AllenCahnProblem

Formulation of the Allen Cahn problem.

class AllenCahnProblem(alpha=0.0001, beta=5)

Bases: TimeDependentProblem, SpatialProblem

Implementation of the Allen Cahn problem in the spatial interval \([-1, 1]\) and temporal interval \([0, 1]\).

See also

Original reference: Sokratis J. Anagnostopoulos, Juan D. Toscano, Nikolaos Stergiopulos, and George E. Karniadakis. Residual-based attention and connection to information bottleneck theory in PINNs. Computer Methods in Applied Mechanics and Engineering 421 (2024): 116805 DOI: 10.1016/ j.cma.2024.116805.

Example:

>>> problem = AllenCahnProblem()

Initialization of the AllenCahnProblem.

Parameters:

• alpha (float | int) – The diffusion coefficient.

• beta (float | int) – The reaction coefficient.