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The Theory of Combinatory Differentiation and Locality in Quantum Chemistry
The Theory of Combinatory Differentiation and Locality in Quantum Chemistry
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152710
- ISBN
- 9798384052999
- DDC
- 004
- 저자명
- Li, Kangbo.
- 서명/저자
- The Theory of Combinatory Differentiation and Locality in Quantum Chemistry
- 발행사항
- [Sl] : Cornell University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 123 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Damle, Anil.
- 학위논문주기
- Thesis (Ph.D.)--Cornell University, 2024.
- 초록/해제
- 요약The goal of this thesis is to document three of the ideas from my PhD study related to quantum Chemistry. These ideas are alternative mathematical foundations to their respective problems. Two of the three ideas come with a working implementation that empirically demonstrates significant advantages over the state of the art with no tradeoffs or caveats. The implementation of the other idea has not gathered enough evidence to show a practical advantage, but it appears promising.Chapter one is the theory of combinatory differentiation, which practically brings symbolic differentiation up to speed with algorithmic differentiation and enables the analytic automation of the backpropagation and differential tensor calculus. At the center of this model of differentiation is a serendipitous connection between the combinatory logic and path integrals through a little bit of differential geometry captured in just two equations. This work started as an attempt to automate the differentiation process in quantum mechanics using fundamental concepts in programming language theories. It turned into a theoretical model when the connection between the combinators and the path integral emerged during the first few implementation attempts.Chapter two challenges the self-consistent field (SCF) narrative that uncorrelated electrons occupy the canonical orbitals, which are the eigenstates of a so-called effective mean-field Hamiltonian. We argue that this pseudo-physical interpretation attached to the SCF is appealing but not physical. In particular, the electron delocalization is a numerical artifact camouflaged as a quantum mechanical phenomenon under the SCF narrative. We show that a manifold HF with localization avoids delocalizing the electrons at all times without any compromise to the energy. This approach points a way to reliably overcome the cubic scaling of independent electron theories through a divide and conquer strategy.Chapter three is a reformulation of the Wannier localization problem with a more consistent Physical model and a more appropriate mathematical optimization framework. This reformulation has lead to a simpler theory that practically accelerates Wannier90 by about 100x on average when starting from a random initial guess. This project was started as a digression from another project that extends the selected columns of the density matrix (SCDM) algorithm to localize the virtual orbitals. We never returned to writing up the original project even though many questions has been answered.
- 일반주제명
- Computer science
- 일반주제명
- Condensed matter physics
- 일반주제명
- Mathematics
- 일반주제명
- Computational chemistry
- 기타저자
- Cornell University Computer Science
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211152710
■006m o d
■007cr#unu||||||||
■020 ▼a9798384052999
■035 ▼a(MiAaPQ)AAI31488629
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a004
■1001 ▼aLi, Kangbo.▼0(orcid)0000-0001-6972-3600
■24510▼aThe Theory of Combinatory Differentiation and Locality in Quantum Chemistry
■260 ▼a[Sl]▼bCornell University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a123 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Damle, Anil.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aThe goal of this thesis is to document three of the ideas from my PhD study related to quantum Chemistry. These ideas are alternative mathematical foundations to their respective problems. Two of the three ideas come with a working implementation that empirically demonstrates significant advantages over the state of the art with no tradeoffs or caveats. The implementation of the other idea has not gathered enough evidence to show a practical advantage, but it appears promising.Chapter one is the theory of combinatory differentiation, which practically brings symbolic differentiation up to speed with algorithmic differentiation and enables the analytic automation of the backpropagation and differential tensor calculus. At the center of this model of differentiation is a serendipitous connection between the combinatory logic and path integrals through a little bit of differential geometry captured in just two equations. This work started as an attempt to automate the differentiation process in quantum mechanics using fundamental concepts in programming language theories. It turned into a theoretical model when the connection between the combinators and the path integral emerged during the first few implementation attempts.Chapter two challenges the self-consistent field (SCF) narrative that uncorrelated electrons occupy the canonical orbitals, which are the eigenstates of a so-called effective mean-field Hamiltonian. We argue that this pseudo-physical interpretation attached to the SCF is appealing but not physical. In particular, the electron delocalization is a numerical artifact camouflaged as a quantum mechanical phenomenon under the SCF narrative. We show that a manifold HF with localization avoids delocalizing the electrons at all times without any compromise to the energy. This approach points a way to reliably overcome the cubic scaling of independent electron theories through a divide and conquer strategy.Chapter three is a reformulation of the Wannier localization problem with a more consistent Physical model and a more appropriate mathematical optimization framework. This reformulation has lead to a simpler theory that practically accelerates Wannier90 by about 100x on average when starting from a random initial guess. This project was started as a digression from another project that extends the selected columns of the density matrix (SCDM) algorithm to localize the virtual orbitals. We never returned to writing up the original project even though many questions has been answered.
■590 ▼aSchool code: 0058.
■650 4▼aComputer science
■650 4▼aCondensed matter physics
■650 4▼aMathematics
■650 4▼aComputational chemistry
■653 ▼aCombinatory logic
■653 ▼aCombinatory differentiation
■653 ▼aManifold optimization
■653 ▼aWannier functions
■653 ▼aQuantum chemistry
■690 ▼a0984
■690 ▼a0611
■690 ▼a0405
■690 ▼a0219
■71020▼aCornell University▼bComputer Science.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163456▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
