arXiv subjects

Kai Fukami

Publications and source records attributed to Kai Fukami.

At least 19 recordsLinked to original sources

arXiv2026

Extracting informative vortical structures of turbulent wake-extreme vortex gust interactions with machine learning

This study considers extracting causally important vortical structures from the extreme vortex gust-airfoil interaction at a chord-based Reynolds number of $5000$. This extraction is achieved by decomposing a given vortical flow snapshot into its informative and residual components based on the contribution to an arbitrary future target variable with convolutional information-theoretic learning. For the current vortex-airfoil interactions that exhibit transient and multiscale flow characteristics, we first examine the important vortical structures with respect to a future lift coefficient. While the vortex cores are primarily highlighted before vortex impingement, the emerging shear layers are additionally captured after the massive separation, which is evident from a comparison to an instantaneous force-element analysis. We further take the scale-dependent energy transfer as a future variable of interest to examine its impact on the extracted informative structures compared to the lift-associated structures. They are distinct from the lift-based structures in the early stage of the gust encounter yet become similar after impingement, revealing an analogy between informative structures across different transient aerodynamic mechanisms. The present data-driven approach selectively extracts the specific important flow structures responsible for the physics of interest, which can support studying a range of transient aerodynamic flows from the causal, data-driven perspective.

physics.flu-dyn↗

arXiv2026

Convolutional causal learning for aerodynamic flows

This study aims to capture aerodynamic causality from snapshot data with a time-varying mode decomposition technique referred to as information-theoretic machine learning. The current approach extracts time-dependent informative vortical structures, contributing to the future evolution of the aerodynamic coefficients. The present decomposition is employed with a convolutional neural network, enabling the identification of the spatial continuous mode. In addition, a low-order representation, characterizing the informative vortical structures and their corresponding aerodynamic coefficients, can also be identified by considering autoencoder-based data compression. The present technique is applied to a range of aerodynamic examples, including extreme vortex-gust airfoil interactions, experimentally measured transverse jet-wing interaction, and a turbulent separated wake across different Reynolds numbers. For the cases of gust-wing interaction, the time-varying gust effect on the lift response is extracted in an interpretable manner. With the example of a turbulent wake, the relationship between large-scale vortical motion and lift force is identified without any spatial length-scale information. The proposed approach could serve as a foundation for data-driven causal modeling and control for a range of unsteady flows.

physics.flu-dyn↗

arXiv2026

Data-driven modeling and decomposition for nanoscale liquid-film dynamics: Application to superspreading nanofluid droplets

Understanding ultrathin liquid-film dynamics is crucial for unraveling complex interfacial phenomena, yet deriving governing equations directly from experimental observations remains challenging. This study proposes a data-driven approach to model droplet dynamics, capturing liquid-film thickness on the nanometer scale in the form of a partial differential equation. As a challenging test case, we examine the superspreading wetting of surfactant-free nanofluids, a phenomenon whose physical mechanism defies standard theoretical explanations. We apply a sparse identification algorithm to spatiotemporal film-thickness profiles resolved at the nanometer scale using phase-shifting imaging ellipsometry. For a pure solvent, the discovered governing equation recovers classical lubrication physics driven by disjoining pressure and evaporation. In contrast, the nanofluid dynamics necessitates an additional, unique transport term scaling with the gradient of the inverse film thickness. Theoretical scaling analysis suggests this term represents a nanoparticle-induced bias flux, consistent with a hypothesized capillary wicking mechanism within the precursor film. The identification of the current nanofluid-specific term underscores the efficacy of integrating high-precision experimental measurements with data-driven modeling to discover hidden physics and generate testable hypotheses in complex wetting dynamics.

physics.flu-dyn↗

arXiv2025

Data-driven time-dependent bases for turbulent airfoil wake-extreme gust interactions

We analyze interactions between turbulent airfoil wakes and extreme gusts using a data-driven framework with time-dependent bases. The current approach represents each snapshot with time-varying bases consisting of two-dimensional in-plane modes and one-dimensional spanwise modes, together with a reduced covariance matrix. By deriving closed-form evolution equations, we advance these components using a small rolling window, eliminating the need for full-history storage. Applied to extreme vortex gust-airfoil interactions at Re=5000, we reveal that the first in-plane mode dominates before impingement, while the second mode gains energy post-impingement, amplified by gust intensity. During impingement, leading modes exhibit multiscale features such as shear-layer roll-up and fine-scale turbulence. The temporal evolution of the mode-energy spectrum and its rank gaps further quantifies these interactions. A large leading-mode gap indicates energy concentrated in a few coherent structures, leading to faster recovery, whereas a smaller gap indicates energy distributed across many modes, consistent with richer multiscale activity and delayed re-stabilization. These trends also follow the transient lift dynamics, with higher amplitude and more oscillations indicated by a rise in the leading singular values. This work may provide a foundation for time-varying data-driven modal analysis of extreme gust encounters.

