서브메뉴
검색
Data-Driven Inference of Symmetry-Equivariant Models of Natural Phenomena
Data-Driven Inference of Symmetry-Equivariant Models of Natural Phenomena
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103702
- ISBN
- 9798293893881
- DDC
- 519
- 서명/저자
- Data-Driven Inference of Symmetry-Equivariant Models of Natural Phenomena
- 발행사항
- [Sl] : Princeton University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 142 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-04, Section: B.
- 주기사항
- Advisor: Rowley, Clarence W.;Fefferman, Charles L.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2025.
- 초록/해제
- 요약This dissertation provides an in-depth description of the SPIDER (Sparse Physics-Informed Discovery of Empirical Relations) framework for data-driven inference of symmetry-equivariant models of spatiotemporally extended physical systems. The homogeneity and isotropy of physical space require mathematical models of natural phenomena to be equivariant with respect to symmetries including translations, rotations, and reflections. Unstructured data-driven model inference leads to an intractable optimization problem due to the high dimensionality of both the spatiotemporal data and the model search space. In contrast, SPIDER exploits tensor representations of the symmetry group, alongside other physical constraints such as local or short-range interactions, to describe systems via sets of tensor-valued partial differential or integro-differential equations, which can parsimoniously and interpretably parametrize a wide range of models.While prior work touches on necessary ingredients for the successful application of SPIDER to complex real-world problems, such as weak formulation of differential equations and sparse regression, this manuscript addresses essential gaps that have precluded more widespread adoption. Namely, it (1) formalizes an algorithm for automatically generating and manipulating libraries of symmetry-equivariant tensors, (2) describes how to synthesize all logically independent equations in the search space, and (3) generalizes SPIDER to discover mean-field models of many-body systems composed of discrete particles or agents. These innovations are implemented as part of a software package, PySPIDER, and illustrated using two examples representing an incompressible fluid flow in the continuum limit and a compressible fluid consisting of discrete interacting particles.
- 일반주제명
- Applied mathematics
- 일반주제명
- Computational physics
- 일반주제명
- Computer science
- 키워드
- Machine learning
- 키워드
- SPIDER
- 키워드
- Physical space
- 키워드
- PySPIDER
- 기타저자
- Princeton University Applied and Computational Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008260126s2025 us c eng d■001000017358228
■00520260202103702
■006m o d
■007cr#unu||||||||
■020 ▼a9798293893881
■035 ▼a(MiAaPQ)AAI32113023
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aGurevich, Daniel.▼0(orcid)0000-0002-3659-407X
■24510▼aData-Driven Inference of Symmetry-Equivariant Models of Natural Phenomena
■260 ▼a[Sl]▼bPrinceton University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a142 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-04, Section: B.
■500 ▼aAdvisor: Rowley, Clarence W.;Fefferman, Charles L.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2025.
■520 ▼aThis dissertation provides an in-depth description of the SPIDER (Sparse Physics-Informed Discovery of Empirical Relations) framework for data-driven inference of symmetry-equivariant models of spatiotemporally extended physical systems. The homogeneity and isotropy of physical space require mathematical models of natural phenomena to be equivariant with respect to symmetries including translations, rotations, and reflections. Unstructured data-driven model inference leads to an intractable optimization problem due to the high dimensionality of both the spatiotemporal data and the model search space. In contrast, SPIDER exploits tensor representations of the symmetry group, alongside other physical constraints such as local or short-range interactions, to describe systems via sets of tensor-valued partial differential or integro-differential equations, which can parsimoniously and interpretably parametrize a wide range of models.While prior work touches on necessary ingredients for the successful application of SPIDER to complex real-world problems, such as weak formulation of differential equations and sparse regression, this manuscript addresses essential gaps that have precluded more widespread adoption. Namely, it (1) formalizes an algorithm for automatically generating and manipulating libraries of symmetry-equivariant tensors, (2) describes how to synthesize all logically independent equations in the search space, and (3) generalizes SPIDER to discover mean-field models of many-body systems composed of discrete particles or agents. These innovations are implemented as part of a software package, PySPIDER, and illustrated using two examples representing an incompressible fluid flow in the continuum limit and a compressible fluid consisting of discrete interacting particles.
■590 ▼aSchool code: 0181.
■650 4▼aApplied mathematics
■650 4▼aComputational physics
■650 4▼aComputer science
■653 ▼aMachine learning
■653 ▼aSparse regression
■653 ▼aSPIDER
■653 ▼aPhysical space
■653 ▼aPySPIDER
■690 ▼a0364
■690 ▼a0216
■690 ▼a0984
■690 ▼a0800
■71020▼aPrinceton University▼bApplied and Computational Mathematics.
■7730 ▼tDissertations Abstracts International▼g87-04B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358228▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
