arXiv subjects

Koji Fukagata

Publications and source records attributed to Koji Fukagata.

At least 19 recordsLinked to original sources

arXiv2026

Machine-learning based flow field estimation using floating sensor locations

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.

physics.flu-dyn↗

arXiv2025

Compressing fluid flows with nonlinear machine learning: mode decomposition, latent modeling, and flow control

An autoencoder is a self-supervised machine-learning network trained to output a quantity identical to the input. Owing to its structure possessing a bottleneck with a lower dimension, an autoencoder works to achieve data compression, extracting the essence of the high-dimensional data into the resulting latent space. We review the fundamentals of flow field compression using convolutional neural network-based autoencoder (CNN-AE) and its applications to various fluid dynamics problems. We cover the structure and the working principle of CNN-AE with an example of unsteady flows while examining the theoretical similarities between linear and nonlinear compression techniques. Representative applications of CNN-AE to various flow problems, such as mode decomposition, latent modeling, and flow control, are discussed. Throughout the present review, we show how the outcomes from the nonlinear machine-learning-based compression may support modeling and understanding a range of fluid mechanics problems.

physics.flu-dyn↗

arXiv2024

Implementation of spectral methods on Ising machines: toward flow simulations on quantum annealer

We investigate the possibility and current limitations of flow computations using quantum annealers by solving a fundamental flow problem on Ising machines. As a fundamental problem, we consider the one-dimensional advection-diffusion equation. We formulate it in a form suited to Ising machines (i.e., both classical and quantum annealers), perform extensive numerical tests on a classical annealer, and finally test it on an actual quantum annealer. To make it possible to process with an Ising machine, the problem is formulated as a minimization problem of the residual of the governing equation discretized using either the spectral method or the finite difference method. The resulting system equation is then converted to the Quadratic Unconstrained Binary Optimization (QUBO) form though quantization of variables. It is found in the numerical tests using a classical annealer that the spectral method requiring smaller number of variables has a particular merit over the finite difference method because the accuracy deteriorates with the increase of the number of variables. We also found that the computational error varies depending on the condition number of the coefficient matrix. In addition, we extended it to a two-dimensional problem and confirmed its fundamental applicability. From the numerical test using a quantum annealer, however, it turns out that the computation using a quantum annealer is still challenging due largely to the structural difference from the classical annealer, which leaves a number of issues toward its practical use.

physics.flu-dyn↗

arXiv2024

Defiltering turbulent flow fields for Lagrangian particle tracking using machine learning techniques

We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical applications require an affordable grid size due to the limitation of computational resources; for instance, a large-eddy simulation reduces the number of grid points with a filtering operator. However, low resolution flow fields usually underestimate the fluctuations of particle velocity. We thus present a novel approach to defilter the fluid velocity to improve the particle motion in coarse-grid (i.e., filtered) fields. The proposed method, which is based on the machine learning techniques, intends to reconstruct the fluid velocity at a particle location. We assess this method in a priori manner using a turbulent channel flow at the friction Reynolds number ${\rm Re}_τ=$ $180$. The investigation is conducted for the filter size, $n_{\rm filter}$, of $4$, $8$, and $16$. In the case of $n_{\rm filter} = 4$, the proposed method can perfectly reconstruct the fluid velocity fluctuations. The results of $n_{\rm filter} = 8$ and $16$ also exhibit substantial improvements in the fluctuation statistics although with some underestimations. Subsequently, the particle motion computed using the present method is analyzed. The trajectories, the velocity fluctuations, and the deposition velocity of particles are reconstructed accurately. Moreover, the generalizability of the present method is also demonstrated using the fields whose computational domain is larger than that used for the training. The present findings suggest that machine learning-based velocity reconstruction will enable us precise particle tracking in coarse-grid flow fields.

