Learning Robust Marking Policies for Adaptive Mesh Refinement
DOI10.1137/22m1510613arXiv2207.06339OpenAlexW4391170793WikidataQ129445669 ScholiaQ129445669MaRDI QIDQ6189171
Brendan Keith, Socratis Petrides, Andrew Gillette
Publication date: 8 February 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.06339
finite element methodadaptive mesh refinementreinforcement learningmachine learning\(hp\)-refinement
Computational learning theory (68Q32) Learning and adaptive systems in artificial intelligence (68T05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
Cites Work
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- Axioms of adaptivity
- Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
- Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation
- Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
- On an h-type mesh-refinement strategy based on minimization of interpolation errors
- A collection of 2D elliptic problems for testing adaptive grid refinement algorithms
- The h-p version of the finite element method. I. The basic approximation results
- Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
- A fully automatic \(hp\)-adaptivity
- A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations
- Recurrent neural networks as optimal mesh refinement strategies
- Refinement of polygonal grids using convolutional neural networks with applications to polygonal discontinuous Galerkin and virtual element methods
- MFEM: a modular finite element methods library
- Output-based adaptive aerodynamic simulations using convolutional neural networks
- Optimality of a standard adaptive finite element method
- Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods
- Lower bounds of the discretization error for piecewise polynomials
- Moving Mesh Generation Using the Parabolic Monge–Ampère Equation
- The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
- The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
- Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
- Sobolev regularity estimation for hp-adaptive finite element methods
- Convergence of Adaptive Finite Element Methods
- A Convergent Adaptive Algorithm for Poisson’s Equation
- A Comparison of hp -Adaptive Strategies for Elliptic Partial Differential Equations
- A systematic strategy for simultaneous adaptive \(hp\) finite element mesh modification using nonlinear programming
- On residual-based a posteriori error estimation in hp-FEM
- Efficient Time-Stepping for Numerical Integration Using Reinforcement Learning