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Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows.

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Title: Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows.
Authors: de Wit, Xander M.1,2,3 x.m.d.wit@tue.nl, Gabbana, Alessandro2,3,4, Woodward, Michael2,3, Lin, Yen Ting5, Toschi, Federico1,5, Livescu, Daniel2 livescu@lanl.gov
Source: Proceedings of the National Academy of Sciences of the United States of America. 3/31/2026, Vol. 123 Issue 13, p1-9. 9p.
Subjects: Turbulence, Particle dynamics analysis, Turbulent flow, Dynamical systems, Langevin equations, Reduced-order models, Machine learning, Computer simulation
Abstract: The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows.
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  Data: <searchLink fieldCode="AR" term="%22de+Wit%2C+Xander+M%2E%22">de Wit, Xander M.</searchLink><relatesTo>1,2,3</relatesTo><i> x.m.d.wit@tue.nl</i><br /><searchLink fieldCode="AR" term="%22Gabbana%2C+Alessandro%22">Gabbana, Alessandro</searchLink><relatesTo>2,3,4</relatesTo><br /><searchLink fieldCode="AR" term="%22Woodward%2C+Michael%22">Woodward, Michael</searchLink><relatesTo>2,3</relatesTo><br /><searchLink fieldCode="AR" term="%22Lin%2C+Yen+Ting%22">Lin, Yen Ting</searchLink><relatesTo>5</relatesTo><br /><searchLink fieldCode="AR" term="%22Toschi%2C+Federico%22">Toschi, Federico</searchLink><relatesTo>1,5</relatesTo><br /><searchLink fieldCode="AR" term="%22Livescu%2C+Daniel%22">Livescu, Daniel</searchLink><relatesTo>2</relatesTo><i> livescu@lanl.gov</i>
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  Data: <searchLink fieldCode="DE" term="%22Turbulence%22">Turbulence</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+dynamics+analysis%22">Particle dynamics analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Turbulent+flow%22">Turbulent flow</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Langevin+equations%22">Langevin equations</searchLink><br /><searchLink fieldCode="DE" term="%22Reduced-order+models%22">Reduced-order models</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink>
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  Data: The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Proceedings of the National Academy of Sciences of the United States of America is the property of National Academy of Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1073/pnas.2525390123
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        Text: English
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      – SubjectFull: Turbulence
        Type: general
      – SubjectFull: Particle dynamics analysis
        Type: general
      – SubjectFull: Turbulent flow
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      – SubjectFull: Dynamical systems
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      – SubjectFull: Langevin equations
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      – SubjectFull: Reduced-order models
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      – SubjectFull: Machine learning
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      – SubjectFull: Computer simulation
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      – TitleFull: Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows.
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              M: 03
              Text: 3/31/2026
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              Y: 2026
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