Prerequisites for Lyapunov-Based Machine Learning for Chaos

Direct prerequisites (2)

1. Nonlinear Dynamics and Chaos Fundamentalslayer 4, tier 3
2. Physics-Informed Neural Networkslayer 4, tier 2

Reachable through the chain (17)

These topics are not directly cited as prerequisites but are reached transitively by following the chain upward. Working through the direct prerequisites pulls these in.

• Classical ODEs: Existence, Stability, and Numerical Methodslayer 1, tier 1
• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
• The Jacobian Matrixlayer 0A, tier 1
• Eigenvalues and Eigenvectorslayer 0A, tier 1
• Matrix Operations and Propertieslayer 0A, tier 1
• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Automatic Differentiationlayer 1, tier 1
• Feedforward Networks and Backpropagationlayer 2, tier 1
• Differentiation in Rnlayer 0A, tier 1
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Matrix Calculuslayer 1, tier 1
• The Hessian Matrixlayer 0A, tier 1
• Activation Functionslayer 1, tier 1
• Convex Optimization Basicslayer 1, tier 1
• Gradient Descent Variantslayer 1, tier 1