國立虎尾科技大學 |

Deep Learning Algorithms for Computational Mechanics on Irregular Geometries.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Deep Learning Algorithms for Computational Mechanics on Irregular Geometries./
Author:	Kashefi, Ali.
Description:	1 online resource (200 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
Subject:	Pressure distribution. -
Online resource:	click for full text (PQDT)
ISBN:	9798380266925

Deep Learning Algorithms for Computational Mechanics on Irregular Geometries.
Kashefi, Ali.

Deep Learning Algorithms for Computational Mechanics on Irregular Geometries. - 1 online resource (200 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

Thesis (Ph.D.)--Stanford University, 2023.

Includes bibliographical references

The current dissertation proposes novel fully supervised and weakly supervised learning frameworks in the area of computational physics.Concerning the supervised deep learning framework, we present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver while maintaining excellent to a reasonable accuracy.Additionally, we propose a novel deep-learning framework for predicting the permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the boundary between solid matrix and pore spaces as point clouds and feed them as inputs to a neural network based on the PointNet architecture. This approach overcomes the challenge of memory restriction of graphics processing units and its consequences on the choice of batch size, and convergence. Compared to convolutional neural networks, the proposed deep learning methodology provides freedom to select larger batch sizes, due to reducing significantly the size of network inputs. Specifically, we use the classification branch of PointNet and adjust it for a regression task. As a test case, two and three-dimensional synthetic digital rock images are considered. We investigate the effect of different components of our neural network on its performance. We compare our deep learning strategy with a convolutional neural network from various perspectives, specifically for the maximum possible batch size. We inspect the generalizability of our network by predicting the permeability of real-world rock samples as well as synthetic digital rocks that are statistically different from the samples used during training. The network predicts the permeability of digital rocks a few thousand times faster than a Lattice Boltzmann solver with a high level of prediction accuracy.Concerning the weakly supervised deep learning framework, we present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud-based neural network to capture geometric features of computational domains and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network to capture the physics. While the solution of the continuity and Navier-Stokes equations is a function of the geometry of the computational domain, current versions of physics-informed neural networks have no mechanism to express this functionally in their outputs, and thus are restricted to obtaining the solutions only for one computational domain with each training procedure. Using the proposed framework, three new facilities become available. First, the governing equations are solvable on a set of computational domains containing irregular geometries with high variations with respect to each other but requiring training only once. Second, after training the introduced framework on the set, it is now able to predict the solutions on domains with unseen geometries from seen and unseen categories as well. The former and the latter both lead to savings in computational costs. Finally, all the advantages of the point-cloud-based neural network for irregular geometries, already used for supervised learning, are transferred to the proposed physics-informed framework. The effectiveness of our framework is shown through the method of manufactured solutions and thermally-driven flow for forward and inverse problems.Furthermore, we predict steady-state Stokes flow of fluids within porous media at pore scales using sparse point observations and physics-informed PointNet (PIPN). Taking the advantages of PIPN into account, three new features become available compared to physics-informed convolutional neural networks for porous medium applications. First, the input of PIPN is exclusively the pore spaces of porous media (rather than both the pore and grain spaces). This feature significantly diminishes computational costs. Second, PIPN represents the boundary of pore spaces smoothly and realistically (rather than pixel-wise representations). Third, spatial resolution can vary over the physical domain (rather than equally spaced resolutions). This feature enables users to reach an optimal resolution with a minimum computational cost. The performance of our framework is evaluated by the study of the influence of noisy sensor data, pressure observations, and spatial correlation length.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380266925Subjects--Topical Terms:

1413590
Pressure distribution.
Index Terms--Genre/Form:

554714
Electronic books.

Deep Learning Algorithms for Computational Mechanics on Irregular Geometries.
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500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
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502 $a Thesis (Ph.D.)--Stanford University, 2023.
504 $a Includes bibliographical references
520 $a The current dissertation proposes novel fully supervised and weakly supervised learning frameworks in the area of computational physics.Concerning the supervised deep learning framework, we present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural network based on the PointNet architecture, which learns an end-to-end mapping between spatial positions and CFD quantities. Using our approach, (i) the network inherits desirable features of unstructured meshes (e.g., fine and coarse point spacing near the object surface and in the far field, respectively), which minimizes network training cost; (ii) object geometry is accurately represented through vertices located on object boundaries, which maintains boundary smoothness and allows the network to detect small changes between geometries; and (iii) no data interpolation is utilized for creating training data; thus accuracy of the CFD data is preserved. None of these features are achievable by extant methods based on projecting scattered CFD data into Cartesian grids and then using regular convolutional neural networks. Incompressible laminar steady flow past a cylinder with various shapes for its cross section is considered. The mass and momentum of predicted fields are conserved. We test the generalizability of our network by predicting the flow around multiple objects as well as an airfoil, even though only single objects and no airfoils are observed during training. The network predicts the flow fields hundreds of times faster than our conventional CFD solver while maintaining excellent to a reasonable accuracy.Additionally, we propose a novel deep-learning framework for predicting the permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the boundary between solid matrix and pore spaces as point clouds and feed them as inputs to a neural network based on the PointNet architecture. This approach overcomes the challenge of memory restriction of graphics processing units and its consequences on the choice of batch size, and convergence. Compared to convolutional neural networks, the proposed deep learning methodology provides freedom to select larger batch sizes, due to reducing significantly the size of network inputs. Specifically, we use the classification branch of PointNet and adjust it for a regression task. As a test case, two and three-dimensional synthetic digital rock images are considered. We investigate the effect of different components of our neural network on its performance. We compare our deep learning strategy with a convolutional neural network from various perspectives, specifically for the maximum possible batch size. We inspect the generalizability of our network by predicting the permeability of real-world rock samples as well as synthetic digital rocks that are statistically different from the samples used during training. The network predicts the permeability of digital rocks a few thousand times faster than a Lattice Boltzmann solver with a high level of prediction accuracy.Concerning the weakly supervised deep learning framework, we present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud-based neural network to capture geometric features of computational domains and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network to capture the physics. While the solution of the continuity and Navier-Stokes equations is a function of the geometry of the computational domain, current versions of physics-informed neural networks have no mechanism to express this functionally in their outputs, and thus are restricted to obtaining the solutions only for one computational domain with each training procedure. Using the proposed framework, three new facilities become available. First, the governing equations are solvable on a set of computational domains containing irregular geometries with high variations with respect to each other but requiring training only once. Second, after training the introduced framework on the set, it is now able to predict the solutions on domains with unseen geometries from seen and unseen categories as well. The former and the latter both lead to savings in computational costs. Finally, all the advantages of the point-cloud-based neural network for irregular geometries, already used for supervised learning, are transferred to the proposed physics-informed framework. The effectiveness of our framework is shown through the method of manufactured solutions and thermally-driven flow for forward and inverse problems.Furthermore, we predict steady-state Stokes flow of fluids within porous media at pore scales using sparse point observations and physics-informed PointNet (PIPN). Taking the advantages of PIPN into account, three new features become available compared to physics-informed convolutional neural networks for porous medium applications. First, the input of PIPN is exclusively the pore spaces of porous media (rather than both the pore and grain spaces). This feature significantly diminishes computational costs. Second, PIPN represents the boundary of pore spaces smoothly and realistically (rather than pixel-wise representations). Third, spatial resolution can vary over the physical domain (rather than equally spaced resolutions). This feature enables users to reach an optimal resolution with a minimum computational cost. The performance of our framework is evaluated by the study of the influence of noisy sensor data, pressure observations, and spatial correlation length.
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