Mapping surface height dynamics to subsurface flow physics in free-surface turbulent flow using a shallow recurrent decoder

2025/10/07 by Moen, Kristoffer S., Jørgen R. Aarnes, Simen Å. Ellingsen +4
Earth and Planetary Sciences · Environmental Science · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Hydrology and Sediment Transport Processes #Hydrology and Watershed Management Studies #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.2510.06202

openalex publication_date 2025/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a novel neural network algorithm known as the \em SHallow REcurrent Decoder (SHRED). The reconstruction of turbulent flow fields from limited, partial, or indirect measurements remains a grand challenge in science and engineering. The central goal in such applications is to leverage easy-to-measure proxy variables in order to estimate quantities which have not been, and perhaps cannot in practice be, measured. Specifically, in the application considered here, the aim is to use a sparse number of surface height point measurements of a flow field, or drone video footage of surface features, in order to infer the turbulent flow field beneath the surface. SHRED is a deep learning architecture that learns a delay-coordinate embedding from a few surface height (point) sensors and maps it, via a shallow decoder trained in a compressed basis, to full subsurface fields, enabling fast, robust training from minimal data. We demonstrate the SHRED sensing architecture on two types of turbulent data from recent studies (Aarnes et al. J.~Fluid Mech. 1007 A38, 2025 and Babiker et al. arXiv:251003732, 2025, respectively): fully resolved DNS data and PIV laboratory data from a turbulent water tank. SHRED is capable of robustly mapping surface height fluctuations to full-state flow fields up to about two integral length scales deep, with as few as three surface measurements.

Citations

• Simultaneous measurement of surface topography and subsurface velocity field in free-surface turbulent flow
• The relationship between surface features and sub-surface turbulence: simulations and experiments
• From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility
• Reduced order modeling with shallow recurrent decoder networks
• Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks
• Robust State Estimation from Partial Out-Core Measurements with Shallow Recurrent Decoder for Nuclear Reactors
• Vortex structures under dimples and scars in turbulent free-surface flows
• Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction
• Sensing with shallow recurrent decoder networks
• Deep Learning for Efficient Reconstruction of High-Resolution Turbulent DNS Data
• Convolutional-network models to predict wall-bounded turbulence from wall quantities
• Machine Learning for Fluid Mechanics
• Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures
• Image quality assessment: from error visibility to structural similarity

Cited by

• The relationship between surface features and sub-surface turbulence: simulations and experiments

Related

• CS-SHRED: Enhancing SHRED for Robust Recovery of Spatiotemporal Dynamics
• Reconstructing unsteady flows from sparse, noisy measurements with a physics-constrained convolutional neural network
• Sensing with shallow recurrent decoder networks
• Assessment of non-intrusive sensing in wall-bounded turbulence through explainable deep learning
• Inferring Parameters and Reconstruction of Two-Dimensional Turbulent Flows with Physics-Informed Neural Networks