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Differentiable Programming for Compu...

McGreivy, Nicholas Bradley.

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Differentiable Programming for Computational Plasma Physics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differentiable Programming for Computational Plasma Physics./
Author:	McGreivy, Nicholas Bradley.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
Description:	355 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Plasma physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31294774
ISBN:	9798382810317

Differentiable Programming for Computational Plasma Physics.
McGreivy, Nicholas Bradley.

Differentiable Programming for Computational Plasma Physics. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 355 p.

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

Thesis (Ph.D.)--Princeton University, 2024.

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of differentiable programming to computational plasma physics. First, we consider how differentiable programming can be used to simplify and improve stellarator optimization. We introduce a stellarator coil design code (FOCUSADD) that uses gradient-based optimization to produce stellarator coils with finite build. Because we use reverse mode AD, which can compute gradients of scalar functions with the same computational complexity as the function, FOCUSADD is simple, flexible, and efficient. We then discuss two additional applications of AD in stellarator optimization: finding non-axisymmetric magnetic fields that satisfy magnetohydrodynamic (MHD) equilibrium, and optimizing those magnetic fields subject to MHD equilibrium. Second, we explore how machine learning (ML) can be used to improve or replace the numerical methods used to solve partial differential equations (PDEs), focusing on time-dependent PDEs in fluid mechanics relevant to plasma physics. Differentiable programming allows neural networks and other techniques from ML to be embedded within numerical methods. This is a promising, but relatively new, research area. We focus on two basic questions. First, can we design ML-based PDE solvers that have the same guarantees of conservation, stability, and positivity that standard numerical methods do? The answer is yes; we introduce error-correcting algorithms that preserve invariants of time-dependent PDEs. Second, which types of ML-based solvers work best at solving PDEs? We perform a systematic review of the scientific literature on solving PDEs with ML. Unfortunately, we discover two issues, weak baselines and reporting biases, that affect the interpretation reproducibility of a significant majority of published research. We conclude that using ML to solve PDEs is not as promising as we initially believed.

ISBN: 9798382810317Subjects--Topical Terms:

3175417
Plasma physics.
Subjects--Index Terms:

Automatic differentiation

Differentiable Programming for Computational Plasma Physics.
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100 1 $a McGreivy, Nicholas Bradley. $0 (orcid)0000-0003-2073-9593 $3 3773286
245 1 0 $a Differentiable Programming for Computational Plasma Physics.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 355 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisor: Hakim, Ammar H.
502 $a Thesis (Ph.D.)--Princeton University, 2024.
520 $a Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of differentiable programming to computational plasma physics. First, we consider how differentiable programming can be used to simplify and improve stellarator optimization. We introduce a stellarator coil design code (FOCUSADD) that uses gradient-based optimization to produce stellarator coils with finite build. Because we use reverse mode AD, which can compute gradients of scalar functions with the same computational complexity as the function, FOCUSADD is simple, flexible, and efficient. We then discuss two additional applications of AD in stellarator optimization: finding non-axisymmetric magnetic fields that satisfy magnetohydrodynamic (MHD) equilibrium, and optimizing those magnetic fields subject to MHD equilibrium. Second, we explore how machine learning (ML) can be used to improve or replace the numerical methods used to solve partial differential equations (PDEs), focusing on time-dependent PDEs in fluid mechanics relevant to plasma physics. Differentiable programming allows neural networks and other techniques from ML to be embedded within numerical methods. This is a promising, but relatively new, research area. We focus on two basic questions. First, can we design ML-based PDE solvers that have the same guarantees of conservation, stability, and positivity that standard numerical methods do? The answer is yes; we introduce error-correcting algorithms that preserve invariants of time-dependent PDEs. Second, which types of ML-based solvers work best at solving PDEs? We perform a systematic review of the scientific literature on solving PDEs with ML. Unfortunately, we discover two issues, weak baselines and reporting biases, that affect the interpretation reproducibility of a significant majority of published research. We conclude that using ML to solve PDEs is not as promising as we initially believed.
590 $a School code: 0181.
650 4 $a Plasma physics. $3 3175417
650 4 $a Computational physics. $3 3343998
650 4 $a Computer science. $3 523869
653 $a Automatic differentiation
653 $a Machine learning
653 $a Partial differential equations
653 $a Stellarator optimization
690 $a 0759
690 $a 0216
690 $a 0984
690 $a 0800
710 2 $a Princeton University. $b Astrophysical Sciences-Plasma Physics Program. $3 3437719
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0181
791 $a Ph.D.
792 $a 2024
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31294774