非线性动力学稀疏辨识理论及应用
非线性稀疏回归方法(SINDy)是由Steven L. Brunton组提出的识别微分方程形式的机器学习方法。SINDy方法在各个领域有着广泛的应用，例如航空航天领域实时预测气动弹性模型、生物化学领域对基因控制网络的推断。同时也有一些研究人员对稀疏回归算法的收敛性给出理论推导。本课程将主要介绍SINDy的理论及应用。除此之外，还会介绍经典的机器学习方法，如线性回归、非线性回归、模型选择、特征提取、k-means 聚类、支持向量机、多层神经网络与激活函数等等。
讲师
日期
2023年03月14日 至 06月06日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 13:30 - 15:05 | A3-3-103 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
微积分，数理统计
课程大纲
Lecture 1:
- An overview of forward and inverse problems in machine learning.
-The basic network architecture of residual networkNeural network Ordinary Differential Equations (Neural ODEs)
- Linear regression and Nonlinear regression
Lecture 2:
- Sparse identification of nonlinear dynamical systems (SINDy) and its extensions
- PySINDy: A Python package.
- Model selection: cross validation and information criteria
Lecture 3:
- PDE-FIND:Data-driven discovery of partial differential equations
- Feature selection and data mining
Lecture 4:
- PINN-SR: Physics-informed learning of governing equations from scarce data
- Physics-informed Spline Learning for Nonlinear Dynamics Discovery
- Supervised versus unsupervised learning
Lecture 5:
- DeepXDE: Interpretation and implementation
- Ensemble-SINDy: Robust sparse model discovery in the low-data, high noise limit, with active learning and control
- k-means clustering
Lecture 6:
- Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data
- Model selection for dynamical systems via sparse regression and information criteria
- Support vector machines (SVM)
Lecture 7:
- Autonomous inference of complex network dynamics from incomplete and noisy data
- Nonlinear stochastic modelling with Langevin regression
Classification trees and random forest
Lecture 8:
- Detecting the maximum likelihood transition path from data of stochastic dynamical systems
- Multi-layer networks and activation functions
Lecture 9:
- Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
- Principal component analysis (PCA)
Lecture 10:
- PyNumDiff: A Python package for numerical differentiation of noisy time-series data
- Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
Lecture 11:
- Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
- Interpretable machine learning for high-dimensional trajectories of aging health
- An overview of forward and inverse problems in machine learning.
-The basic network architecture of residual networkNeural network Ordinary Differential Equations (Neural ODEs)
- Linear regression and Nonlinear regression
Lecture 2:
- Sparse identification of nonlinear dynamical systems (SINDy) and its extensions
- PySINDy: A Python package.
- Model selection: cross validation and information criteria
Lecture 3:
- PDE-FIND:Data-driven discovery of partial differential equations
- Feature selection and data mining
Lecture 4:
- PINN-SR: Physics-informed learning of governing equations from scarce data
- Physics-informed Spline Learning for Nonlinear Dynamics Discovery
- Supervised versus unsupervised learning
Lecture 5:
- DeepXDE: Interpretation and implementation
- Ensemble-SINDy: Robust sparse model discovery in the low-data, high noise limit, with active learning and control
- k-means clustering
Lecture 6:
- Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data
- Model selection for dynamical systems via sparse regression and information criteria
- Support vector machines (SVM)
Lecture 7:
- Autonomous inference of complex network dynamics from incomplete and noisy data
- Nonlinear stochastic modelling with Langevin regression
Classification trees and random forest
Lecture 8:
- Detecting the maximum likelihood transition path from data of stochastic dynamical systems
- Multi-layer networks and activation functions
Lecture 9:
- Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
- Principal component analysis (PCA)
Lecture 10:
- PyNumDiff: A Python package for numerical differentiation of noisy time-series data
- Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
Lecture 11:
- Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
- Interpretable machine learning for high-dimensional trajectories of aging health
参考资料
Brunton S.L., Kutz J.N., Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022.
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
中文
讲师介绍
Dr. Wuyue Yang is currently an Assistant Professor at BIMSA. She received her PhD degree from Tsinghua University in 2022 and was honored as an Outstanding Graduate of Beijing. Her main research directions are artificial intelligence, machine learning theory and applications. She has published papers in internationally renowned academic journals such as "Journal of Computational Physics," "Journal of Chemical Physics," and "Physics of Fluids," with over 1,000 Google citations. She is the PI of a National Natural Science Foundation of China Youth Fund project and has participated as a researcher in National Key R&D Program Special Projects. She serves as a review expert for international journals including "BMC Infectious Diseases" and "AIMS Mathematics." She teaches courses including "Theory and Application of Sparse Identification of Nonlinear Dynamics (SINDy)," "Complex System Dynamics and Control," and "Collective Dynamics of Active Matter."