NPLIC: A Machine Learning Approach to Piecewise Linear Interface Construction

• URL: http://arxiv.org/abs/2007.04244v2
• Date: Mon, 25 Jan 2021 04:23:19 GMT
• Title: NPLIC: A Machine Learning Approach to Piecewise Linear Interface Construction
• Authors: Mohammadmehdi Ataei, Markus Bussmann, Vahid Shaayegan, Franco Costa, Sejin Han, Chul B. Park
• Abstract summary: We propose an alternative neural network based method called NPLIC to perform PLIC calculations. We show that this data-driven approach results in accurate calculations at a fraction of the usual computational cost.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Volume of fluid (VOF) methods are extensively used to track fluid interfaces in numerical simulations, and many VOF algorithms require that the interface be reconstructed geometrically. For this purpose, the Piecewise Linear Interface Construction (PLIC) technique is most frequently used, which for reasons of geometric complexity can be slow and difficult to implement. Here, we propose an alternative neural network based method called NPLIC to perform PLIC calculations. The model is trained on a large synthetic dataset of PLIC solutions for square, cubic, triangular, and tetrahedral meshes. We show that this data-driven approach results in accurate calculations at a fraction of the usual computational cost, and a single neural network system can be used for interface reconstruction of different mesh types.

Related papers

• Fusing CFD and measurement data using transfer learning [49.1574468325115]
  We introduce a non-linear method based on neural networks combining simulation and measurement data via transfer learning.<n>In a first step, the neural network is trained on simulation data to learn spatial features of the distributed quantities.<n>The second step involves transfer learning on the measurement data to correct for systematic errors between simulation and measurement by only re-training a small subset of the entire neural network model.
  arXiv  Detail & Related papers  (2025-07-28T07:21:46Z)
• Geometric Operator Learning with Optimal Transport [77.16909146519227]
  We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries.<n>For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space.<n> Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses.
  arXiv  Detail & Related papers  (2025-07-26T21:28:25Z)
• A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction [0.0]
  We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains.<n>One of the novelties of the method is that the flux fraction is computed by evaluating a previously trained neural network.<n>We observe numerical convergence as the size of the mesh tends to zero $h=1/N_hsearrow 0$, with a better rate than two reference schemes.
  arXiv  Detail & Related papers  (2025-07-07T17:30:00Z)
• 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)
• Geometry-Informed Neural Operator for Large-Scale 3D PDEs [76.06115572844882]
  We propose the geometry-informed neural operator (GINO) to learn the solution operator of large-scale partial differential equations. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points.
  arXiv  Detail & Related papers  (2023-09-01T16:59:21Z)
• Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics [1.8749305679160366]
  We introduce a framework for embedding deep learning models within a generic finite element solver to solve the Navier-Stokes equations. We validate our method for flow over a backwards-facing step and test its performance on novel geometries. We show that our GNN-based closure model may be learned in a data-limited scenario by interpreting closure modeling as a solver-constrained optimization.
  arXiv  Detail & Related papers  (2023-07-25T14:27:49Z)
• Machine Learning model for gas-liquid interface reconstruction in CFD numerical simulations [59.84561168501493]
  The volume of fluid (VoF) method is widely used in multi-phase flow simulations to track and locate the interface between two immiscible fluids. A major bottleneck of the VoF method is the interface reconstruction step due to its high computational cost and low accuracy on unstructured grids. We propose a machine learning enhanced VoF method based on Graph Neural Networks (GNN) to accelerate the interface reconstruction on general unstructured meshes.
  arXiv  Detail & Related papers  (2022-07-12T17:07:46Z)
• DeepPhysics: a physics aware deep learning framework for real-time simulation [0.0]
  We propose a solution to simulate hyper-elastic materials using a data-driven approach. A neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond.
  arXiv  Detail & Related papers  (2021-09-17T12:15:47Z)
• A Deep Learning Algorithm for Piecewise Linear Interface Construction (PLIC) [0.0]
  Piecewise Linear Interface Construction (PLIC) is frequently used to geometrically reconstruct fluid interfaces in Computational Fluid Dynamics. In this work, we propose a deep learning model for the solution to the forward problem of PLIC by only making use of its inverse problem. The proposed model is up to several orders of magnitude faster than traditional schemes, which significantly reduces the computational bottleneck of PLIC in CFD simulations.
  arXiv  Detail & Related papers  (2021-07-27T20:04:51Z)
• Data-Driven Shadowgraph Simulation of a 3D Object [50.591267188664666]
  We are replacing the numerical code by a computationally cheaper projection based surrogate model. The model is able to approximate the electric fields at a given time without computing all preceding electric fields as required by numerical methods. This model has shown a good quality reconstruction in a problem of perturbation of data within a narrow range of simulation parameters and can be used for input data of large size.
  arXiv  Detail & Related papers  (2021-06-01T08:46:04Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)
• DeepCFD: Efficient Steady-State Laminar Flow Approximation with Deep Convolutional Neural Networks [5.380828749672078]
  DeepCFD is a convolutional neural network (CNN) based model that efficiently approximates solutions for the problem of non-uniform steady laminar flows. Using DeepCFD, we found a speedup of up to 3 orders of magnitude compared to the standard CFD approach at a cost of low error rates.
  arXiv  Detail & Related papers  (2020-04-19T12:00:37Z)
• Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems [83.98774574197613]
  We take one of the simplest inference methods, a truncated max-product Belief propagation, and add what is necessary to make it a proper component of a deep learning model. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs) The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.
  arXiv  Detail & Related papers  (2020-03-13T13:11:35Z)

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.