Advanced sequence · 5 modules · Agent direction
Computational & AI-Driven Differential Equations
Neural differential equations, physics-informed neural networks, neural operators, reinforcement learning for dynamical systems, and data-driven discovery of governing equations.
Requires completion of Level 1 and Level 2. Proceed to Level 4: Capstone Projects after completion.
Modules
-
3.1 — Neural Differential Equations
Replace hand-crafted dynamics with learned vector fields. Neural ODEs parameterize the right-hand side with a neural network and solve with ODE integrators.
-
3.2 — Physics-Informed Neural Networks (PINNs)
Embed PDE residuals directly into the loss function to solve forward and inverse problems without labeled data.
-
3.3 — Neural Operators and Function Space Learning
Learn mappings between function spaces: DeepONet, Fourier Neural Operator, and their application to parametric PDEs.
-
3.4 — Agent-Based Control and Reinforcement Learning for Dynamical Systems
Frame ODE/PDE control as a Markov decision process. Implement policy gradient and Q-learning for a damped pendulum swing-up task.
-
3.5 — Data-Driven Discovery of Unknown Equations
Recover governing equations from time-series data using SINDy (Sparse Identification of Nonlinear Dynamics) and symbolic regression.