Lorenz System

anypinn create my-project --template lorenz

Chaotic 3-field ODE. Recovers σ, ρ, and β simultaneously from trajectory observations.

Problem

Three fields (x, y, z), three learnable parameters:

\[ \dot{x} = \sigma(y - x), \qquad \dot{y} = x(\rho - z) - y, \qquad \dot{z} = xy - \beta z \]

Features Demonstrated

• Multi-parameter recovery (3 simultaneous parameters)
• Huber loss via PINNHyperparameters.criterion for robustness to chaotic trajectories
• 3-field system

Results