Data Analysis with Applications in Physics and Machine Learning
Course Description:
This course trains students in modern data-analysis principles and practical tools, with focused applications to physics and machine learning. Core topics include probability and inference (frequentist and Bayesian), time-series and spectral methods, uncertainty quantification, model selection, and interpretable discovery (symbolic regression / sparse identification).
A complementary thread introduces gravitational-wave (GW) astronomy as a motivating physics application: basic GW generation, detectors (ground and low-frequency concepts such as Pulsar Timing Arrays and space missions), representative sources, and how real GW data pipelines are constructed and used for parameter estimation and tests of General Relativity.
Learning Objectives:
After completing the course students will be able to:
Formulate scientific inference problems and choose appropriate analysis frameworks (hypothesis testing, estimation, or model comparison).
Apply frequentist and Bayesian tools for parameter estimation and uncertainty quantification.
Implement and diagnose time-series and spectral-analysis pipelines (filtering, windowing, PSD estimation, matched filtering).
Build, train, and evaluate machine-learning models for regression, classification, and surrogate modeling; understand their limitations and failure modes.
Use symbolic-regression and sparse-identification tools (e.g., PySR, SINDy) to extract interpretable models from data.
Integrate domain knowledge (physical priors, symmetries, conservation laws) into ML models and statistical analyses.
This course trains students in modern data-analysis principles and practical tools, with focused applications to physics and machine learning. Core topics include probability and inference (frequentist and Bayesian), time-series and spectral methods, uncertainty quantification, model selection, and interpretable discovery (symbolic regression / sparse identification).
A complementary thread introduces gravitational-wave (GW) astronomy as a motivating physics application: basic GW generation, detectors (ground and low-frequency concepts such as Pulsar Timing Arrays and space missions), representative sources, and how real GW data pipelines are constructed and used for parameter estimation and tests of General Relativity.
Learning Objectives:
After completing the course students will be able to:
Formulate scientific inference problems and choose appropriate analysis frameworks (hypothesis testing, estimation, or model comparison).
Apply frequentist and Bayesian tools for parameter estimation and uncertainty quantification.
Implement and diagnose time-series and spectral-analysis pipelines (filtering, windowing, PSD estimation, matched filtering).
Build, train, and evaluate machine-learning models for regression, classification, and surrogate modeling; understand their limitations and failure modes.
Use symbolic-regression and sparse-identification tools (e.g., PySR, SINDy) to extract interpretable models from data.
Integrate domain knowledge (physical priors, symmetries, conservation laws) into ML models and statistical analyses.
讲师
日期
2025年09月29日 至 12月29日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周三 | 13:30 - 15:05 | A14-101 | Zoom 17 | 442 374 5045 | BIMSA |
修课要求
Software Installation: Python, Jupyter Notebooks, PyCBC, PySINDy, PySR.
课程大纲
Part I: Foundations - The Physics & The Tools (Weeks 1-6)
Objective: Establish the motivating physical phenomenon (GWs) and the core statistical frameworks for scientific inference.
Week 1-2: Course Overview & The GW Universe
Topic: Course introduction, software setup, and the story of LIGO's first detection. Overview of GW sources (binary black holes, neutron stars) and the data analysis challenge.
Tools: Python/Jupyter, PyCBC installation.
Week 2-4: Gravitational Waves in Theory
Topic: Linearized GR, the Transverse-Traceless gauge, and how moving masses generate GWs.
Objective: Understand the fundamental physics behind the signals we want to detect.
Week 5: The Statistician's Toolkit I - Frequentist Inference
Topic: Hypothesis testing, maximum likelihood estimation, confidence intervals, p-values, p-p plot, bootstrap method, and the principles of uncertainty quantification.
Objective: Learn the first framework for making probabilistic statements about scientific data.
Week 6: The Statistician's Toolkit II - Bayesian Inference
Topic: Bayes' Theorem, priors, posteriors, marginalization, and introduction to Markov Chain Monte Carlo (MCMC) sampling. Corner plot and violin plot.
Tools: PyCBC.
Objective: Learn a powerful framework for parameter estimation and model comparison that incorporates prior knowledge.
Part II: The Data Analysis Pipeline (Weeks 7-10)
Objective: Translate theoretical knowledge into practical skills for processing and analyzing time-series data, specifically for GW detection.
Week 7: Time-Series & Spectral Analysis
Topic: Stationarity, Power Spectral Density (PSD) estimation, windowing, filtering, and whitening.
