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