PhD course: Learning dynamical systems

This course will provide a comprehensive introduction to the fundamentals of learning dynamical systems. The primary objectives of this course are twofold: to estimate unknown physical quantities and to develop models for time-series prediction, such as forecasting the yearly energy consumption of buildings. The theoretical foundation of this course lies at the intersection of system identification (a sub-discipline of control theory), econometrics, statistics, and machine learning. We will explore autoregressive models, state-space models, parameter estimation, and learning predictive black-box models.

The course is divided into two parts. The first part consists of 18 hours of introduction to the theoretical tools associated withh exercises. The second part, 6 hours, will focus on a complete case study.

Part I (Mihaly Petreczky): 

We will begin by delving into autoregressive models for time-series analysis, followed by an exploration of state-space models. Regarding autoregressive models, we will start with classical linear models (ARX, ARMA) before progressing to models inspired by machine learning, such as neural networks, SVM, decision trees, and transformers In the context of state-space models, we will initially focus on linear state-space models and the associated algorithms like the Kalman filter and subspace methods. Furthermore, we will explore recurrent neural networks.

• 02/04/2024:  basics of machine learning, linear regression, ARX models. 

 Handwritten notes: part1, part2 , part3, part4 ,part5, part6 

Python code: kaggle link 

• 15/04/2024: Continuation on ARX models and non-linear regression using neural networks:  kaggle notebook ,  handwritten notes: 

• 22/04/2024: ARMAX models: kaggle notebook https://www.kaggle.com/code/mihalypetreczky/notebookaafbf777df, 

Linear state-space models:  state-space identification using subspace method in Python, using SLIPPY package:  file 

Handwritten notes: 

• 24/04/2024:   

State space models/ARMAX models  using  Matlab System Identification Toolbox: example: Matlab file.

RNNs using Keras: kaggle notebook: notebook 

      CDC player data from DAISY data set, csv  file: HW use this data set for forecasting 

      Notes on seasonality: Part 1, Part 2 

Part II (Damien Marchal)

In the second part, students will have the opportunity to apply the techniques learned in Part I to a specific use case. The use case will be related to energy consumption optimization and forecasting of public buildings (like the one of University of Lille). The objective of the work will be to predict energy consumption and the building GhG (green house gaz) emissions based on uncontrolled parameters (eg: weather conditions) as well as controlled one (eg: opening hours).

Zoom link: link