March 13, 2025
[2411.08760] Energy Dissipation Preserving Physics Informed Neural Network for Allen-Cahn Equations
[Submitted on 13 Nov 2024 (v1), last revised 12 Mar 2025 (this version, v2)] View a PDF of the paper titled Energy Dissipation Preserving Physics Informed Neural Network for Allen-Cahn Equations, by Mustafa K\”ut\”uk and Hamdullah Y\”ucel View PDF HTML (experimental) Abstract:This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic and random initial functions, and with advective term in one, two, and three spatial dimensions, based on the physics-informed neural network (PINN). To improve the learning capacity of the PINN, we incorporate the energy dissipation property of