07 — Differential Equations in Deep Learning¶
This module bridges the gap between classical numerical analysis and modern deep learning. We explore how continuous-time dynamical systems, represented by Ordinary, Stochastic, and Partial Differential Equations (ODEs, SDEs, PDEs), provide a powerful framework for modeling complex physical phenomena and generative processes.
Prerequisite Tier: Tier 2-3 — Intermediate / Advanced (Requires Multivariable Calculus, Linear Algebra, and basic ODE knowledge)
📚 Course Modules¶
- Lecture: Unified Mathematical Foundations
- Practice: Exercises and Coding Tasks
- Project: Neural ODEs and PINNs Implementation
📄 Core Literature¶
- Chen, R. T., et al. (2018): Neural Ordinary Differential Equations - The seminal paper on continuous-depth networks.
- Ho, J., et al. (2020): Denoising Diffusion Probabilistic Models - Foundations of modern generative diffusion.
- Raissi, M., et al. (2019): Physics-informed neural networks - Solving PDEs using neural networks.
- Karniadakis, G. E., et al. (2021): Physics-informed machine learning - A comprehensive review.