Unit 1: Introduction to Dynamical Systems
Unit 2: Introduction to Chaos
Unit 3: Dynamical Invariants
Unit 4: Chaos in the Real World
Deep Learning for Chaotic and Complex Dynamical Systems: Lyapunov Exponents, Embedding Dimension, and Fractal Dimension Estimation
Master deep learning techniques to analyze chaotic and complex systems, estimate key dynamical invariants, and predict system evolution from time series data.
Unit 1: Lyapunov Exponents Estimation
Unit 2: Embedding Dimension Estimation
Unit 3: Fractal Dimension Estimation
Unit 1: Introduction to Deep Learning for Chaotic Systems
Unit 2: Implementing RNNs for Chaotic System Prediction
Unit 3: Implementing Reservoir Computing for Chaotic System Prediction
Unit 4: Advanced Techniques and Challenges
Unit 1: DL for Lyapunov Exponents
Unit 2: DL for Fractal Dimensions
Unit 3: Comparing DL and Traditional Methods
Unit 4: Interpreting DL Results
Unit 1: Climate Science Applications
Unit 2: Financial Time Series Analysis
Unit 3: Neuroscience and Brain Dynamics
Unit 4: Ethical Considerations and Limitations