Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction

• URL: http://arxiv.org/abs/2007.04439v3
• Date: Sun, 16 Aug 2020 16:32:02 GMT
• Title: Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
• Authors: Filipe de Avila Belbute-Peres, Thomas D. Economon, J. Zico Kolter
• Abstract summary: We develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. We show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions.
• Score: 79.81193813215872
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the PDE solutions, yet the simulation results predicted from these approaches typically do not generalize well to truly novel scenarios. In this work, we develop a hybrid (graph) neural network that combines a traditional graph convolutional network with an embedded differentiable fluid dynamics simulator inside the network itself. By combining an actual CFD simulator (run on a much coarser resolution representation of the problem) with the graph network, we show that we can both generalize well to new situations and benefit from the substantial speedup of neural network CFD predictions, while also substantially outperforming the coarse CFD simulation alone.

Related papers

• Graph Neural Networks and Differential Equations: A hybrid approach for data assimilation of fluid flows [0.0]
  This study presents a novel hybrid approach that combines Graph Neural Networks (GNNs) with Reynolds-Averaged Navier Stokes (RANS) equations. The results demonstrate significant improvements in the accuracy of the reconstructed mean flow compared to purely data-driven models.
  arXiv  Detail & Related papers  (2024-11-14T14:31:52Z)
• Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries [0.6299766708197884]
  This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. For the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks.
  arXiv  Detail & Related papers  (2024-01-12T18:42:42Z)
• Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media [0.0]
  Data-driven surrogate modeling provides inexpensive alternatives to high-fidelity numerical simulators. CNNs are powerful in approximating partial differential equation solutions, but it remains challenging for CNNs to handle irregular and unstructured simulation meshes. We construct surrogate models based on Graph Convolutional Networks (GCNs) to approximate the spatial-temporal solutions of multi-phase flow and transport processes in porous media.
  arXiv  Detail & Related papers  (2023-07-10T09:59:35Z)
• Predictions Based on Pixel Data: Insights from PDEs and Finite Differences [0.0]
  This paper deals with approximation of time sequences where each observation is a matrix. We show that with relatively small networks, we can represent exactly a class of numerical discretizations of PDEs based on the method of lines. Our network architecture is inspired by those typically adopted in the approximation of time sequences.
  arXiv  Detail & Related papers  (2023-05-01T08:54:45Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• MAgNet: Mesh Agnostic Neural PDE Solver [68.8204255655161]
  Climate predictions require fine-temporal resolutions to resolve all turbulent scales in the fluid simulations. Current numerical model solveers PDEs on grids that are too coarse (3km to 200km on each side) We design a novel architecture that predicts the spatially continuous solution of a PDE given a spatial position query.
  arXiv  Detail & Related papers  (2022-10-11T14:52:20Z)
• Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations [63.8376359764052]
  We propose an approach to solving partial differential equations (PDEs) using a set of neural networks. We regress a set of neural networks onto a reduced order Proper Orthogonal Decomposition (POD) basis. These networks are then used in combination with a branch network that ingests the parameters of the prescribed PDE to compute a reduced order approximation to the PDE.
  arXiv  Detail & Related papers  (2022-08-02T18:27:13Z)
• 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)
• 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)
• CFDNet: a deep learning-based accelerator for fluid simulations [1.5649420473539182]
  CFD is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. Many systems of interest are prohibitively expensive for design optimization, due to the expense of evaluating CFD simulations. This paper introduces CFDNet -- a physical simulation and deep learning coupled framework.
  arXiv  Detail & Related papers  (2020-05-09T18:06:09Z)

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.