Objective: Learn to characterize and manipulate noisy data in the time and frequency domains.
Week 8: The Search - Matched Filtering
Topic: The theory of optimal filtering, calculating Signal-to-Noise Ratio (SNR), building a template bank, and dealing with non-Gaussian noise.
Tools: PyCBC for matched filtering.
Objective: Understand the core algorithm used to find GW signals buried in noise.
Week 9: Hands-On Gravitational-Wave Data
Topic: Working with real LIGO data from the GW Open Science Center (GWOSC). Downloading data, estimating PSDs, whitening, and performing a matched filter search for a known signal.
Objective: Apply weeks 5-6 to a real dataset.
Week 10: Parameter Estimation - Extracting Science from Signals
Topic: How Bayesian inference (from Week 4) is used to measure the properties of binary systems (masses, spins, distance) from a detected signal.
Tools: PyCBC's parameter estimation modules.
Objective: See how the full inverse problem is solved to do astronomy with GWs.
Part III: Integrating Physics with Machine Learning (Weeks 11-14)
Objective: Move beyond traditional methods and explore how modern, interpretable ML can be integrated with physical principles for discovery.
Week 11: Physics-Informed Neural Networks (PINNs)
Topic: Embedding physical laws (PDEs, boundary conditions) into neural network loss functions to solve inverse problems and improve generalizability.
Objective: Learn to make ML models respect known physics.
Week 12: Symbolic Regression & Sparse Identification (PySR & PySINDy)
Topic: Using algorithms to discover interpretable mathematical expressions and governing equations directly from data.
Tools: PySR, PySINDy.
Objective: Move from "black box" ML to transparent, discoverable models.
Week 13: Testing Gravity I - The Ringdown and Black Hole Spectroscopy
Topic: Using the tools from Weeks 8 (PE) to analyze the "ringdown" signal of a black hole and test if its properties match GR's predictions of quasi-normal modes.
Objective: A deep dive into a specific, cutting-edge application of the course's methods.
Week 14: Testing Gravity II & The Low-Frequency Universe
Topic: Tests of GR with inspiral signals. Introduction to Pulsar Timing Arrays (PTAs) and the space-based detector LISA, and the unique data analysis challenges they present.
Objective: Look to the future of the field and understand how the core concepts scale to different data types.
Objective: Establish the motivating physical phenomenon (GWs) and the core statistical frameworks for scientific inference.
Week 1-2: Course Overview & The GW Universe
Topic: Course introduction, software setup, and the story of LIGO's first detection. Overview of GW sources (binary black holes, neutron stars) and the data analysis challenge.
Tools: Python/Jupyter, PyCBC installation.
Week 2-4: Gravitational Waves in Theory
Topic: Linearized GR, the Transverse-Traceless gauge, and how moving masses generate GWs.
Objective: Understand the fundamental physics behind the signals we want to detect.
Week 5: The Statistician's Toolkit I - Frequentist Inference
Topic: Hypothesis testing, maximum likelihood estimation, confidence intervals, p-values, p-p plot, bootstrap method, and the principles of uncertainty quantification.
Objective: Learn the first framework for making probabilistic statements about scientific data.
Week 6: The Statistician's Toolkit II - Bayesian Inference
Topic: Bayes' Theorem, priors, posteriors, marginalization, and introduction to Markov Chain Monte Carlo (MCMC) sampling. Corner plot and violin plot.
Tools: PyCBC.
Objective: Learn a powerful framework for parameter estimation and model comparison that incorporates prior knowledge.
Part II: The Data Analysis Pipeline (Weeks 7-10)
Objective: Translate theoretical knowledge into practical skills for processing and analyzing time-series data, specifically for GW detection.
Week 7: Time-Series & Spectral Analysis
Topic: Stationarity, Power Spectral Density (PSD) estimation, windowing, filtering, and whitening.
Objective: Learn to characterize and manipulate noisy data in the time and frequency domains.
Week 8: The Search - Matched Filtering
Topic: The theory of optimal filtering, calculating Signal-to-Noise Ratio (SNR), building a template bank, and dealing with non-Gaussian noise.
Tools: PyCBC for matched filtering.
Objective: Understand the core algorithm used to find GW signals buried in noise.
Week 9: Hands-On Gravitational-Wave Data
Topic: Working with real LIGO data from the GW Open Science Center (GWOSC). Downloading data, estimating PSDs, whitening, and performing a matched filter search for a known signal.
Objective: Apply weeks 5-6 to a real dataset.
