Allen-Cahn

anypinn create my-project --template allen-cahn

Stiff reaction-diffusion PDE with sharp interfaces. Forward problem demonstrating adaptive sampling and periodic boundary conditions.

Problem

\[ \frac{\partial u}{\partial t} = \varepsilon^2 \frac{\partial^2 u}{\partial x^2} + u - u^3 \]

Features Demonstrated

• AdaptiveSampler for resolving sharp interfaces
• Periodic boundary conditions
• Stiff PDE dynamics (small ε)
• Forward problem (no parameter recovery)

Results