Adaptive Mesh Refinement

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Overview

Adaptive Mesh Refinement (AMR) studies how to vary mesh resolution during computation so that sharp gradients, interfaces, contacts, or other important features receive more detail without refining the entire domain. Classical methods use error, residual, or gradient indicators to refine and coarsen cells, while newer approaches learn these decisions with neural networks, reinforcement learning, or physics-informed models. AMR is also being incorporated into neural PDE solvers and transformers through multiscale representations and adaptive tokenization, and applied to problems such as fluid flow, solid mechanics, imaging, and geometry reconstruction. A central challenge is deciding where and when to refine under a fixed compute budget: learned strategies can improve accuracy or efficiency, but their gains depend on the problem, reliable baselines, and the cost of adaptation itself.

Latest papers

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17 papers5 papers in the last four weeks, up 25% on the four weeks before. 0.0% of all new papers.

  1. Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions

    Oct 19, 2026Somnath Giri, Muslim Malik, Rishikesh YadavPDE SolvingPartial Differential Equations

    School of Mathematical & Statistical Sciences, Indian Institute of Technology Mandi, Mandi, 175005, Himachal Pradesh, India

  2. Refine Where It Matters: Contact-Adaptive Meshing for Deformable Object Manipulation

    Oct 9, 2026Gabriel Johnson, Tom Olesch, Fei LiuDeformable Object SimulationAdaptive Mesh Refinement

    The University of Tennessee, Knoxville Knoxville, Tennessee

  3. Learned Adaptive Multiresolution Diffusion Imaging

    Oct 6, 2026Christian Tantardini, Stig Rune Jensen, Roberto Di Remigio Eikås +1Reinforcement LearningAdaptive Mesh Refinement

    Center for Integrative Petroleum Research, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia · Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway · Algorithmiq S.r.l., c/o STLex, Via della Chiusa 15, 20123, Milano, Italia

  4. Dynamic Quadtree Tokenization and Transformer for Adaptive Mesh PDE Forecasting

    Oct 2, 2026Yilin Zhuang, Noah Zambrano, Karthik DuraisamyAdaptive TokenizationPDE Surrogate Modeling

    Department of Aerospace Engineering University of Michigan Ann Arbor, MI 48105 · University of Michigan Ann Arbor, MI 48105

  5. MeshOctave: Vertex Split-and-Rewire Cascades for Native Mesh Generation

    Sep 30, 2026Junkai Lin, Tianhao Zhao, Hang Long +103D Mesh GenerationAdaptive Mesh Refinement

    Huazhong University of Science and Technology · Meshy AI · Independent Researcher +1

  6. Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers

    Sep 19, 2026Ange TongReinforcement LearningNeural Operators

    National Research Tomsk State University, 36 Lenin Avenue, Tomsk 634050, Russian Federation

  7. Where to Compute and How to Interact: Operator-Readable Adaptation with Gauge-Aware Transport

    Sep 14, 2026Zixuan Shen, Quanxu Wan, Bingchuan Wang +2Adaptive Mesh RefinementPhysics-Informed Neural Operators

    Central South University · Nanjing University

  8. ADELE - Adaptive Delaunay Grids for High-Fidelity Mesh-Native Reconstruction

    Sep 6, 2026Johannes Weidenfeller, Shaofei Wang, Philipp Fürnstahl +13D Mesh ReconstructionAdaptive Mesh Refinement

    ETH Zurich, Zurich, Switzerland · Beijing Institute for General Artificial Intelligence, Beijing, China · University of Zurich, Zurich, Switzerland +1

  9. ToCo-Mesh: Topology-Consistent Dynamic Mesh Reconstruction via Adaptive Tessellation and Surface-Aligned 2DGS

    Sep 1, 2026Chuanjin Fan, Wenjie Chang, Aibing Li +3Dynamic Scene ReconstructionMulti-View 3D Reconstruction

    University of Science and Technology of China, Hefei, China

  10. pyALDIC: A Python Implementation of Augmented Lagrangian Digital Image Correlation with a GUI, Adaptive Meshing, and Mask-Aware Subset Splitting

    Jul 23, 2026Zixiang Tong, Jin YangAdaptive Mesh Refinement

    Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712, USA · Texas Materials Institute, The University of Texas at Austin, Austin, TX 78712, USA

  11. Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

    Jul 13, 2026Zixuan Shen, Bingchuan Wang, Zhi Wang +1Neural PDE SolversPDE Surrogate Modeling

    Central South University · Central South University, Changsha, Hunan 410083, China · Nanjing University +1

  12. GReFEM: Multimodal LLMs as Zero-Shot Semantic Assistants for Physics-Guided 3D Mesh Refinement

    Jul 8, 2026Kartik Bali, Mahish K. Guru, Christian J Cyron +1Multimodal GroundingMultimodal Large Language Models

    Institute of Material Systems Modeling Helmholtz Zentrum Hereon Max-Planck-Straße 1, 21502 Geesthacht · Institute of Material and Process Design Helmholtz Zentrum Hereon Max-Planck-Straße 1, 21502 Geesthacht · Data-Driven Simulation and Analysis in Materials Science German Research Center for Artificial Intelligence Campus D3 2, 66123 Saarbrücken

  13. Learning Interface Breakup: A Geometry-Conditioned Latent Surrogate for Spray Formation

    Jun 15, 2026Julius H Ramlau, Friedrich Hastedt, Tolga Birdal +3PDE Surrogate ModelingAdaptive Mesh Refinement

    Department of Chemical Engineering, Imperial College London, London, United Kingdom · CMAC, CEDAR, an EPSRC Center for Doctoral Training in Cyber-Physical Systems for Medicines Development and Manufacturing, Imperial College London, London, United Kingdom · Sargent Centre for Process Systems Engineering, Imperial College London, London, United Kingdom +2

  14. ExMesh: Explicit Mesh Reconstruction with Topology Adaptation

    Jun 5, 2026Chuanjin Fan, Lifan Wu, Wenjie Chang +33D Mesh Generation3D Reconstruction

    University of Science and Technology of China · 2National Key Laboratory of Deep Space Exploration, Deep Space Exploration Laboratory

  15. MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers

    Jun 3, 2026Yanshun Zhao, Xiaoyu Peng, Jiamin Jiang +2Neural PDE SolversPDE Surrogate Modeling

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China.

  16. Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers

    Jun 1, 2026Henry Kasumba, Ronald KatendePDE SolvingAdaptive Mesh Refinement

    Department of Mathematics · Makerere University · 7062, Kampala, Uganda +2

  17. Accelerating PDE Surrogates via RL-Guided Mesh Optimization

    Mar 2, 2026Yang Meng, Ruoxi Jiang, Zhuokai Zhao +3PDE Surrogate ModelingData-Efficient Learning

    UChicago · Fudan University · UAlbany