physics.comp-ph↗

arXiv2025

Compact representation of transonic airfoil buffet flows with observable-augmented machine learning

Transonic buffet presents time-dependent aerodynamic characteristics associated with shock, turbulent boundary layer, and their interactions. Despite strong nonlinearities and a large degree of freedom, there exists a dominant dynamic pattern of a buffet cycle, suggesting the low dimensionality of transonic buffet phenomena. This study seeks a low-dimensional representation of transonic airfoil buffet at a high Reynolds number with machine learning. Wall-modeled large-eddy simulations of flow over the OAT15A supercritical airfoil at two Mach numbers, $M_\infty = 0.715$ and 0.730, respectively producing non-buffet and buffet conditions, at a chord-based Reynolds number of $Re = 3\times 10^6$ are performed to generate the present datasets. We find that the low-dimensional nature of transonic airfoil buffet can be extracted as a sole three-dimensional latent representation through lift-augmented autoencoder compression. The current low-order representation not only describes the shock movement but also captures the moment when the separation occurs near the trailing edge in a low-order manner. We further show that it is possible to perform sensor-based reconstruction through the present low-dimensional expression while identifying the sensitivity with respect to aerodynamic responses. The present model trained at $Re = 3\times 10^6$ is lastly evaluated at the level of a real aircraft operation of $Re = 3\times 10^7$, exhibiting that the phase dynamics of lift is reasonably estimated from sparse sensors. The current study may provide a foundation toward data-driven real-time analysis of transonic buffet conditions under aircraft operation.

physics.flu-dyn↗

arXiv2025

Machine learning in fluid dynamics: A critical assessment

The fluid dynamics community has increasingly adopted machine learning to analyze, model, predict, and control a wide range of flows. These methods offer powerful computational capabilities for regression, compression, and optimization. In some cases, machine learning has even outperformed traditional approaches. However, many fluid mechanics problems remain beyond the reach of current machine learning techniques. As the field moves from its current state toward a more mature paradigm, this article offers a critical assessment of the key challenges that must be addressed. Tackling these technical issues will not only deepen our understanding of flow physics but also expand the applicability of machine learning beyond fundamental research. We also highlight the importance of community-maintained datasets and open-source code repositories to accelerate progress in this area. Furthermore, the future success of machine learning in fluid dynamics will depend on effective training -- not only for the next generation of researchers but also for established fluid mechanicians adapting to this evolving landscape. Data-driven fluid dynamics is in its critical transitional state over the next few years to shape its future. This perspective article aims to spark discussions and encourage collaborative efforts to advance the integration of machine learning in fluid dynamics.

physics.flu-dyn↗

arXiv2025

Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Based on the phase autoencoder [Yawata {\it et al.}, Chaos {\bf 34}, 063111 (2024)], we map high-dimensional field variables of the reaction-diffusion system to low-dimensional latent variables characterizing the asymptotic phase and amplitudes of the field variables. This yields a reduced phase description of the limit cycle underlying the rhythmic spatiotemporal dynamics in a data-driven manner. We propose a method to drive the system along the tangential direction of the limit cycle, enabling phase control without inducing amplitude deviations. With examples of 1D oscillating spots and 2D spiral waves in the FitzHugh-Nagumo reaction-diffusion system, we show that the method achieves rapid synchronization in both reference-based and coupling-based settings. These results demonstrate the potential of data-driven phase description based on the phase autoencoder for synchronization of high-dimensional spatiotemporal dynamics.

nlin.AO↗

arXiv2025

Information-theoretic machine learning for time-varying mode decomposition of separated aerodynamic flows

We perform an information-theoretic mode decomposition for separated aerodynamic flows. The current data-driven approach based on a neural network referred to as deep sigmoidal flow enables the extraction of an informative component from a given flow field snapshot with respect to a target variable at a future time stamp, thereby capturing the causality as a time-varying modal structure. We consider four examples of separated flows around a wing, namely, 1. laminar periodic wake at post-stall angles of attack, strong gust-wing interactions of 2. numerical and 3. experimental measurements, and 4. a turbulent wake in a spanwise-periodic domain. The present approach reveals informative vortical structures associated with a time-varying lift response. For the periodic shedding cases, the informative structures vary in time corresponding to the fluctuation level from their mean values. With the examples of gust-wing interactions, how the effect of gust on a wing emerges in the lift response over time is identified in an interpretable manner. Furthermore, for the case of turbulent wake, the present model highlights structures near the wing and vortex cores as informative components based solely on the information metric without any prior knowledge of aerodynamics and length scales. This study provides causality-based insights into a range of unsteady aerodynamic problems.

