Numerical Approximations of the Allen-Cahn-Ohta-Kawasaki (ACOK) Equation with Modified Physics Informed Neural Networks (PINNs)

TL;DR

This paper introduces a modified PINNs approach to improve numerical approximations of the Allen-Cahn-Ohta-Kawasaki equation, a phase field model with volume constraints, addressing previous PINNs limitations.

Contribution

The paper proposes a modified PINNs framework specifically designed for the ACOK equation with volume constraints, enhancing approximation accuracy for phase field models.

Findings

Improved accuracy in approximating ACOK equations.

Effective handling of volume constraints in phase field models.

Demonstrated advantages over traditional PINNs methods.

Abstract

The physics informed neural networks (PINNs) has been widely utilized to numerically approximate PDE problems. While PINNs has achieved good results in producing solutions for many partial differential equations, studies have shown that it does not perform well on phase field models. In this paper, we partially address this issue by introducing a modified physics informed neural networks. In particular, they are used to numerically approximate Allen-Cahn-Ohta-Kawasaki (ACOK) equation with a volume constraint.