Lecturer
Cassio Oishi
Sao Paulo State University (UNESP), Brazil
Schedule and Place
When: This 5-hour course will take place over 2 days, with morning sessions of 2.5 hours each, from May 5-6, 2025.
Where: UCLouvain
Euler building (Room A.002), Avenue Georges Lemaître,4 - 1348 Louvain-la-Neuve
Planned Schedule
- 9:20 - 9:45: Welcome coffee
- 9:45 - 12:35: Session of 2.5 hours (lecture, 20-min coffee break)
Abstract
One of the main goals in Science is the understanding of the basic principles that govern the natural world. In this context, mathematical models are crucial to clarify and formalize scientific hypotheses. They allow scientists to translate the behavior of complex systems into a set of equations describing the relation between the key variables. Among different types of mathematical models, differential equations constitute a powerful tool for modelling the evolution of systems over time. Usually, the derivation of the differential equations that describe a specific phenomenon is done from the first principles. However, this can be a complex and challenging task for nonlinear and multi-scale phenomena, such turbulent fluids, networks of neurons, and epidemiological systems. Recent advances in Machine Learning have motivated several attempts to automate the discovery of differential equations directly from data available about the system. The goal of this short course is to describe a very promising data-driven approach called Sparse Identification of Nonlinear Dynamics (SINDy). Specifically, this course will cover an introduction to SINDy and its variants, the optimization techniques it requires, and the basic concepts of Reduced-Order Models combined with system identification strategies. Finally, some applications involving spatiotemporal data obtained from numerical simulations of fluid mechanics problems will be presented.
Description
- Physical Modeling: Examples
- Dynamical system and Data Driven method
- SINDy approach: Classic Implementation
- Data driven challenges: Noise and missing data
- SINDy variants and library selection
- Reduced Order Models
- Space-temporal data: ROM-SINDy
- Application on fluid mechanics
Course Material
- Course Slides: Day 1.1, Day 1.2, Day 2
- Brunton, S.L., Proctor, J.L., Kutz, J.N.: Discoveing governing equations from data by sparse identification of nonlinear dynamical systems. PNAS 113, 3932-3937 (2016) https://www.pnas.org/doi/10.1073/pnas.1517384113
- Messenger, D.A., Bortz, D.M.: Weak SINDy: Galerkin-Based Data-Driven Model Selection. Multiscale Modeling & Simulation 19 (2021) https://epubs.siam.org/doi/10.1137/20M1343166
- Oishi, C.M., Kaptanoglo, A.A., Kutz, J.N., Brunton, S.L.: Nonlinear parametric models of viscoelastic fluid flows. Royal Society Open Science 11: 240995 (2024) https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.240995
- Fung, L., Fasel, U., Juniper, M.: Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data. Proc. R. Soc. A 481 (2025) https://royalsocietypublishing.org/doi/epdf/10.1098/rspa.2024.0200
Evaluation
TBD - Students who request an evaluation are invited to approach the teacher in the first lecture.
Registration
Mandatory. See "Registration to courses" in the left column.