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

Single-snapshot machine learning for super-resolution of turbulence

Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning settings. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a {\it single} snapshot of turbulent flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two examples of two-dimensional isotropic turbulence and three-dimensional turbulent channel flow. First, we reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers for two-dimensional decaying turbulence. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We also show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. Second, we perform the single-snapshot super-resolution analysis for turbulent channel flow, showing that it is possible to extract physical insights from a single flow snapshot even with inhomogeneity. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.

physics.flu-dyn↗

arXiv2024

Data-driven transient lift attenuation for extreme vortex gust-airfoil interactions

We present a data-driven feedforward control to attenuate large transient lift experienced by an airfoil disturbed by an extreme level of discrete vortex gust. The current analysis uses a nonlinear machine-learning technique to compress the high-dimensional flow dynamics onto a low-dimensional manifold. While the interaction dynamics between the airfoil and extreme vortex gust are parameterized by its size, gust ratio, and position, the wake responses are well-captured on this simple manifold. The effect of extreme vortex disturbance about the undisturbed baseline flows can be extracted in a physically-interpretable manner. Furthermore, we call on phase-amplitude reduction to model and control the complex nonlinear extreme aerodynamic flows. The present phase-amplitude reduction model reveals the sensitivity of the dynamical system in terms of the phase shift and amplitude change induced by external forcing with respect to the baseline periodic orbit. By performing the phase-amplitude analysis for a latent dynamical model identified by sparse regression, the sensitivity functions of low-dimensionalized aerodynamic flows for both phase and amplitude are derived. With the phase and amplitude sensitivity functions, optimal forcing can be determined to quickly suppress the effect of extreme vortex gusts towards the undisturbed states in a low-order space. The present optimal flow modification built upon the machine-learned low-dimensional subspace quickly alleviates the impact of transient vortex gusts for a variety of extreme aerodynamic scenarios, providing a potential foundation for flight of small-scale air vehicles in adverse atmospheric conditions.

physics.flu-dyn↗

arXiv2024

Phase autoencoder for limit-cycle oscillators

We present a phase autoencoder that encodes the asymptotic phase of a limit-cycle oscillator, a fundamental quantity characterizing its synchronization dynamics. This autoencoder is trained in such a way that its latent variables directly represent the asymptotic phase of the oscillator. The trained autoencoder can perform two functions without relying on the mathematical model of the oscillator: first, it can evaluate the asymptotic phase and phase sensitivity function of the oscillator; second, it can reconstruct the oscillator state on the limit cycle in the original space from the phase value as an input. Using several examples of limit-cycle oscillators, we demonstrate that the asymptotic phase and phase sensitivity function can be estimated only from time-series data by the trained autoencoder. We also present a simple method for globally synchronizing two oscillators as an application of the trained autoencoder.

nlin.AO↗

arXiv2024

Data-driven nonlinear turbulent flow scaling with Buckingham Pi variables

Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow structures. This study presents a data-driven approach to reveal scale-invariant vortical structures across Reynolds numbers that provide insights for supporting nonlinear machine-learning-based studies of turbulent flows. To uncover conditions for which nonlinear models are likely to perform well, we use a Buckingham Pi-based sparse nonlinear scaling to find the influence of the Pi groups on the turbulent flow data. We consider nonlinear scalings of the invariants of the velocity gradient tensor for an example of three-dimensional decaying isotropic turbulence. The present scaling not only enables the identification of vortical structures that are interpolatory and extrapolatory for the given flow field data but also captures non-equilibrium effects of the energy cascade. As a demonstration, the present findings are applied to machine-learning-based super-resolution analysis of three-dimensional isotropic turbulence. We show that machine-learning models reconstruct vortical structures well in the interpolatory space with reduced performance in the extrapolatory space revealed by the nonlinearly scaled invariants. The present approach enables us to depart from labeling turbulent flow data with a single parameter of Reynolds number and comprehensively examine the flow field to support training and testing of nonlinear machine-learning techniques.

