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Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields // James T Duvall.
Author:	Duvall, James T.,
Description:	1 electronic resource (258 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Aerospace engineering. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31348915
ISBN:	9798382739045

Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields /
Duvall, James T.,

Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields /James T Duvall. - 1 electronic resource (258 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Computational simulations have become central in many engineering and scientific disciplines, providing insight and understanding into the behavior of complex systems. High-fidelity models (HFMs) of physical phenomena are frequently expressed using partial differential equations which require expensive and complex numerical methods for solution. This limits their application in many-query scenarios such as design optimization, model-based control, and inverse problems. The complexity may be decreased through simplifying assumptions regarding the underlying physics and coarse-graining. Alternatively, data-driven approaches may be used, whereby the HFM solutions or scalar quantities of interest (QoIs) are approximated using a surrogate regression model.Surrogate modeling techniques aim to decrease computational expense while retaining dominant solution features and characteristics. In the context of optimization, "surrogate modeling" typically corresponds to approximation of scalar QoIs which comprise terms in the objective function or constraints. The scalar QoIs are usually extracted from HFM solutions, often as integral quantities, and represent a distillation of the information present in the solution. Research into driving engineering design optimization with data-driven or deep-learning-based QoI surrogates has become widespread and seen many successes. However, QoI surrogates are limited in their portability, as a change in the objective function possibly requires retraining new surrogates. This may be remedied by approximating the HFM solution fields instead of the extracted QOIs as the solutions are objective agnostic. However, this is a more difficult task, not only due to the much greater problem dimensionality, but also due to practical considerations regarding the required varying mesh topologies across parameter or design-variable space.This thesis is concerned with development of HFM surrogates or emulators which are discretization independent. The problem physics drives modeling choices regarding numerical scheme and spatial/temporal discretization, and in many engineering-relevant scenarios the meshes must be adapted or changed among solution instances to effectively capture variation in all important solution-field features. These changes are often driven by alteration of the physical design or operating conditions as described by the problem parameters or design variables. Existing frameworks based on convolutional neural networks and snapshot-matrix decomposition often rely on lossy pixelization and data-preprocessing, limiting their effectiveness in realistic engineering scenarios. The interpolation represents a loss of important information in regions with large solution-field gradients where mesh points are tightly spaced, such as through fluid boundary layers and free-shear layers in the wake of aerodynamic bodies. The methods developed here, however, can learn from heterogeneous data sources by handling each point in every mesh separately, bypassing the need for constructing snapshot matrices of consistent dimension for each case.Developed methods include decoder convolutional neural network (DCNN) models for situations where the computational domain has a regular Cartesian or block-Cartesian structure. DCNN models map directly between the design variables and full solution fields, providing richer information than QoI surrogates. This addresses information loss due to interpolation, but not variation in mesh topology among solution instances. Recently, coordinate-based multi-layer-perceptron networks have been found to be effective at representing 3D objects and scenes by regressing volumetric implicit fields, with applications in computer graphics. A key distinction is that coordinate-inputs are taken pointwise instead of as full-domain solution snapshots. These concepts are leveraged and adapted in the context of physical-field surrogate modeling, and allow for full discretization independence where each solution may have a unique and varying domain, boundary, mesh topology, and operating conditions.Generalization across solution instances is achieved by conditioning the neural networks through a combination of local and global variables. Local conditioning relates to use of the signed-distance function or minimum-distance function as an additional network input to provide geometric information. Global conditioning utilizes the problem design variables as the conditional input. Various methods of global conditioning are explored, including concatenation-based conditioning and the use of hypernetworks for full or partial network-weight conditioning. The methods are applied to predict solutions around complex, parametrically-defined geometries on non-parametrically-defined meshes with model predictions obtained many orders of magnitude faster than the full-order models. The incorporation of random Fourier features enhances prediction and generalization accuracy in some situations, as does incorporation of layer-normalization in the main network.The HFM surrogates are applied to a variety of steady-state problems, including 2D external vehicle aerodynamics, jet-engine-compressor aerodynamics, the 2D poisson equation with a source term, and finally 3D Ahmed body aerodynamics. Additionally, the HFM surrogates are used to drive aerodynamic design optimization of jet-engine-compressor airfoils in subsonic and transonic regimes, with orders-of-magnitude reduction in online time to attain optimal designs as compared to CFD-driven optimization. In summary, this work develops and demonstrates HFM surrogates with promising potential as practical tools in industrial analysis and design.

