Kai Fukami

This paper discusses how machine learning could support studying fluid mechanics. We first offer the so-called encoder–decoder perspective that can accommodate a range of problem settings fluid mechanicians often tackle with data-driven techniques. Focusing on nonlinear machine-learning analyses, representative efforts on regression, data compression, prediction and system control are introduced, following the given picture of data-driven fluid mechanics. We then provide a step-by-step guideline for studying fluid flows in a data-driven manner – (i) setting the problem up, (ii) curating the data, (iii) constructing a model, (iv) training a model, (v) assessing the machine-learned outcomes, and (vi) improving the techniques – while discussing what we fluid mechanicians should be mindful of. Importantly, each step necessitates carefully incorporating prior knowledge of flow physics to appropriately design machine-learning studies for complex fluid flows, rather than naively applying black-box techniques. We further perform a case study on data-driven compression of a turbulent wake around an aerofoil, offering example approaches for investigating three-dimensional, unsteady turbulent flows. We hope that this perspective will serve as a practical guide for designing machine-learning studies in fluid mechanics.

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 [Formula: see text], we reveal that the first in-plane mode dominates before impingement, while the second mode gains energy postimpingement, 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 restabilization. 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.

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, characterising 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 aerofoil 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 modelling and control for a range of unsteady 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 flowfield 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 poststall 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 a 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.

Superspreading wetting is traditionally attributed to surfactant-driven mechanisms. However, recent observations of superspreading in surfactant-free nanofluids defy standard theoretical explanations. This study considers a data-driven approach to model droplet dynamics with the thickness of liquid films on the nanometer-micrometer scale in a compact form of a partial differential equation. We examine spatiotemporal film-thickness profiles resolved at the nanometer scale via phase-shifting imaging ellipsometry. For a pure solvent, the present governing equation recovers the classical lubrication physics driven by disjoining pressure and evaporation. In contrast, the nanofluid dynamics necessitates a unique transport term scaling with the gradient of the inverse film thickness. Theoretical 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 unravel complex wetting dynamics.

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Extending the phase autoencoder [Yawata et al., Chaos 34, 063111 (2024)1054-150010.1063/5.0205718] for low-dimensional oscillators, we develop a framework to 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.

We analyze interactions between turbulent airfoil wake and an extremely strong gust 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. We derive closed-form evolution equations for these time-varying components and advance them over time, requiring only a small rolling window and avoiding full-history storage. Applied to extreme vortex gust-airfoil interaction at Re=5000, we examine how in-plane modes and their associated energy level evolve across gust conditions of varying intensity and size. Before impingement, the first in-plane mode dominates; after impingement, the second mode gains energy_amplified by stronger/larger gusts. A larger leading-mode energy gap implies coherent structure and faster recovery; a smaller gap with slower decay indicates richer multiscale activity and delayed re-stabilization. These trends follow the transient lift dynamics as well, with higher amplitude and more oscillations indicated by a rise in the leading singular values. This work provides an interpretable, time-varying data-driven modal analysis of extreme gust encounter.