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Topics on sparse identification of nonlinear dynamics(SINDy) theory and application \(ICBS\)
Topics on sparse identification of nonlinear dynamics(SINDy) theory and application
Sparse Identification of Nonlinear Dynamics (SINDy) is a machine learning method proposed by Steven L. Brunton group to identify the form of differential equations. SINDy method has been widely used in various fields, such as real-time prediction of aeroelastic model in aerospace field, inference of gene control network in biochemistry field. At the same time, some researchers also give theoretical derivation of the convergence of sparse regression algorithm. This course will mainly introduce the theory and application of SINDy. In addition, classical machine learning methods, such as linear regression, nonlinear regression, model selection, feature extraction, k-means clustering, support vector machines, multilayer neural networks and activation functions, will be introduced.
Lecturer
Date
14th March ~ 6th June, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 13:30 - 15:05 | A3-3-103 | ZOOM 04 | 482 240 1589 | BIMSA |
Prerequisite
Calculus, Mathematics Statistics
Syllabus
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
Reference
Brunton S.L., Kutz J.N., Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022.
Audience
Undergraduate
, Graduate
Video Public
No
Notes Public
No
Language
Chinese