Machine-Learning Based Flow Field Estimation Using Floating Sensor Locations - A Preprint

Aug 3, 2026

Machine-learning-based flow field estimation method uses only floating sensor locations. The approach removes the need for ground-truth velocity fields and avoids requiring governing equations for fluid motion. The model generates velocity fields whose time variation is consistent with the observed sensor trajectories. Validation examines estimation accuracy, sensor count dependence, time intervals in location data, and robustness to noise across three two-dimensional flow cases: flow around a circular cylinder, forced homogeneous isotropic turbulence, and ocean currents.

LanguageEnglish

CategoryResearch & Report

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Pages14

Reading Time35 min

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Abstract

Method overview

Validation settings and cases

MACHINE-LEARNING BASED FLOW FIELD ESTIMATION USING FLOATING SENSOR LOCATIONS A PREPRINT arXiv :2311 .08754v3 [physics .flu-dyn] 6 Apr 2026 Tomoya Oura Department of Mechanical Engineering Keio University Yokohama, 223-8522, Japan [oura.tomoya@keio.jp](oura.tomoya@keio.jp) Reno Miura Department of Mechanical Engineering Keio University Yokohama, 223-8522, Japan Koji Fukagata Department of Mechanical Engineering Keio University Yokohama, 223-8522, Japan April 7, 2026 ABSTRACT Based on machine learning techniques, we propose a novel method to estimate flow fields using only floating sensor locations. This method does not require either ground-truth velocity fields or governing equations for fluid flows, which is attractive for practical applications. The machine learning model is supposed to generate accurate velocity fields so that the time variation of sensor motion is consistent with the given data of sensor locations. To validate the method, the estimation accuracy, the dependence on the number of sensors, the time intervals for the sensor location data, and the robustness to noise are investigated using three examples of two-dimensional flows: the flow around a circular cylinder, the forced homogeneous isotropic turbulence, and the ocean currents. These investigations demonstrate the performance and practicality of this method, revealing that the accuracy can be comparable to the state-of-the-art physics-informed neural networks (PINNs) -based method even without any assumption of governing equations. Moreover, we observe that the present method can estimate the major structures, such as periodic wakes behind a cylinder, coherent structures in the forced turbulence, and stable ocean currents, with only a few sensors. We believe the present method can provide effective utilization of floating sensor observations in various fields. Keywords machine learning · flow field estimation · isotropic turbulence · ocean circulatione 1 Introduction Estimation of turbulent flow fields is an essential issue, particularly in the context of environmental problems these days. For instance, accurate observations of near-surface ocean currents are important for understanding the climate of the earth. To measure flow fields, several projects using floating buoys, called drifters, are globally conducted in oceanography Wong et al. [2020], Hansen and Poulain [1996] . Because fluid dynamics are nonlinear phenomena, conventional linear methods, such as the linear interpolation and the proper orthogonal decomposition Mokhasi et al.[2009], Podvin et al. [2018], have potential drawbacks in the accuracy of the estimation. Thus, effective methods to utilize the sparse sensor measurements are desired. One such method is data assimilation, which is the process of integrating measurement data into numerical simulations. In data assimilation, model equations cover the nonlinearity, whereas the observations assist the accuracy of model predictions. Using this method, the global ocean state has been estimated with an ocean general circulation model as the nonlinear model equations Wunsch and Heimbach [2007] . Other studies are also conducted for the river state Figure 1: The schematic drawing of the present method. estimation with two-dimensional shallow water equations and floating sensor measurements Tossavainen et al. [2008], Tinka et al. [2013] . The limitation of this method is that the estimation requires an assumption of governing equations for fluid flows. Another candidate is using machine learning (ML) techniques. Because ML contains nonlinearity as activation functions, it has the ability to handle the nonlinear fluid flow phenomena. Using ML, several studies Callaham et al. [2019], Erichson et al. [2020] have been conducted to estimate two-dimensional flow fields from sparse sensor measurements for various targets, such as the flow around a circular cylinder, mixing layer, sea surface temperature, forced

FAQs

What input data does the proposed method require for flow field estimation?

It uses only the sequential positions of floating sensors. No ground-truth velocity fields are required.

Does the method depend on fluid governing equations?

No. The method is designed to work without assuming governing equations for fluid flows.

How is the method validated in the paper?

The study evaluates accuracy, sensor-number dependence, time-interval effects, and noise robustness using three two-dimensional flows: a circular cylinder wake, forced homogeneous isotropic turbulence, and ocean currents.

Aug 3, 2026

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