physics.flu-dyn↗

arXiv2024

Flow control by a hybrid use of machine learning and control theory

Flow control has a great potential to contribute to the sustainable society through mitigation of environmental burden. However, high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws. This paper aims to propose a hybrid method (i.e., machine learning and control theory) for feedback control of fluid flows. We propose a partially nonlinear linear-system extraction autoencoder (pn-LEAE), which consists of convolutional neural networks-based autoencoder (CNN-AE) and a custom layer to extract a low-dimensional latent dynamics. This pn-LEAE basically extracts a linear dynamical system so that the modern control theory can easily be applied, but at the same time, it is designed to capture a nonlinear development of the latent dynamics. We demonstrate the effectiveness of the linear system extracted by the pn-LEAE, as well as the designed control law's effectiveness for a flow around a circular cylinder at the Reynolds number of ${\rm Re}_{D}=100$. This is the first attempt utilizing CNN-AE for linearization of fluid flows involving transient development to design a feedback control law.

physics.flu-dyn↗

arXiv2023

Reconstructing three-dimensional bluff body wake from sectional flow fields with convolutional neural networks

The recent development of high-performance computing enables us to generate spatio-temporal high-resolution data of nonlinear dynamical systems and to analyze them for a deeper understanding of their complex nature. This trend can be found in a wide range of science and engineering, which suggests that detailed investigations on efficient data handling in physical science must be required in the future. This study considers the use of convolutional neural networks (CNNs) to achieve efficient data storage and estimation of scientific big data derived from nonlinear dynamical systems. The CNN is used to reconstruct three-dimensional data from a few numbers of two-dimensional sections in a computationally friendly manner. The present model is a combination of two- and three-dimensional CNNs, which allows users to save only some of the two-dimensional sections to reconstruct the volumetric data. As examples, we consider a flow around a square cylinder at the diameter-based Reynolds number $Re_D = 300$. We demonstrate that volumetric fluid flow data can be reconstructed with the present method from as few as five sections. Furthermore, we propose a combination of the present CNN-based reconstruction with an adaptive sampling-based super-resolution analysis to augment the data compressibility. Our report can serve as a bridge toward practical data handling for not only fluid mechanics but also a broad range of physical sciences.

physics.flu-dyn↗

arXiv2023

Machine learning based dimension reduction for a stable modeling of periodic flow phenomena

In designing efficient feedback control laws for fluid flow, the modern control theory can serve as a powerful tool if the model can be represented by a linear ordinary differential equation (ODE). However, it is generally difficult to find such a linear model for strongly nonlinear and high-dimensional fluid flow phenomena. In this study, we propose an autoencoder which maps the periodic flow phenomena into a latent dynamics governed by a linear ODE, referred to as a pseudo-symplectic Linear system Extracting AutoEncoder (LEAE). In addition to the normal functionality of autoencoder, pseudo-symplectic LEAE emulates a symplectic time integration scheme so that the Hamiltonian (i.e., the pseudo-energy) of the latent variables is conserved. We demonstrate that the stability of the derived ODE is improved by considering the integration stepping forward and backward at the same time. Here, we consider the circular cylinder wake at $Re_D=100$ as a typical periodic flow phenomenon.

physics.flu-dyn↗

arXiv2023

Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows

This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction. In addition to surveying a variety of recent super-resolution applications, we provide case studies of super-resolution analysis for an example of two-dimensional decaying isotropic turbulence. We demonstrate that physics-inspired model designs enable successful reconstruction of vortical flows from spatially limited measurements. We also discuss the challenges and outlooks of machine-learning-based super-resolution analysis for fluid flow applications. The insights gained from this study can be leveraged for super-resolution analysis of numerical and experimental flow data.

physics.flu-dyn↗

arXiv2022

Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression

We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight, given training data, and a constant learning rate. Having access to this distribution, it is able to create multiple models with various combinations of sampled weights, which can be used to obtain ensemble predictions. The average of such an ensemble can be regarded as the `mean estimation', whereas its standard deviation can be used to construct `confidence intervals', which enable us to perform uncertainty quantification (UQ) with regard to the training process of neural networks. We utilize representative neural-network-based function approximation tasks for the following cases: (i) a two-dimensional circular-cylinder wake; (ii) the DayMET dataset (maximum daily temperature in North America); (iii) a three-dimensional square-cylinder wake; and (iv) urban flow, to assess the generalizability of the present idea for a wide range of complex datasets. SWAG-based UQ can be applied regardless of the network architecture, and therefore, we demonstrate the applicability of the method for two types of neural networks: (i) global field reconstruction from sparse sensors by combining convolutional neural network (CNN) and multi-layer perceptron (MLP); and (ii) far-field state estimation from sectional data with two-dimensional CNN. We find that SWAG can obtain physically-interpretable confidence-interval estimates from the perspective of model-form uncertainty. This capability supports its use for a wide range of problems in science and engineering.

