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Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory.

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Title: Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory.
Authors: Wu, Hua-Lin1 (AUTHOR), Xu, Ao1,2 (AUTHOR) axu@nwpu.edu.cn, Xi, Heng-Dong1,2 (AUTHOR)
Source: Journal of Fluid Mechanics. 1/10/2026, Vol. 1026, p1-32. 32p.
Subjects: Turbulent flow, Deep learning, Artificial neural networks, Particle motion, Transformer models, Convolutional neural networks, Rayleigh-Bénard convection
Abstract: We studied the reconstruction of turbulent flow fields from trajectory data recorded by actively migrating Lagrangian agents. We propose a deep-learning model, track-to-flow (T2F), which employs a vision transformer as the encoder to capture the spatiotemporal features of a single agent trajectory, and a convolutional neural network as the decoder to reconstruct the flow field. To enhance the physical consistency of the T2F model, we further incorporate a physics-informed loss function inspired by the framework of physics-informed neural network (PINN), yielding a variant model referred to as T2F+PINN. We first evaluate both models in a laminar cylinder wake flow at a Reynolds number of $\textit{Re} = 800$ as a proof of concept. The results show that the T2F model achieves velocity reconstruction accuracy comparable to that of existing flow reconstruction methods, while the T2F+PINN model reduces the normalised error in vorticity reconstruction relative to the T2F model. We then apply the models in turbulent Rayleigh–Bénard convection at a Rayleigh number of $Ra = 10^{8}$ and a Prandtl number of $\textit{Pr} = 0.71$. The results show that the T2F model accurately reconstructs both the velocity and temperature fields, whereas the T2F+PINN model further improves the reconstruction accuracy of gradient-related physical quantities, such as temperature gradients, vorticity and the $Q$ value, with a maximum improvement of approximately 60 % compared to the T2F model. Overall, the T2F model is better suited for reconstructing primitive flow variables, while the T2F+PINN model provides advantages in reconstructing gradient-related quantities. Our models open a promising avenue for accurate flow reconstruction from a single Lagrangian trajectory. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We studied the reconstruction of turbulent flow fields from trajectory data recorded by actively migrating Lagrangian agents. We propose a deep-learning model, track-to-flow (T2F), which employs a vision transformer as the encoder to capture the spatiotemporal features of a single agent trajectory, and a convolutional neural network as the decoder to reconstruct the flow field. To enhance the physical consistency of the T2F model, we further incorporate a physics-informed loss function inspired by the framework of physics-informed neural network (PINN), yielding a variant model referred to as T2F+PINN. We first evaluate both models in a laminar cylinder wake flow at a Reynolds number of $\textit{Re} = 800$ as a proof of concept. The results show that the T2F model achieves velocity reconstruction accuracy comparable to that of existing flow reconstruction methods, while the T2F+PINN model reduces the normalised error in vorticity reconstruction relative to the T2F model. We then apply the models in turbulent Rayleigh–Bénard convection at a Rayleigh number of $Ra = 10^{8}$ and a Prandtl number of $\textit{Pr} = 0.71$. The results show that the T2F model accurately reconstructs both the velocity and temperature fields, whereas the T2F+PINN model further improves the reconstruction accuracy of gradient-related physical quantities, such as temperature gradients, vorticity and the $Q$ value, with a maximum improvement of approximately 60 % compared to the T2F model. Overall, the T2F model is better suited for reconstructing primitive flow variables, while the T2F+PINN model provides advantages in reconstructing gradient-related quantities. Our models open a promising avenue for accurate flow reconstruction from a single Lagrangian trajectory. [ABSTRACT FROM AUTHOR]
ISSN:00221120
DOI:10.1017/jfm.2025.11033