWSC1)

HW, LZ. arXiv:2508.03661 [cs.AI]

From Black-Box AI to Algorithmic Co-Design

LLMs as agents that optimize physics-based algorithms

A new axis: adaptivity over algorithm design

LLMs allow us to search over algorithms, not just over parameters.

Numerical orbits (of Taiji)
Unequal-arm
TDI-2.0

MH Du+, arXiv:2505.16500 [gr-qc]

The Global Fitting Challenge

Analyze Non-overlapping Galactic Binaries

The analysis of the best currently known LISA binaries, even making maximal use of the available information about the sources, is susceptible to ambiguity or biases when not simultaneously fitting to the rest of the galactic population. (copied from Littenberg et al. 2404.03046)

credit: Karnesis et al, arXiv:2303.02164v2

credit: M. Katz, The 15th International LISA Symposium

Numerical orbits (of Taiji)
Unequal-arm
TDI-2.0

preliminary

MH Du+, arXiv:2505.16500 [gr-qc]

MDP Element	GW Interpretation
State	Residuals, PSD drift, candidate list
Action	Propose/subtract/refine/allocate compute
Reward	Evidence gain, residual stationarity
Horizon	Entire observing run

A trajectory tree of global-fitting decisions over time

Nodes: residual states
Edges: modeling actions

(HW+, in preparation)

Global fitting as a Markov Decision Process (MDP)

A RL Perspective on Global Fitting

Global fitting is not a single inference — it is a long-horizon control problem.

I don’t claim this is solved. I claim the framing matters.”

preliminary

Numerical orbits (of Taiji)
Unequal-arm
TDI-2.0

MH Du+, arXiv:2505.16500 [gr-qc]

A trajectory tree of global-fitting decisions over time

Nodes: residual states
Edges: modeling actions

(HW+, in preparation)

A RL Perspective on Global Fitting

Global fitting is not a single inference — it is a long-horizon control problem.

I don’t claim this is solved. I claim the framing matters.”

See：第八分会场, 5-105
18:00-18:10 张丁锴：Learning Null Channels for Instrumental Noise Characterization in Taiji

preliminary

GW Data Analysis as a Markov Decision Process

Many GW pipelines already define an MDP — implicitly and inconsistently.

“Once you phrase the problem this way,
RL and MCTS are not exotic — they are obvious.”

Key Takeaways

What is the right reward for discovery?
When does adaptivity beat optimality?

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

空间引力波探测数据仿真及分析春季学习班通知
（第一轮）

空间引力波探测已被列入《国家空间科学中长期发展规划（2024—2050 年）》“时空涟漪”主题下的优先发展方向。为加速形成我国自主的空间引力波探测数据仿真与分析系统，支撑科学目标论证和科学应用系统建设，挖掘和培养青年科研队伍，“空间引力波探测数据仿真及分析春季学习班”将于 2026 年 4 月 23 日-27 日在中国科学院微小卫星创新研究院举办。

课程大纲：空间引力波探测系统仿真（轨道动力学、无拖曳控制、光学、激光链路、引力波信号响应等）｜引力波数据预处理（时间延迟干涉等）｜空间引力波探测目标波源分析（大质量双黑洞、恒星级双黑洞、极端质量比旋近系统、银河系致密双星）｜人工智能数据分析方法｜引力波模型及引力波物理前沿
开班地点：中国科学院微小卫星创新研究院（张江园区） + 腾讯会议
课程咨询：杜明辉 duminghui@imech.ac.cn
会务咨询：张江朋 18621820740；唐奇芹 18221006158

太极实验室 2026 年度“大学生创新实践训练计划’

(引力波数据分析与 AI for Science 方向)

中国科学院大学引力波宇宙太极实验室(北京)引力波数据分析与机器学习课题组长期面向全国高校学生开放科研训练机会,现面向全国优秀学生招募参加太极实验室2026年度“大学生创新实践训练计划”,本课题组致力于探索引力波天文学、数值模拟与人工智能技术的交叉研究，重点发展新一代 Al for Science 方法，用于解决复杂物理系统建模、信号处理与科学数据分析问题,欢迎对 引力波科学、人工智能算法与科学计算 充满兴趣的同学加入，在真实科研项目中接受系统训练，并参与国际前沿研究。

此外，本实验室长期欢迎对相关研究方向感兴趣的同学联系咨询，本广告长期有效.

Open Questions for the Community

What is the right reward for discovery?
Should we train ensembles instead of curating them?
When does adaptivity beat optimality?

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

Call for Speakers - MLA F2F @ March LVK 2026 (Pisa)

Just a gentle reminder that we’re collecting contributions for the Machine Learning Algorithms (MLA) section!

🔗 MLA Wiki: https://wiki.ligo.org/MLA/WebHome
🔗 Mattermost channel

This slide: https://slides.com/iphysresearch/2026jan_gwfreeride

王赫

国际理论物理中心（亚太地区）

中国科学院大学

hewang@ucas.ac.cn

机器学习如何改变引力波天文学？

Abstract

Gravitational Wave

Gravitational Wave Astronomy

Multi-messenger astronomy

GW's Scientific Objectives

GW & Data Analysis

GW & Data Analysis

GW & Data Analysis

Challenge: Detecting Signals in GW Data

科学智能：AI for Science

科学智能：AI for Science

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

CNN for GW Detection

Pioneering Approaches

MFCNN for GW Detection

Feature Extraction

Feature Extraction

MFCNN for GW Detection

First Benchmark for GW Detection

Exploring Beyond General Relativity

Parameter Estimation: Holy Grail of GW data analysis

Parameter Estimation

Parameter Estimation: AI application

Parameter Estimation: AI application

DINGO

Interpretability Challenges: Discoveries vs. Validation

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 (3/4)

ABC of Normalizing Flow Model (4/4)

Part II: Evo-MCTS, LLM-informed mutations, and principled discovery beyond hand-designed GW pipelines

科学智能：AI for Science

科学智能：AI for Science

Discover new knowledge and efficient algorithms using AI

Discover new knowledge and efficient algorithms using AI

Discover new knowledge and efficient algorithms using AI

Discover new knowledge and efficient algorithms using AI

When LLMs Enter the Algorithmic Loop

When LLMs Enter the Algorithmic Loop

When LLMs Enter the Algorithmic Loop

When LLMs Enter the Algorithmic Loop

When LLMs Enter the Algorithmic Loop

When LLMs Enter the Algorithmic Loop

Algorithmic Synergy: MCTS, Evolution & LLM Agents

Algorithmic Synergy: MCTS, Evolution & LLM Agents

When LLMs Enter the Algorithmic Loop

Interpretability Analysis

Framework Mechanism Analysis

Framework Mechanism Analysis

Interpretable AI for Gravitational-Wave Discovery

Key Takeaways: ... against Symbolic Regression

Key Takeaways

How can LLMs be used for scientific discovery?

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

The "Real" Reasons We Apply LLMs to Scientific Discovery

Traditional Physics

Black-box AI

InterpretableAlgorithmic Discovery

Interpretable AI for Gravitational-Wave Discovery

From Black-Box AI to Algorithmic Co-Design

The Global Fitting Challenge

A RL Perspective on Global Fitting

A RL Perspective on Global Fitting

GW Data Analysis as a Markov Decision Process

Key Takeaways

Open Questions for the Community

机器学习如何改变引力波天文学？

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

Parameter Estimation:
Holy Grail of GW data analysis

Interpretability Challenges:
Discoveries vs. Validation

Part II: Evo-MCTS, LLM-informed
mutations, and principled discovery
beyond hand-designed GW pipelines

Interpretable
Algorithmic Discovery