physics.flu-dyn↗

arXiv2023

Grasping Extreme Aerodynamics on a Low-Dimensional Manifold

Modern air vehicles perform a wide range of operations, including transportation, defense, surveillance, and rescue. These aircraft can fly in calm conditions but avoid operations in gusty environments, encountered in urban canyons, over mountainous terrains, and in ship wakes. With extreme weather becoming ever more frequent due to global warming, it is anticipated that aircraft, especially those that are smaller in size, will encounter sizeable atmospheric disturbances and still be expected to achieve stable flight. However, there exists virtually no theoretical fluid-dynamic foundation to describe the influence of extreme vortical gusts on wings. To compound this difficulty, there is a large parameter space for gust-wing interactions. While such interactions are seemingly complex and different for each combination of gust parameters, we show that the fundamental physics behind extreme aerodynamics is far simpler and lower-rank than traditionally expected. We reveal that the nonlinear vortical flow field over time and parameter space can be compressed to only three variables with a lift-augmented autoencoder while holding the essence of the original high-dimensional physics. Extreme aerodynamic flows can be compressed through machine learning into a low-dimensional manifold, which can enable real-time sparse reconstruction, dynamical modeling, and control of extremely unsteady gusty flows. The present findings offer support for the stable flight of next-generation small air vehicles in atmosphere conditions traditionally considered unflyable.

physics.flu-dyn↗

arXiv2023

A cyclic perspective on transient gust encounters through the lens of persistent homology

Large amplitude gust encounters exhibit a range of separated flow phenomena, making them difficult to characterize using the traditional tools of aerodynamics. In this work, we propose a dynamical systems approach to gust encounters, viewing the flow as a cycle (or a closed trajectory) in state space. We posit that the topology of this cycle, or its shape and structure, provides a compact description of the flow, and can be used to identify coordinates in which the dynamics evolve in a simple, intuitive way. To demonstrate this idea, we consider flowfield measurements of a transverse gust encounter. For each case in the dataset, we characterize the full-state dynamics of the flow using persistent homology, a tool that identifies holes in point cloud data, and transform the dynamics to a reduced-order space using a nonlinear autoencoder. Critically, we constrain the autoencoder such that it preserves topologically relevant features of the original dynamics, or those features identified by persistent homology. Using this approach, we are able to transform six separate gust encounters to a three-dimensional latent space, in which each gust encounter reduces to a simple circle, and from which the original flow can be reconstructed. This result shows that topology can guide the creation of low-dimensional state representations for strong transverse gust encounters, a crucial step toward the modeling and control of airfoil-gust interactions.

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↗

arXiv2023

Sparse sensor reconstruction of vortex-impinged airfoil wake with machine learning

Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex-airfoil wake interaction using only a limited amount of training data. The present machine learning models accurately reconstruct the aerodynamic force coefficients, pressure distributions over airfoil surface, and two-dimensional vorticity field for a variety of untrained cases. Multi-layer perceptron is used for estimating aerodynamic forces and pressure profiles over the surface, establishing a nonlinear model between the pressure sensor measurements and the output variables. A combination of multi-layer perceptron with convolutional neural network is utilized to reconstruct the vortical wake. Furthermore, the use of transfer learning and long short-term memory algorithm combined in the training models greatly improves the reconstruction of transient wakes by embedding the dynamics. The present machine-learning methods are able to estimate the transient flow features while exhibiting robustness against noisy sensor measurements. Finally, appropriate sensor locations over different time periods are assessed for accurately estimating the wakes. The present study offers insights into the dynamics of vortex-airfoil interaction and the development of data-driven flow estimation.

physics.flu-dyn↗

arXiv2023

Image and video compression of fluid flow data

We study the compression of spatial and temporal features in fluid flow data using multimedia compression techniques. The efficacy of spatial compression techniques, including JPEG and JPEG2000 (JP2), and spatio-temporal video compression techniques, namely H.264, H.265, and AV1, in limiting the introduction of compression artifacts and preserving underlying flow physics are considered for laminar periodic wake around a cylinder, two-dimensional turbulence, and turbulent channel flow. These compression techniques significantly compress flow data while maintaining dominant flow features with negligible error. AV1 and H.265 compressions present the best performance across a variety of canonical flow regimes and outperform traditional techniques such as proper orthogonal decomposition in some cases. These image and video compression algorithms are flexible, scalable, and generalizable holding potential for a wide range of applications in fluid dynamics in the context of data storage and transfer.

physics.flu-dyn↗