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Consistent Approximations of Koopman Operators and Their Applications to Climate
Consistent Approximations of Koopman Operators and Their Applications to Climate
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103048
- ISBN
- 9798286424382
- DDC
- 519
- 저자명
- Valva, Claire.
- 서명/저자
- Consistent Approximations of Koopman Operators and Their Applications to Climate
- 발행사항
- [Sl] : New York University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 238 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Gerber, Edwin P.;Giannakis, Dimitrios.
- 학위논문주기
- Thesis (Ph.D.)--New York University, 2025.
- 초록/해제
- 요약Koopman operator-theoretic methods translates problems of nonlinear dynamics, to equivalent linear, if infinite dimensional, problems about linear evolution operators which act on observables by composition with the flow map. As such problems in the sciences, such as coherent feature extraction or statistical prediction, can be analyzed with linear techniques without the need of a linear approximations. However, the extraction of approximate Koopman eigenfunctions (and the associated eigenfrequencies) from an unknown system is nontrivial, particularly if the system has mixed or continuous spectrum.In this thesis, we develop two algorithms that approximate the spectrum of the Koopman operator from trajectory data with spectral convergence guarantees in a large-data limit. First, we approximate the skew-adjoint Koopman generator from data by a "compactification" of its resolvent, which ensures that the resulting generator has a purely discrete and computable spectrum. We provide a second, similar approximation method that is physics-informed in the sense of making direct use of dynamical vector field information through automatic differentiation of kernel functions. Following this, we pose Koopman operator formalism as a tool for identifying and understanding oscillations of the climate system, with analysis of the QBO as a motivating example. Through an analysis of zonal-mean zonal-wind, we establish a data-driven index for a "pure'' QBO that is independent of the annual cycle and investigate how the annual cycle modulates the QBO, including quantifying how the annual cycle changes the descent rate of the QBO.
- 일반주제명
- Applied mathematics
- 일반주제명
- Atmospheric sciences
- 일반주제명
- Mathematics
- 기타저자
- New York University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103048
■006m o d
■007cr#unu||||||||
■020 ▼a9798286424382
■035 ▼a(MiAaPQ)AAI31931169
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aValva, Claire.
■24510▼aConsistent Approximations of Koopman Operators and Their Applications to Climate
■260 ▼a[Sl]▼bNew York University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a238 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Gerber, Edwin P.;Giannakis, Dimitrios.
■5021 ▼aThesis (Ph.D.)--New York University, 2025.
■520 ▼aKoopman operator-theoretic methods translates problems of nonlinear dynamics, to equivalent linear, if infinite dimensional, problems about linear evolution operators which act on observables by composition with the flow map. As such problems in the sciences, such as coherent feature extraction or statistical prediction, can be analyzed with linear techniques without the need of a linear approximations. However, the extraction of approximate Koopman eigenfunctions (and the associated eigenfrequencies) from an unknown system is nontrivial, particularly if the system has mixed or continuous spectrum.In this thesis, we develop two algorithms that approximate the spectrum of the Koopman operator from trajectory data with spectral convergence guarantees in a large-data limit. First, we approximate the skew-adjoint Koopman generator from data by a "compactification" of its resolvent, which ensures that the resulting generator has a purely discrete and computable spectrum. We provide a second, similar approximation method that is physics-informed in the sense of making direct use of dynamical vector field information through automatic differentiation of kernel functions. Following this, we pose Koopman operator formalism as a tool for identifying and understanding oscillations of the climate system, with analysis of the QBO as a motivating example. Through an analysis of zonal-mean zonal-wind, we establish a data-driven index for a "pure'' QBO that is independent of the annual cycle and investigate how the annual cycle modulates the QBO, including quantifying how the annual cycle changes the descent rate of the QBO.
■590 ▼aSchool code: 0146.
■650 4▼aApplied mathematics
■650 4▼aAtmospheric sciences
■650 4▼aMathematics
■653 ▼aAtmospheric dynamics
■653 ▼aData-driven techniques
■653 ▼aKoopman operators
■653 ▼aQuasi-biennial oscillation
■653 ▼aSpectral approximation
■690 ▼a0364
■690 ▼a0725
■690 ▼a0405
■71020▼aNew York University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0146
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356849▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
