An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations

• URL: http://arxiv.org/abs/2206.14709v1
• Date: Wed, 29 Jun 2022 15:18:30 GMT
• Title: An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations
• Authors: Florent Bonnet, Jocelyn Ahmed Mazari, Thibaut Munzer, Pierre Yser, Patrick Gallinari
• Abstract summary: We propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime. We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities.
• Score: 9.067455882308073
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recent progress in \emph{Geometric Deep Learning} (GDL) has shown its potential to provide powerful data-driven models. This gives momentum to explore new methods for learning physical systems governed by \emph{Partial Differential Equations} (PDEs) from Graph-Mesh data. However, despite the efforts and recent achievements, several research directions remain unexplored and progress is still far from satisfying the physical requirements of real-world phenomena. One of the major impediments is the absence of benchmarking datasets and common physics evaluation protocols. In this paper, we propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime (from $10^6$ and beyond). We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities. Moreover, we provide extensive GDL baselines.

Related papers

• Physically Interpretable Representation and Controlled Generation for Turbulence Data [39.42376941186934]
  This paper proposes a data-driven approach to encode high-dimensional scientific data into low-dimensional, physically meaningful representations. We validate our approach using 2D Navier-Stokes simulations of flow past a cylinder over a range of Reynolds numbers.
  arXiv  Detail & Related papers  (2025-01-31T17:51:14Z)
• Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction [84.26340606752763]
  In this paper, we introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework. The network is designed to conform to the general symmetry conservation law via symmetry where conservative and non-conservative information passes over a multiscale space by a latent temporal marching strategy. Results demonstrate that CiGNN exhibits remarkable baseline accuracy and generalizability, and is readily applicable to learning for prediction of varioustemporal dynamics.
  arXiv  Detail & Related papers  (2024-12-30T13:55:59Z)
• A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils [61.60175086194333]
  aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Here, we consider modeling of incompressible flows over solid objects, wherein geometric structures are a key factor in determining aerodynamics. To effectively incorporate geometries, we propose a message passing scheme that efficiently and expressively integrates the airfoil shape with the mesh representation. These design choices lead to a purely data-driven machine learning framework known as GeoMPNN, which won the Best Student Submission award at the NeurIPS 2024 ML4CFD Competition, placing 4th overall.
  arXiv  Detail & Related papers  (2024-12-12T16:05:39Z)
• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems [31.006807854698376]
  We propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN) We incorporate a GNN into a numerical integrator to approximate the temporal marching of partialtemporal dynamics for a given PDE system. PhyMPGN is capable of accurately predicting various types of operatortemporal dynamics on coarse unstructured meshes.
  arXiv  Detail & Related papers  (2024-10-02T08:54:18Z)
• Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey [51.87875066383221]
  This paper introduces fundamental concepts, traditional methods, and benchmark datasets, then examine the various roles Machine Learning plays in improving CFD. We highlight real-world applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, combustion, atmosphere & ocean science, biology fluid, plasma, symbolic regression, and reduced order modeling. We draw the conclusion that ML is poised to significantly transform CFD research by enhancing simulation accuracy, reducing computational time, and enabling more complex analyses of fluid dynamics.
  arXiv  Detail & Related papers  (2024-08-22T07:33:11Z)
• A Survey of Data-Efficient Graph Learning [16.053913182723143]
  We introduce a novel concept of Data-Efficient Graph Learning (DEGL) as a research frontier. We systematically review recent advances on several key aspects, including self-supervised graph learning, semi-supervised graph learning, and few-shot graph learning.
  arXiv  Detail & Related papers  (2024-02-01T09:28:48Z)
• AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions [9.561442022004808]
  We develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem.
  arXiv  Detail & Related papers  (2022-12-15T00:41:09Z)
• Data Augmentation for Deep Graph Learning: A Survey [66.04015540536027]
  We first propose a taxonomy for graph data augmentation and then provide a structured review by categorizing the related work based on the augmented information modalities. Focusing on the two challenging problems in DGL (i.e., optimal graph learning and low-resource graph learning), we also discuss and review the existing learning paradigms which are based on graph data augmentation.
  arXiv  Detail & Related papers  (2022-02-16T18:30:33Z)
• Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters [2.169919643934826]
  We formulate the problem as regression with the Fused Gromov-Wasserstein (FGW) loss. We propose a predictive model relying on a FGW barycenter whose weights depend on inputs.
  arXiv  Detail & Related papers  (2022-02-08T12:15:39Z)
• Distributionally Robust Semi-Supervised Learning Over Graphs [68.29280230284712]
  Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. Despite their success in practice, most of existing methods are unable to handle graphs with uncertain nodal attributes. Challenges also arise due to distributional uncertainties associated with data acquired by noisy measurements. A distributionally robust learning framework is developed, where the objective is to train models that exhibit quantifiable robustness against perturbations.
  arXiv  Detail & Related papers  (2021-10-20T14:23:54Z)
• Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study [100.27567794045045]
  Training deep graph neural networks (GNNs) is notoriously hard. We present the first fair and reproducible benchmark dedicated to assessing the "tricks" of training deep GNNs.
  arXiv  Detail & Related papers  (2021-08-24T05:00:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.