A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators
DOI10.1016/j.jcp.2023.112589MaRDI QIDQ6117687
Yuwei Geng, Lili Ju, Zhu Wang, Yuankai Teng
Publication date: 21 February 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Allen-Cahn equationsconvolutional neural networkmass-conservingbound limiterfully-discrete operatortraining strategy
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Parabolic equations and parabolic systems (35Kxx)
Cites Work
- Unnamed Item
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- An efficient algorithm for solving the phase field crystal model
- Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- A finite difference method for a conservative Allen-Cahn equation on non-flat surfaces
- Geometrical image segmentation by the Allen-Cahn equation
- On the stability and accuracy of partially and fully implicit schemes for phase field modeling
- Unconditionally maximum bound principle preserving linear schemes for the conservative Allen-Cahn equation with nonlocal constraint
- A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations
- Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A posteriori error estimates and an adaptive finite element method for the Allen-Cahn equation and the mean curvature flow
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
- An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
- Nonlocal reaction—diffusion equations and nucleation
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection
- Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
- Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
- A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality
- Color Image Segmentation by the Vector-Valued Allen–Cahn Phase-Field Model: A Multigrid Solution
This page was built for publication: A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators