A conservative hybrid deep learning method for Maxwell-Ampère-Nernst-Planck equations
DOI10.1016/j.jcp.2024.112791arXiv2312.05891MaRDI QIDQ6126572
Tieyong Zeng, Zhouping Xin, Cheng Chang
Publication date: 9 April 2024
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2312.05891
equationsdeep learningconservative numerical schemephysics-informed neural networkMaxwell-Ampère-Nernst-Planck
Artificial intelligence (68Txx) 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)
Cites Work
- Unnamed Item
- A free energy satisfying finite difference method for Poisson-Nernst-Planck equations
- Finite element approximation of the Navier-Stokes equations
- A conservative discretization of the Poisson-Nernst-Planck equations on adaptive Cartesian grids
- Weak adversarial networks for high-dimensional partial differential equations
- M-matrix characterizations. I: nonsingular M-matrices
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- DGM: a deep learning algorithm for solving partial differential equations
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Discretizationnet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization
- Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
- Hybrid FEM-NN models: combining artificial neural networks with the finite element method
- A neural network multigrid solver for the Navier-Stokes equations
- CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model
- New Poisson–Boltzmann type equations: one-dimensional solutions
- Neural‐network‐based approximations for solving partial differential equations
- Solving parametric PDE problems with artificial neural networks
- Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
- The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system via the Deep Neural Network Approach
- A Maxwell–Ampère Nernst–Planck Framework for Modeling Charge Dynamics
This page was built for publication: A conservative hybrid deep learning method for Maxwell-Ampère-Nernst-Planck equations
