Data-driven Model Learning of Dynamic Systems

Like in 2023 and 2024, the 2025-edition will be held in hybrid mode. Participants can thus attend the Spring School in person (on the campus of Ecole Centrale de Lyon) or virtually.

For this purpose, we will make use of the brandnew lecture hall of Ecole Centrale de Lyon that is completely dedicated to hybrid teaching. This lecture hall is located in the SKYLAB of Ecole Centrale.

Like in the previous editions, the 2025-edition will welcome an international guest lecturer.

Dynamical models play a key role in many branches of science. In engineering they have a paramount role in model-based simulation, health monitoring, control and optimization. The accuracy of the models is often crucial to their subsequent use in model-based operations.

Data-driven modeling (system identification) and statistical parameter estimation are established fields for determining mathematical models of dynamical systems on the basis of measurement data from dedicated experiments.

The 5-days Spring School aims at covering the fundamentals of data-driven modeling approaches (ranging from parameter estimation algorithms (PEM and ETFE) and experiment design to model validation) as well as more advanced topics. In this year edition, these advanced topics will pertain to adaptive parameter estimation, to subspace identification, to gray-box identification and to the use of statistical tools (such as the maximum likelihood theory) to learn the dynamics of linear and nonlinear systems.

The school consists of a series of lectures and of (computer) exercise sessions.

For the computer exercices, participants should have a computer with one of the latest versions of Matlab (version R2018a at least) installed. The Matlab System Identification Toolbox must be available.

The school is mainly aimed at an audience of PhD students in control engineering (or related fields), but the course is also open to any other persons interested in the topic of data-based modeling.

The course is eligible for scientific doctoral modules (+/- 20 hours). A certificate of attendance will be delivered to all participants at the end of the course.

Basics of linear system identification

Lectures on Monday 7 April (afternoon) and on Tuesday 8 April (all day)

Exercises on Wednesday 9 April (morning)

Lecturer: Xavier Bombois, CNRS Research Director, Laboratoire Ampère, Ecole Centrale de Lyon

Theme 1: Introduction;concepts; identification cycle

Theme 2: Parametric (prediction error) identification methods: prediction criterion and model structures, linear and pseudo-linear regressions, conditions on data, statistical and asymptotic properties, model set selection and model validation

Theme 3: Non-parametric identification (ETFE)

Theme 4: Experiment design.

Adaptive parameter estimation - coping with time-varying systems

Lecture on Wednesday 9 April (beginning of the afternoon)

Lecturer: Xavier Bombois, CNRS Research Director, Laboratoire Ampère, Ecole Centrale de Lyon

Theme 1: Recursive identification methods for black-box models

Theme 2: Adaptive parameter estimation for gray-box models via extended Kalman filter

Gray-box and black-box state-space model learning

Lectures on Wednesday 9 April (end of the afternoon) and Thursday 10 April (morning)

Lecturer: Guillaume Mercère, Associate Professor, Laboratoire LIAS, Université de Poitiers

Theme 1: Black-box model learning: subspace state-space model identification

Theme 2: Gray-box model learning: nonlinear least-squares state-space model identification

Theme 3: From black-box to gray-box models

Dynamic model learning

Lectures on Thursday 10 April (afternoon) and on Friday 11 April (morning)

Lecturer: Håkan Hjalmarsson, Professor, KTH, Stockholm, Sweden

Theme 1: Fundamental parameter estimation concepts: Sufficient statistics, the Cramér-Rao bound, the maximum likelihood estimator, estimator-based methods

Theme 2: Minimum MSE estimators: Bayes estimators, empirical Bayes methods, risk estimation methods, Gaussian processes, asymptotic analysis

Theme 3: Application to dynamical models: linear models, non-linear input-output models, non-linear state-space models

Theme 4: Computational tools: Sampling, Markov Chain Monte Carlo methods, particle filtering and smoothing

Fees for participants attending in person and requiring accommodation

• 550 euros (VAT included) for PhD students
  
• 730 euros (VAT included) for other participants
  

These fees include the participation at the Spring School, the accommodation in the Résidence Paul Comparat from April 7 till April 12 (five nights) and the lunches on on April 8, 9, 10 and 11.

Fees for participants attending in person (without accommodation)

• 350 euros (VAT included) for PhD students
  
• 530 euros (VAT included) for other participants
  

These fees include the participation at the Spring School and the lunches on April 8, 9, 10 and 11.

Fees for participants attending virtually

• 150 euros (VAT included) for PhD students
  
• 250 euros (VAT included) for other participants
  

These fees include the participation at the Spring School in a fully virtual fashion.