A quantum-inspired approach to exploit turbulence structures

Nikita Gourianov; Michael Lubasch; Sergey Dolgov; Quincy Y. van den Berg; Hessam Babaee; Peyman Givi; Martin Kiffner; Dieter Jaksch

doi:10.1038/s43588-021-00181-1

A quantum-inspired approach to exploit turbulence structures

Nikita Gourianov, Michael Lubasch, Sergey Dolgov, Quincy Y. van den Berg, Hessam Babaee, Peyman Givi, Martin Kiffner, Dieter Jaksch

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Abstract

Understanding turbulence is key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multiscale nature, describing the coupling between different-sized eddies in space and time. Here we analyze the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present the results for interscale correlations of two paradigmatic flow examples, and use these insights along with tensor network theory to design a structure-resolving algorithm for simulating turbulent flows. With this algorithm, we find that the incompressible Navier–Stokes equations can be accurately solved even when reducing the number of parameters required to represent the velocity field by more than one order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers.

Original language	English
Pages (from-to)	30-37
Number of pages	8
Journal	Nature Computational Science
Volume	2
Issue number	1
Early online date	13 Jan 2022
DOIs	https://doi.org/10.1038/s43588-021-00181-1
Publication status	Published - 31 Jan 2022

Bibliographical note

Funding Information:
The work at the University of Oxford was supported by the EPSRC Programme Grant DesOEQ (EP/P009565/1), and M.K. and D.J. acknowledge financial support from the National Research Foundation, Prime Ministers Office, Singapore, and the Ministry of Education, Singapore, under the Research Centres of Excellence programme. D.J. also acknowledges support by the Excellence Cluster ‘The Hamburg Centre for Ultrafast Imaging—Structure, Dynamics and Control of Matter at the Atomic Scale’ of the Deutsche Forschungsgemeinschaft. Current work at the University of Pittsburgh is supported by the National Science Foundation under grant no. CBET-2042918. S.D. is thankful for support from the EPSRC New Investigator Award (EP/T031255/1) and New Horizons grant (EP/V04771X/1). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We also acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work ( https://doi.org/10.5281/zenodo.22558 ). Finally, we thank the scientists and engineers at BAE Systems, Bristol for fruitful discussions and advice.

Data availability
Our Code Ocean capsule49 contains the raw output data from our MPS simulations. These data were generated using the C functions tntMpsBoxTurbulence2DTimeEvolutionRK2(...) and tntMpsBoxTurbulence3DTimeEvolutionRK2(...), using the initial conditions and parameters defined in the Set-up of numerical experiments section in the Methods. Source data for Figs. 1, 2 and 3 are available via Code Ocean49.

Funding

The work at the University of Oxford was supported by the EPSRC Programme Grant DesOEQ (EP/P009565/1), and M.K. and D.J. acknowledge financial support from the National Research Foundation, Prime Ministers Office, Singapore, and the Ministry of Education, Singapore, under the Research Centres of Excellence programme. D.J. also acknowledges support by the Excellence Cluster ‘The Hamburg Centre for Ultrafast Imaging—Structure, Dynamics and Control of Matter at the Atomic Scale’ of the Deutsche Forschungsgemeinschaft. Current work at the University of Pittsburgh is supported by the National Science Foundation under grant no. CBET-2042918. S.D. is thankful for support from the EPSRC New Investigator Award (EP/T031255/1) and New Horizons grant (EP/V04771X/1). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We also acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work ( https://doi.org/10.5281/zenodo.22558 ). Finally, we thank the scientists and engineers at BAE Systems, Bristol for fruitful discussions and advice. The work at the University of Oxford was supported by the EPSRC Programme Grant DesOEQ (EP/P009565/1), and M.K. and D.J. acknowledge financial support from the National Research Foundation, Prime Ministers Office, Singapore, and the Ministry of Education, Singapore, under the Research Centres of Excellence programme. D.J. also acknowledges support by the Excellence Cluster ?The Hamburg Centre for Ultrafast Imaging?Structure, Dynamics and Control of Matter at the Atomic Scale? of the Deutsche Forschungsgemeinschaft. Current work at the University of Pittsburgh is supported by the National Science Foundation under grant no. CBET-2042918. S.D. is thankful for support from the EPSRC New Investigator Award (EP/T031255/1) and New Horizons grant (EP/V04771X/1). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. We also acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work (https://doi.org/10.5281/zenodo.22558). Finally, we thank the scientists and engineers at BAE Systems, Bristol for fruitful discussions and advice.

ASJC Scopus subject areas

Computer Networks and Communications
Computer Science Applications
Computer Science (miscellaneous)

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10.1038/s43588-021-00181-1

2106.05782.PDFAccepted author manuscript, 9.7 MBLicence: CC BY-NC

https://arxiv.org/pdf/2106.05782.pdfLicence: CC BY

Cite this

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abstract = "Understanding turbulence is key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multiscale nature, describing the coupling between different-sized eddies in space and time. Here we analyze the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present the results for interscale correlations of two paradigmatic flow examples, and use these insights along with tensor network theory to design a structure-resolving algorithm for simulating turbulent flows. With this algorithm, we find that the incompressible Navier–Stokes equations can be accurately solved even when reducing the number of parameters required to represent the velocity field by more than one order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers.",

author = "Nikita Gourianov and Michael Lubasch and Sergey Dolgov and {van den Berg}, {Quincy Y.} and Hessam Babaee and Peyman Givi and Martin Kiffner and Dieter Jaksch",

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AU - Kiffner, Martin

AU - Jaksch, Dieter

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A quantum-inspired approach to exploit turbulence structures

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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Tensor decomposition sampling algorithms for Bayesian inverse problems

Overcoming the curse of dimensionality in dynamic programming by tensor decompositions

Cite this

A quantum-inspired approach to exploit turbulence structures

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Tensor decomposition sampling algorithms for Bayesian inverse problems

Overcoming the curse of dimensionality in dynamic programming by tensor decompositions

Cite this