skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Mesh deep Q network: A deep reinforcement learning framework for improving meshes in computational fluid dynamics
Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be updated automatically to produce an accurate solution for the problem at hand. Existing classical techniques for adaptive meshing require either additional functionality out of solvers, many training simulations, or both. Current machine learning techniques often require substantial computational cost for training data generation, and are restricted in scope to the training data flow regime. Mesh Deep Q Network (MeshDQN) is developed as a general purpose deep reinforcement learning framework to iteratively coarsen meshes while preserving target property calculation. A graph neural network based deep Q network is used to select mesh vertices for removal and solution interpolation is used to bypass expensive simulations at each step in the improvement process. MeshDQN requires a single simulation prior to mesh coarsening, while making no assumptions about flow regime, mesh type, or solver, only requiring the ability to modify meshes directly in a CFD pipeline. MeshDQN successfully improves meshes for two 2D airfoils.  more » « less
Award ID(s):
1953222
PAR ID:
10597439
Author(s) / Creator(s):
;
Publisher / Repository:
American Institute of Physics
Date Published:
Journal Name:
AIP Advances
Volume:
13
Issue:
1
ISSN:
2158-3226
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Computational fluid dynamics (CFD) modeling of left ventricle (LV) flow combined with patient medical imaging data has shown great potential in obtaining patient-specific hemodynamics information for functional assessment of the heart. A typical model construction pipeline usually starts with segmentation of the LV by manual delineation followed by mesh generation and registration techniques using separate software tools. However, such approaches usually require significant time and human efforts in the model generation process, limiting large-scale analysis. In this study, we propose an approach toward fully automating the model generation process for CFD simulation of LV flow to significantly reduce LV CFD model generation time. Our modeling framework leverages a novel combination of techniques including deep-learning based segmentation, geometry processing, and image registration to reliably reconstruct CFD-suitable LV models with little-to-no user intervention.1 We utilized an ensemble of two-dimensional (2D) convolutional neural networks (CNNs) for automatic segmentation of cardiac structures from three-dimensional (3D) patient images and our segmentation approach outperformed recent state-of-the-art segmentation techniques when evaluated on benchmark data containing both magnetic resonance (MR) and computed tomography(CT) cardiac scans. We demonstrate that through a combination of segmentation and geometry processing, we were able to robustly create CFD-suitable LV meshes from segmentations for 78 out of 80 test cases. Although the focus on this study is on image-to-mesh generation, we demonstrate the feasibility of this framework in supporting LV hemodynamics modeling by performing CFD simulations from two representative time-resolved patient-specific image datasets. 
    more » « less
  2. Faithful, accurate, and successful cardiac biomechanics and electrophysiological simulations require patient-specific geometric models of the heart. Since the cardiac geometry consists of highly-curved boundaries, the use of high-order meshes with curved elements would ensure that the various curves and features present in the cardiac geometry are well-captured and preserved in the corresponding mesh. Most other existing mesh generation techniques require computer-aided design files to represent the geometric boundary, which are often not available for biomedical applications. Unlike such methods, our technique takes a high-order surface mesh, generated from patient medical images, as input and generates a high-order volume mesh directly from the curved surface mesh. In this paper, we use our direct high-order curvilinear tetrahedral mesh generation method [1] to generate several second-order cardiac meshes. Our meshes include the left ventricle myocardia of a healthy heart and hearts with dilated and hypertrophic cardiomyopathy. We show that our high-order cardiac meshes do not contain inverted elements and are of sufficiently high quality for use in cardiac finite element simulations. 
    more » « less
  3. For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary con- straints or limitations of current meshing methods. By tackling mesh gen- eration and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms. 
    more » « less
  4. Osteoarthritis of the knee is increasingly prevalent as our population ages, representing an increasing financial burden, and severely impacting quality of life. The invasiveness of in vivo procedures and the high cost of cadaveric studies has left computational tools uniquely suited to study knee biomechanics. Developments in deep learning have great potential for efficiently generating large-scale datasets to enable researchers to perform population-sized investigations, but the time and effort associated with producing robust hexahedral meshes has been a limiting factor in expanding finite element studies to encompass a population. Here we developed a fully automated pipeline capable of taking magnetic resonance knee images and producing a working finite element simulation. We trained an encoder-decoder convolutional neural network to perform semantic image segmentation on the Imorphics dataset provided through the Osteoarthritis Initiative. The Imorphics dataset contained 176 image sequences with varying levels of cartilage degradation. Starting from an open-source swept-extrusion meshing algorithm, we further developed this algorithm until it could produce high quality meshes for every sequence and we applied a template-mapping procedure to automatically place soft-tissue attachment points. The meshing algorithm produced simulation-ready meshes for all 176 sequences, regardless of the use of provided (manually reconstructed) or predicted (automatically generated) segmentation labels. The average time to mesh all bones and cartilage tissues was less than 2 min per knee on an AMD Ryzen 5600X processor, using a parallel pool of three workers for bone meshing, followed by a pool of four workers meshing the four cartilage tissues. Of the 176 sequences with provided segmentation labels, 86% of the resulting meshes completed a simulated flexion-extension activity. We used a reserved testing dataset of 28 sequences unseen during network training to produce simulations derived from predicted labels. We compared tibiofemoral contact mechanics between manual and automated reconstructions for the 24 pairs of successful finite element simulations from this set, resulting in mean root-mean-squared differences under 20% of their respective min-max norms. In combination with further advancements in deep learning, this framework represents a feasible pipeline to produce population sized finite element studies of the natural knee from subject-specific models. 
    more » « less
  5. The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques. 
    more » « less