physics.flu-dyn↗

arXiv2022

Robust training approach of neural networks for fluid flow state estimations

State estimation from limited sensor measurements is ubiquitously found as a common challenge in a broad range of fields including mechanics, astronomy, and geophysics. Fluid mechanics is no exception -- state estimation of fluid flows is particularly important for flow control and processing of experimental data. However, strong nonlinearities and spatio-temporal high degrees of freedom of fluid flows cause difficulties in reasonable estimations. To handle these issues, neural networks (NNs) have recently been applied to the fluid flow estimation instead of conventional linear methods. The present study focuses on the capability of NNs to various fluid flow estimation problems from a practical viewpoint regarding robust training. Three types of unsteady laminar and turbulent flows are considered for the present demonstration: 1. square cylinder wake, 2. turbulent channel flow, and 3. laminar to turbulent transitional boundary layer. We utilize a convolutional neural network (CNN) to estimate velocity fields from sectional sensor measurements. To assess the practicability of the CNN models, physical quantities required for the input and robustness against lack of sensors are investigated. We also examine the effectiveness of several considerable approaches for model training to gain more robustness against the lack of sensors. The knowledge acquired through the present study in terms of effective training approaches can be transferred towards practical machine learning in fluid flow modeling.

physics.flu-dyn↗

arXiv2022

Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

Neural networks (NNs) and linear stochastic estimation (LSE) have widely been utilized as powerful tools for fluid-flow regressions. We investigate fundamental differences between them considering two canonical fluid-flow problems: 1. the estimation of high-order proper orthogonal decomposition coefficients from low-order their counterparts for a flow around a two-dimensional cylinder, and 2. the state estimation from wall characteristics in a turbulent channel flow. In the first problem, we compare the performance of LSE to that of a multi-layer perceptron (MLP). With the channel flow example, we capitalize on a convolutional neural network (CNN) as a nonlinear model which can handle high-dimensional fluid flows. For both cases, the nonlinear NNs outperform the linear methods thanks to nonlinear activation functions. We also perform error-curve analyses regarding the estimation error and the response of weights inside models. Our analysis visualizes the robustness against noisy perturbation on the error-curve domain while revealing the fundamental difference of the covered tools for fluid-flow regressions.

physics.flu-dyn↗

arXiv2021

Generalization techniques of neural networks for fluid flow estimation

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are considered: 1. interpretability of machine-learned results, 2. bulking out of training data, and 3. generalizability of neural networks. For the interpretability, we first demonstrate two methods to observe the internal procedure of neural networks, i.e., visualization of hidden layers and application of gradient-weighted class activation mapping (Grad-CAM), applied to canonical fluid flow estimation problems -- $(1)$ drag coefficient estimation of a cylinder wake and $(2)$ velocity estimation from particle images. It is exemplified that both approaches can successfully tell us evidences of the great capability of machine learning-based estimations. We then utilize some techniques to bulk out training data for super-resolution analysis and temporal prediction for cylinder wake and NOAA sea surface temperature data to demonstrate that sufficient training of neural networks with limited amount of training data can be achieved for fluid flow problems. The generalizability of machine learning model is also discussed by accounting for the perspectives of inter/extrapolation of training data, considering super-resolution of wakes behind two parallel cylinders. We find that various flow patterns generated by complex interaction between two cylinders can be reconstructed well, even for the test configurations regarding the distance factor. The present paper can be a significant step toward practical uses of neural networks for both laminar and turbulent flow problems.

physics.flu-dyn↗

arXiv2021

Model order reduction with neural networks: Application to laminar and turbulent flows

We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of a convolutional neural network and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) $y-z$ sectional field of turbulent channel flow, in terms of a number of latent modes, a choice of nonlinear activation functions, and a number of weights contained in the AE model. We find that the AE models are sensitive against the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in fluid dynamics community.

physics.flu-dyn↗

arXiv2021

Experimental velocity data estimation for imperfect particle images using machine learning

