A conservative and positivity-preserving method for solving anisotropic diffusion equations with deep learning
From MaRDI portal
Publication:6537080
DOI10.4208/cicp.oa-2023-0180zbMATH Open1536.6513MaRDI QIDQ6537080
Li Liu, Heng Yong, Chuanlei Zhai, Hui Xie, Xuejun Xu
Publication date: 14 May 2024
Published in: Communications in Computational Physics (Search for Journal in Brave)
Artificial neural networks and deep learning (68T07) Flows in porous media; filtration; seepage (76S05) Finite volume methods applied to problems in fluid mechanics (76M12) Finite volume methods for boundary value problems involving PDEs (65N08)
Cites Work
- Monotone finite volume schemes for diffusion equations on polygonal meshes
- Differencing of the diffusion equation in Lagrangian hydrodynamic codes
- A cell-centered Lagrangian-mesh diffusion differencing scheme
- Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
- Monotone nonlinear finite-volume method for challenging grids
- An introduction to multipoint flux approximations for quadrilateral grids
- DGM: a deep learning algorithm for solving partial differential equations
- A positivity-preserving finite volume scheme with least square interpolation for 3D anisotropic diffusion equation
- Deep least-squares methods: an unsupervised learning-based numerical method for solving elliptic PDEs
- PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
- APFOS-Net: asymptotic preserving scheme for anisotropic elliptic equations with deep neural network
- MIM: a deep mixed residual method for solving high-order partial differential equations
- Scientific machine learning through physics-informed neural networks: where we are and what's next
- Physics-informed neural networks for high-speed flows
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
- Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes. (Schéma volumes finis monotone pour des opérateurs de diffusion fortement anisotropes sur des maillages de triangles non structurés).
- Neural algorithm for solving differential equations
- A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes
- 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids
- Quasi M-Matrix Multifamily Continuous Darcy-Flux Approximations with Full Pressure Support on Structured and Unstructured Grids in Three Dimensions
- A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes
- A Rate of Convergence of Physics Informed Neural Networks for the Linear Second Order Elliptic PDEs
- A Comparison Study of Deep Galerkin Method and Deep Ritz Method for Elliptic Problems with Different Boundary Conditions
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- A Monotone Finite Volume Scheme with Fixed Stencils for 3D Heat Conduction Equation
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- Finite volume schemes for diffusion equations: Introduction to and review of modern methods
- Physics-informed neural networks for the Reynolds-averaged Navier-Stokes modeling of Rayleigh-Taylor turbulent mixing
- Discontinuity computing using physics-informed neural networks
This page was built for publication: A conservative and positivity-preserving method for solving anisotropic diffusion equations with deep learning