Week 10: Parameter Estimation - Extracting Science from Signals
Topic: How Bayesian inference (from Week 4) is used to measure the properties of binary systems (masses, spins, distance) from a detected signal.
Tools: PyCBC's parameter estimation modules.
Objective: See how the full inverse problem is solved to do astronomy with GWs.
Part III: Integrating Physics with Machine Learning (Weeks 11-14)
Objective: Move beyond traditional methods and explore how modern, interpretable ML can be integrated with physical principles for discovery.
Week 11: Physics-Informed Neural Networks (PINNs)
Topic: Embedding physical laws (PDEs, boundary conditions) into neural network loss functions to solve inverse problems and improve generalizability.
Objective: Learn to make ML models respect known physics.
Week 12: Symbolic Regression & Sparse Identification (PySR & PySINDy)
Topic: Using algorithms to discover interpretable mathematical expressions and governing equations directly from data.
Tools: PySR, PySINDy.
Objective: Move from "black box" ML to transparent, discoverable models.
Week 13: Testing Gravity I - The Ringdown and Black Hole Spectroscopy
Topic: Using the tools from Weeks 8 (PE) to analyze the "ringdown" signal of a black hole and test if its properties match GR's predictions of quasi-normal modes.
Objective: A deep dive into a specific, cutting-edge application of the course's methods.
Week 14: Testing Gravity II & The Low-Frequency Universe
Topic: Tests of GR with inspiral signals. Introduction to Pulsar Timing Arrays (PTAs) and the space-based detector LISA, and the unique data analysis challenges they present.
Objective: Look to the future of the field and understand how the core concepts scale to different data types.
参考资料
PyCBC Inference: A Python-based parameter estimation toolkit for compact binary coalescence signals, C. M. Biwer et al.
E. S. Phinney. A Practical theorem on gravitational wave backgrounds. 7 2001.
G. Hobbs, F. Jenet, K. J. Lee, J. P. W. Verbiest, D. Yardley, R. Manchester, A. Lommen, W. Coles, R. Edwards, and C. Shettigara. tempo2: a new pulsar timing package iii. gravitational wave simulation. Monthly Notices of the Royal Astronomical Society, 394(4):1945–1955, April 2009.
Cranmer, Miles. "Interpretable machine learning for science with PySR and SymbolicRegression. jl." arXiv preprint arXiv:2305.01582 (2023).
Kaptanoglu, Alan A., et al. "PySINDy: A comprehensive Python package for robust sparse system identification." arXiv preprint arXiv:2111.08481 (2021).
E. S. Phinney. A Practical theorem on gravitational wave backgrounds. 7 2001.
G. Hobbs, F. Jenet, K. J. Lee, J. P. W. Verbiest, D. Yardley, R. Manchester, A. Lommen, W. Coles, R. Edwards, and C. Shettigara. tempo2: a new pulsar timing package iii. gravitational wave simulation. Monthly Notices of the Royal Astronomical Society, 394(4):1945–1955, April 2009.
Cranmer, Miles. "Interpretable machine learning for science with PySR and SymbolicRegression. jl." arXiv preprint arXiv:2305.01582 (2023).
Kaptanoglu, Alan A., et al. "PySINDy: A comprehensive Python package for robust sparse system identification." arXiv preprint arXiv:2111.08481 (2021).
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
Jahed Abedi is a black hole physicist with a broad interest in gravitational physics, bridging both observational and theoretical domains. On the observational side, his work focuses on the search for gravitational wave (GW) echoes and Quasi-Normal Modes (QNMs) in LIGO/Virgo data, while his theoretical research delves into black hole perturbations, QNMs, and Quantum Field Theory (QFT) in curved space-time. Jahed was awarded the 2019 Buchalter Cosmology First Prize for one of his publications where he served as the lead author, reflecting the high impact of his research. He holds a Bachelor's degree in Electrical Engineering, as well as a Master's and PhD in Physics. His research seeks to answer several critical questions: How can a better pipeline be developed to test the Kerr nature of observed Binary Black Hole Mergers through black hole spectroscopy? With improved methods, can additional subdominant Quasi-Normal Modes (QNMs) be detected? Can these results validate previous searches or reveal deviations from General Relativity in GW data? What quantum effects might be expected from black holes, and if they exist, how significant are they? Can such effects be observed? Lastly, how can gravitational wave data confirm or rule out alternatives to classical black holes or their mimickers? Jahed's work continues to push the frontiers of black hole physics, and he remains open to collaborations and inquiries from those interested in his research.