An adaptive discrete physics-informed neural network method for solving the Cahn-Hilliard equation. (English) Zbl 1537.65151
Summary: In this paper, we propose a new deep learning algorithm based on the physics-informed neural network (PINN) for solving the Cahn-Hilliard (CH) equations. We adopt the discrete time model of the PINN and use Runge-Kutta methods to discretize the time variable. We introduce a novel loss function and update it at each time step so that the computational cost can be significantly reduced compared to some existing methods. Numerical results of several one-dimensional and two-dimensional CH equations are presented to validate the efficiency and accuracy of the proposed method.
MSC:
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 68T07 | Artificial neural networks and deep learning |
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