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Pretraining and Transformers for Accelerating Solutions to Partial Differential Equations
Pretraining and Transformers for Accelerating Solutions to Partial Differential Equations
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103011
- ISBN
- 9798290940779
- DDC
- 621
- 서명/저자
- Pretraining and Transformers for Accelerating Solutions to Partial Differential Equations
- 발행사항
- [Sl] : Carnegie Mellon University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 164 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
- 주기사항
- Advisor: Barati Farimani, Amir.
- 학위논문주기
- Thesis (Ph.D.)--Carnegie Mellon University, 2025.
- 초록/해제
- 요약Solving Partial Differential Equations (PDEs) is the cornerstone of many fields of science, engineering, and mathematics. There are many challenges associated with developing solutions to complex sets of equations. Namely, no universal mathematical theory of PDEs exists, so equations are often difficult or impossible to solve analytically. Computational techniques have been developed based on analytical theory to compute solutions, overcoming analytical limitations. These computational techniques, however, often require significant computational resources, human input, or both. Specifically, constructing the spatial mesh over which equations are solved normally requires human input and intuition. Additionally, solving the equations given a mesh often requires tailor-made numerical solvers, and can be prohibitively slow. This thesis presents four works to address challenges in computational science. First, Mesh Deep Q Network uses Deep Reinforcement Learning to remove vertices in a mesh while maintaining accuracy in coarse property calculation. Physics Informed Contrastive learning utilizes pretraining to improve model performance across multiple systems simultaneously. Lastly, Physics Informed Token transformer and Explain Like I'm Five explore text-based multimodality in PDEs through end-to-end training and using pretrained Large Language models, respectively. Multimodality proves to be a valuable approach to incorporate system information in a flexible way. These works provide an important step towards developing large scale, general purpose PDE solvers.
- 일반주제명
- Mechanical engineering
- 일반주제명
- Fluid mechanics
- 일반주제명
- Computer engineering
- 키워드
- Machine learning
- 키워드
- Meshing
- 키워드
- Neural operators
- 기타저자
- Carnegie Mellon University Mechanical Engineering
- 기본자료저록
- Dissertations Abstracts International. 87-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798290940779
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a621
■1001 ▼aLorsung, Cooper Delaney.▼0(orcid)0000-0003-1410-9077
■24510▼aPretraining and Transformers for Accelerating Solutions to Partial Differential Equations
■260 ▼a[Sl]▼bCarnegie Mellon University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a164 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-02, Section: B.
■500 ▼aAdvisor: Barati Farimani, Amir.
■5021 ▼aThesis (Ph.D.)--Carnegie Mellon University, 2025.
■520 ▼aSolving Partial Differential Equations (PDEs) is the cornerstone of many fields of science, engineering, and mathematics. There are many challenges associated with developing solutions to complex sets of equations. Namely, no universal mathematical theory of PDEs exists, so equations are often difficult or impossible to solve analytically. Computational techniques have been developed based on analytical theory to compute solutions, overcoming analytical limitations. These computational techniques, however, often require significant computational resources, human input, or both. Specifically, constructing the spatial mesh over which equations are solved normally requires human input and intuition. Additionally, solving the equations given a mesh often requires tailor-made numerical solvers, and can be prohibitively slow. This thesis presents four works to address challenges in computational science. First, Mesh Deep Q Network uses Deep Reinforcement Learning to remove vertices in a mesh while maintaining accuracy in coarse property calculation. Physics Informed Contrastive learning utilizes pretraining to improve model performance across multiple systems simultaneously. Lastly, Physics Informed Token transformer and Explain Like I'm Five explore text-based multimodality in PDEs through end-to-end training and using pretrained Large Language models, respectively. Multimodality proves to be a valuable approach to incorporate system information in a flexible way. These works provide an important step towards developing large scale, general purpose PDE solvers.
■590 ▼aSchool code: 0041.
■650 4▼aMechanical engineering
■650 4▼aFluid mechanics
■650 4▼aComputer engineering
■653 ▼aMachine learning
■653 ▼aMeshing
■653 ▼aMultimodal FactFormer
■653 ▼aNeural operators
■653 ▼aPhysics Informed Token Transformer
■690 ▼a0548
■690 ▼a0800
■690 ▼a0204
■690 ▼a0464
■71020▼aCarnegie Mellon University▼bMechanical Engineering.
■7730 ▼tDissertations Abstracts International▼g87-02B.
■790 ▼a0041
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356657▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