We propose a method using supervised machine learning to estimate velocity fields from particle images having missing regions due to experimental limitations. As a first example, a velocity field around a square cylinder at Reynolds number of ${\rm Re}_D=300$ is considered. To train machine learning models, we utilize artificial particle images (APIs) as the input data, which mimic the images of the particle image velocimetry (PIV). The output data are the velocity fields, and the correct answers for them are given by a direct numerical simulation (DNS). We examine two types of the input data: APIs without missing regions (i.e., full APIs) and APIs with missing regions (lacked APIs). The missing regions in the lacked APIs are assumed following the exact experimental situation in our wind tunnel setup. The velocity fields estimated from both full and lacked APIs are in great agreement with the reference DNS data in terms of various statistical assessments. We further apply these machine learned models trained with the DNS data to experimental particle images so that their applicability to the exact experimental situation can be investigated. The velocity fields estimated by the machine learned models contain approximately 40 folds denser data than that with the conventional cross-correlation method. This finding suggests that we may be able to obtain finer and hidden structures of the flow field which cannot be resolved with the conventional cross-correlation method. We also found that even the complex flow structures are hidden due to the alignment of two square cylinders, the machine learned model is able to estimate the field in the missing region reasonably well. The present results indicate a great potential of the proposed machine learning based method as a new data reconstruction method for PIV.

physics.flu-dyn↗

arXiv2021

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso (Alasso) which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$, its transient process, and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy based modeling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyze high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

physics.flu-dyn↗

arXiv2021

Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization

We focus on a convolutional neural network (CNN), which has recently been utilized for fluid flow analyses, from the perspective on the influence of various operations inside it by considering some canonical regression problems with fluid flow data. We consider two types of CNN-based fluid flow analyses; 1. CNN metamodeling and 2. CNN autoencoder. For the first type of CNN with additional scalar inputs, which is one of the common forms of CNN for fluid flow analysis, we investigate the influence of input placements in the CNN training pipeline. As an example, estimation of force coefficients of an inclined flat plate and two side-by-side cylinders in laminar flows is considered. We find that care should be taken for the placement of additional scalar inputs depending on the problem setting and the complexity of flows that users handle. We then discuss the influence of various parameters and operations on the CNN performance, with the utilization of autoencoder (AE). A two-dimensional turbulence is considered for the demonstration of AE. The results of AE highly rely on the decaying nature. Investigation on the influence of padding operation at a convolutional layer is also performed. The zero padding shows reasonable ability compared to other methods which account for the boundary conditions assumed in the numerical data. Moreover, the effect of the dimensional reduction/extension methods inside CNN is also examined. The CNN model is robust against the difference in dimension reduction operations, while it is sensitive to the dimensional extension methods. The findings of this paper will help us better design a CNN architecture for practical fluid flow analysis

physics.flu-dyn↗

arXiv2021

Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning

Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors can be in motion and can become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that the naïve use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In the present work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations enabling the computationally tractable use of convolutional neural networks. One of the central features of the present method is its compatibility with deep-learning based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data, and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors, and thereby overcomes a major limitation with existing reconstruction methods. The presented technique opens a new pathway towards the practical use of neural networks for real-time global field estimation.

physics.flu-dyn↗

arXiv2021

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall ($\sim$ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from $x-z$ sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at ${\rm Re}_τ=180$. The virtual wall-surface velocity is prepared with the extrapolation of the DNS data near the wall. This idea enables us to give a proper wall condition to correct a velocity gradient near the wall. The estimation ability of the model from near wall information is first investigated as a priori test. The estimated velocity fields by the present CNN model are in statistical agreement with the reference DNS data. The model trained in a priori test is then combined with the LES as a posteriori test. We find that the LES can successfully be augmented using the present model at both the friction Reynolds number ${\rm Re}_τ=180$ used for training and the unseen Reynolds number ${\rm Re}_τ=360$ even when the first grid point is located at 5 wall units off the wall. We also investigate the robustness of the present model for the choice of sub-grid scale model and the possibility of transfer learning in a local domain. The observations through the paper suggest that the present model is a promising tool for recovering the accuracy of LES with a coarse grid near the wall.

physics.flu-dyn↗