English

ISBN: 9798382739045Subjects--Topical Terms:

1002622
Aerospace engineering.
Subjects--Index Terms:

Surrogate modeling

Development and Application of Hypernetworks for Discretization-Independent Surrogate Modeling of Physical Fields /
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502 $b Ph.D. $c University of Michigan $d 2024.
520 $a Computational simulations have become central in many engineering and scientific disciplines, providing insight and understanding into the behavior of complex systems. High-fidelity models (HFMs) of physical phenomena are frequently expressed using partial differential equations which require expensive and complex numerical methods for solution. This limits their application in many-query scenarios such as design optimization, model-based control, and inverse problems. The complexity may be decreased through simplifying assumptions regarding the underlying physics and coarse-graining. Alternatively, data-driven approaches may be used, whereby the HFM solutions or scalar quantities of interest (QoIs) are approximated using a surrogate regression model.Surrogate modeling techniques aim to decrease computational expense while retaining dominant solution features and characteristics. In the context of optimization, "surrogate modeling" typically corresponds to approximation of scalar QoIs which comprise terms in the objective function or constraints. The scalar QoIs are usually extracted from HFM solutions, often as integral quantities, and represent a distillation of the information present in the solution. Research into driving engineering design optimization with data-driven or deep-learning-based QoI surrogates has become widespread and seen many successes. However, QoI surrogates are limited in their portability, as a change in the objective function possibly requires retraining new surrogates. This may be remedied by approximating the HFM solution fields instead of the extracted QOIs as the solutions are objective agnostic. However, this is a more difficult task, not only due to the much greater problem dimensionality, but also due to practical considerations regarding the required varying mesh topologies across parameter or design-variable space.This thesis is concerned with development of HFM surrogates or emulators which are discretization independent. The problem physics drives modeling choices regarding numerical scheme and spatial/temporal discretization, and in many engineering-relevant scenarios the meshes must be adapted or changed among solution instances to effectively capture variation in all important solution-field features. These changes are often driven by alteration of the physical design or operating conditions as described by the problem parameters or design variables. Existing frameworks based on convolutional neural networks and snapshot-matrix decomposition often rely on lossy pixelization and data-preprocessing, limiting their effectiveness in realistic engineering scenarios. The interpolation represents a loss of important information in regions with large solution-field gradients where mesh points are tightly spaced, such as through fluid boundary layers and free-shear layers in the wake of aerodynamic bodies. The methods developed here, however, can learn from heterogeneous data sources by handling each point in every mesh separately, bypassing the need for constructing snapshot matrices of consistent dimension for each case.Developed methods include decoder convolutional neural network (DCNN) models for situations where the computational domain has a regular Cartesian or block-Cartesian structure. DCNN models map directly between the design variables and full solution fields, providing richer information than QoI surrogates. This addresses information loss due to interpolation, but not variation in mesh topology among solution instances. Recently, coordinate-based multi-layer-perceptron networks have been found to be effective at representing 3D objects and scenes by regressing volumetric implicit fields, with applications in computer graphics. A key distinction is that coordinate-inputs are taken pointwise instead of as full-domain solution snapshots. These concepts are leveraged and adapted in the context of physical-field surrogate modeling, and allow for full discretization independence where each solution may have a unique and varying domain, boundary, mesh topology, and operating conditions.Generalization across solution instances is achieved by conditioning the neural networks through a combination of local and global variables. Local conditioning relates to use of the signed-distance function or minimum-distance function as an additional network input to provide geometric information. Global conditioning utilizes the problem design variables as the conditional input. Various methods of global conditioning are explored, including concatenation-based conditioning and the use of hypernetworks for full or partial network-weight conditioning. The methods are applied to predict solutions around complex, parametrically-defined geometries on non-parametrically-defined meshes with model predictions obtained many orders of magnitude faster than the full-order models. The incorporation of random Fourier features enhances prediction and generalization accuracy in some situations, as does incorporation of layer-normalization in the main network.The HFM surrogates are applied to a variety of steady-state problems, including 2D external vehicle aerodynamics, jet-engine-compressor aerodynamics, the 2D poisson equation with a source term, and finally 3D Ahmed body aerodynamics. Additionally, the HFM surrogates are used to drive aerodynamic design optimization of jet-engine-compressor airfoils in subsonic and transonic regimes, with orders-of-magnitude reduction in online time to attain optimal designs as compared to CFD-driven optimization. In summary, this work develops and demonstrates HFM surrogates with promising potential as practical tools in industrial analysis and design.
546 $a English
590 $a School code: 0127
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Mechanics. $3 525881
653 $a Surrogate modeling
653 $a Hypernetworks
653 $a Deep learning
653 $a Surrogate based optimization
653 $a High-fidelity models
690 $a 0538
690 $a 0346
690 $a 0800
710 2 $a University of Michigan. $b Aerospace Engineering. $e degree granting institution. $3 3817051
720 1 $a Duraisamy, Karthik $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0127
791 $a Ph.D.
792 $a 2024
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