Neural Canonical Transformation with Symplectic Flows

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. Intriguingly, it has a natural correspondence to normalizing flows with a symplectic constraint. Building on this key insight, we design a neural canonical transformation approach to automatic...

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Autores principales:	Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, Lei Wang
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b7777a0445ae48eea297b3565afeaa27
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spelling	oai:doaj.org-article:b7777a0445ae48eea297b3565afeaa272021-12-02T12:09:20ZNeural Canonical Transformation with Symplectic Flows10.1103/PhysRevX.10.0210202160-3308https://doaj.org/article/b7777a0445ae48eea297b3565afeaa272020-04-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.021020http://doi.org/10.1103/PhysRevX.10.021020https://doaj.org/toc/2160-3308Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. Intriguingly, it has a natural correspondence to normalizing flows with a symplectic constraint. Building on this key insight, we design a neural canonical transformation approach to automatically identify independent slow collective variables in general physical systems and natural datasets. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model based either on the Hamiltonian function or phase-space samples. The learned model maps physical variables onto an independent representation where collective modes with different frequencies are separated, which can be useful for various downstream tasks such as compression, prediction, control, and sampling. We demonstrate the ability of this method first by analyzing toy problems and then by applying it to real-world problems, such as identifying and interpolating slow collective modes of the alanine dipeptide molecule and MNIST database images.Shuo-Hui LiChen-Xiao DongLinfeng ZhangLei WangAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 2, p 021020 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Shuo-Hui Li Chen-Xiao Dong Linfeng Zhang Lei Wang Neural Canonical Transformation with Symplectic Flows
description	Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. Intriguingly, it has a natural correspondence to normalizing flows with a symplectic constraint. Building on this key insight, we design a neural canonical transformation approach to automatically identify independent slow collective variables in general physical systems and natural datasets. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model based either on the Hamiltonian function or phase-space samples. The learned model maps physical variables onto an independent representation where collective modes with different frequencies are separated, which can be useful for various downstream tasks such as compression, prediction, control, and sampling. We demonstrate the ability of this method first by analyzing toy problems and then by applying it to real-world problems, such as identifying and interpolating slow collective modes of the alanine dipeptide molecule and MNIST database images.
format	article
author	Shuo-Hui Li Chen-Xiao Dong Linfeng Zhang Lei Wang
author_facet	Shuo-Hui Li Chen-Xiao Dong Linfeng Zhang Lei Wang
author_sort	Shuo-Hui Li
title	Neural Canonical Transformation with Symplectic Flows
title_short	Neural Canonical Transformation with Symplectic Flows
title_full	Neural Canonical Transformation with Symplectic Flows
title_fullStr	Neural Canonical Transformation with Symplectic Flows
title_full_unstemmed	Neural Canonical Transformation with Symplectic Flows
title_sort	neural canonical transformation with symplectic flows
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/b7777a0445ae48eea297b3565afeaa27
work_keys_str_mv	AT shuohuili neuralcanonicaltransformationwithsymplecticflows AT chenxiaodong neuralcanonicaltransformationwithsymplecticflows AT linfengzhang neuralcanonicaltransformationwithsymplecticflows AT leiwang neuralcanonicaltransformationwithsymplecticflows
_version_	1718394711142563840

Neural Canonical Transformation with Symplectic Flows

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