Energy dissipation preserving physics informed neural network for Allen–Cahn equations

KÜTÜK M., YÜCEL H.

Journal of Computational Science, cilt.87, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 87
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.jocs.2025.102577
  • Dergi Adı: Journal of Computational Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Anahtar Kelimeler: Allen–Cahn equation, Energy dissipation, Phase field models, Physics-informed neural network
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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 the Allen–Cahn equation as a penalty term into the loss function of the network. To facilitate the learning process of random initials, we employ a continuous analogue of the initial random condition by utilizing the Fourier series expansion. Adaptive methods from traditional numerical analysis are also integrated to enhance the effectiveness of the proposed PINN. Numerical results indicate a consistent decrease in the discrete energy, while also revealing phenomena such as phase separation and metastability.