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Data-Driven Modelling - Machine Learning and Dynamical Systems

Fields Institute via YouTube

Overview

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Explore advanced machine learning techniques for modeling dynamical systems through this comprehensive symposium featuring 32 specialized presentations from leading researchers. Delve into cutting-edge topics including interpretable machine learning for control systems, data-driven discovery of governing equations, and the application of neural networks to chaotic dynamics prediction. Learn about Koopman operator theory, sparse identification methods like SINDy-PI, and dynamic mode decomposition for analyzing complex systems. Discover how researchers are tackling challenges in fluid dynamics relaminarization, nuclear reaction system modeling, and multistable system prediction from sparse measurements. Examine probabilistic approaches to Markov chain aggregation, hidden Markov models for dynamical systems, and variational methods for high-dimensional problems. Gain insights into port-Hamiltonian system modeling, transfer operator methods for climate analysis including ENSO cycles, and machine learning approaches for uncertainty quantification in rare events. The symposium covers both theoretical foundations and practical applications, including supervised learning from noisy observations, stochastic parameterization techniques, and the integration of side information in dynamical system learning.

Syllabus

Interpretable and Generalizable Machine Learning for Modeling and Control
Learning Missing Dynamics from Data
Collective variables in complex systems
Data-driven learning of control signals, parameters, and governing equations
Big Data and Machine Learning for Analysis of Numerical PDEs
Data-driven PDE modelling: Trick or treat!
Hidden Markov Models and Dynamical Systems
Optimising linear response of kernel dynamics and transfer operator extraction of the ENSO cycle
Data-Driven Prediction of Multistable Systems from Sparse Measurements
Output-Weighted Active Sampling for Uncertainty Quantification and Prediction of Rare Events
Data driven model reduction and the Koopman-Mori-Zwanzig formalism
Challenges for Building Surrogate Model for Nuclear Reaction Systems
Interpreted machine learning in fluid dynamics: Explaining relaminarisation events in wall-bounded
Recurrent Neural Networks for Spatiotemporal Prediction of Chaotic Dynamics
Data-driven approximation of the Koopman generator and Schrödinger operator
Data Driven Port Hamiltonian systems modelling and control
Learning Dynamical Systems with Side Information
Supervised learning from noisy observations
Probabilistic aggregation of large under-sampled Markov chains
Machine-learning of model error in ODEs
Modeling synchronization in forced turbulent oscillator flows
SINDy-PI: A Robust Algorithym for Parallel Implicit Sparse Identification of Nonlinear Dynamics
On mean subtraction and Dynamic Mode Decomposition
Machine learning enablers for system optimization and design
Transforming Signals to Images Using Attractor Reconstruction for Deep Learning
Gedmd: Data-Driven Analysis of Stochastic Dynamical Systems
Linear response for the dynamic Laplacian and finite-time coherent sets
Learning sparse dynamics of interacting systems
Variational methods and deep learning for high-dimensional dynamical systems
Resampling with neural networks for data-driven stochastic parameterization
Nonparametric Nonlinear Model Reduction for slow-fast SDEs near manifolds
Learning Dynamical Systems using Local Stability Priors

Taught by

Fields Institute

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