Systems Core Courses

Steve Brunton

Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs

Explore higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations in engineering mathematics, with accompanying notes and MATLAB code.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Fields Institute

Efficient Approximation of Infinite-Dimensional Dynamical Systems in Finance

Explore advanced techniques for approximating complex dynamical systems in finance, focusing on efficient methods for infinite-dimensional problems and their applications.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

Fields Institute

Prospects for AI Systems That Can Form Concepts and Abstractions

Explore the potential for AI to develop conceptual thinking and abstraction capabilities, examining current limitations and future possibilities in this cutting-edge field of research.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Fields Institute

Machine Learning and Dynamical Systems Meet in Reproducing Kernel Hilbert Spaces

Explore the intersection of machine learning and dynamical systems in Reproducing Kernel Hilbert Spaces, offering insights into advanced mathematical concepts and their applications.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Fields Institute

Learning Dynamical Systems

Explore cutting-edge research on integrating machine learning with dynamical systems, presented by expert Sayan Mukherjee from University of Leipzig and MPI MiS.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Fields Institute

Deep Learning for Nonlinear Stability Analysis in Dynamical Systems

Explore deep learning techniques for analyzing nonlinear stability in dynamical systems, presented by Bogdan Epureanu from the University of Michigan.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Fields Institute

Dissipative Deep Neural Dynamical Systems

Explore dissipative deep neural dynamical systems and their applications in machine learning, presented by Jan Drgona from Pacific Northwest National Laboratory.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Fields Institute

Koopman Operator Theory Based Machine Learning of Dynamical Systems

Explore advanced machine learning techniques for dynamical systems using Koopman operator theory, presented by Igor Mezic from UC Santa Barbara.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Fields Institute

Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces

Explore Koopman operator regression in reproducing kernel Hilbert spaces for dynamical systems, enhancing understanding of machine learning applications in complex systems analysis.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Fields Institute

Tensor Harish-Chandra–Itzykson–Zuber Integral & Entanglement Detection in Multipartite Quant Systems

Explore tensor integrals and their applications in quantum entanglement detection, focusing on multipartite systems and advanced mathematical concepts in quantum physics.

• YouTube
• 43 minutes
• On-Demand
• Free Video

Fields Institute

Transseries and Discrete Dynamical Systems

Explore transseries and their applications in discrete dynamical systems, focusing on interactions between o-minimal, complex analytic, and nonarchimedean methods.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Fields Institute

Learning Linear Dynamical Systems with Hankel Nuclear Norm Regularization

Explore finite-sample analysis and insights for learning low-order linear dynamical systems using Hankel nuclear norm regularization, with applications in control and reinforcement learning.

• YouTube
• 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 5

Explore advanced techniques in symbolic dynamics for complex hyperbolic systems. Gain insights into infinite Markov partitions and their applications in studying statistical properties of dynamical systems.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 1 of 5

Explore symbolic dynamics for nonuniformly hyperbolic systems, focusing on Markov Partitions and Young Towers. Learn advanced techniques to analyze complex dynamical systems and their statistical properties.

• YouTube
• 2 hours 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Simultaneous Control of Ensembles of Dynamical Systems

Control strategies for managing multiple dynamic systems simultaneously, focusing on mathematical approaches and applications in various fields.

• YouTube
• 57 minutes
• On-Demand
• Free Video