Spatio-temporal Structures Research Articles

Real-Time 3-D Human Action Recognition Based on Hyperpoint Sequence

Real-time 3D human action recognition has broad industrial applications, such as surveillance, human-computer interaction, and healthcare monitoring. By relying on complex spatio-temporal local encoding, most existing point cloud sequence networks capture spatio-temporal local structures to recognize 3D human actions. To simplify the point cloud sequence modeling task, we propose a lightweight and effective point cloud sequence network referred to as SequentialPointNet for real-time 3D action recognition. Instead of capturing spatio-temporal local structures, SequentialPointNet encodes the temporal evolution of static appearances to recognize human actions. Firstly, we define a novel type of point data, Hyperpoint, to better describe the temporally changing human appearances. A theoretical foundation is provided to clarify the information equivalence property for converting point cloud sequences into Hyperpoint sequences. Secondly, the point cloud sequence modeling task is decomposed into a Hyperpoint embedding task and a Hyperpoint sequence modeling task. Specifically, for Hyperpoint embedding, the static point cloud technology is employed to convert point cloud sequences into Hyperpoint sequences, which introduces inherent frame-level parallelism; for Hyperpoint sequence modeling, a Hyperpoint-Mixer module is designed as the basic building block to learning the spatio-temporal features of human actions. Extensive experiments on three widely-used 3D action recognition datasets demonstrate that the proposed SequentialPointNet achieves competitive classification performance with up to 10X faster than existing approaches.

Study of Atmospheric Aerosol in the Baikal Mountain Basin with Shipborne and Ground-Based Lidars

The results of long-term lidar studies of the peculiarities of the vertical structure of atmospheric aerosols over Lake Baikal are presented. The paper provides an analysis of data obtained over the period from 2010 to 2022. The studies were carried out under both the background conditions and the extreme natural conditions associated with severe wildfires in Siberia. The parameters of the lidars used in regular summer expeditions to Lake Baikal are briefly described. The data analysis shows that the vertical structure of the aerosol in the lower troposphere up to 2000 m above Baikal in summer is often a stable structure of several aerosol layers tens to hundreds of meters thick. There can be no mixing of layers because the water in the lake is very cold and the aerosol does not rise to higher layers while the air is warming up during the day. The difference is shown between the spatiotemporal structures of aerosol plumes from local wildfires within the lake area and from distant sources. The Angstrom parameter and the aerosol optical depth are calculated for different atmospheric conditions: ηβ = 1.57 ± 0.16 and τ = 0.09 for background conditions; ηβ = 1.41 ± 0.07 and τ = 0.64 for the cases of the observation of smoke aerosol from distant wildfires; and ηβ = 1.05 ± 0.08 and τ = 0.25 for the cases of the observation of smoke aerosol from nearby wildfires.

Spatio-temporal structures of satellite-derived water quality indicators along the Korean South Coast

The structure of 9-year time series data for Sea Surface Temperature (SST), Chlorophyll a (Chl-a) and Total Suspended Solids (TSS), derived from the Visible Infrared Imaging Radiometer Suite (VIIRS), was examined in this study. Authors found that there exists strong seasonality among the three variables with spatial heterogeneity along the Korean South Coast (KSC). In specific, SST was in phase with Chl-a, but out of phase with TSS by six months. A strong inversed spectral power with six-month phase-lag was found between Chl-a and TSS. This could be attributed to different dynamics and environmental settings. For example, Chl-a concentration seemed to have strong positive correlation with SST indicating typical seasonality of marine biogeochemical processes such as primary production; while a strong negative correlation between TSS and SST might have been influenced by changes in physical oceanographic processes, such as stratification and monsoonal wind-driven vertical mixing. In addition, the strong east–west heterogeneity of Chl-a suggests that the marine coastal environments are predominantly governed by distinct local hydrological conditions and human activities associated with land cover and land use, while the east–west spatial pattern revealed in TSS timeseries was associated with the gradient of tidal forcings and topographical changes keeping tidally induced resuspension low eastward.

Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual receptive fields.

The property of covariance, also referred to as equivariance, means that an image operator is well-behaved under image transformations, in the sense that the result of applying the image operator to a transformed input image gives essentially a similar result as applying the same image transformation to the output of applying the image operator to the original image. This paper presents a theory of geometric covariance properties in vision, developed for a generalised Gaussian derivative model of receptive fields in the primary visual cortex and the lateral geniculate nucleus, which, in turn, enable geometric invariance properties at higher levels in the visual hierarchy. It is shown how the studied generalised Gaussian derivative model for visual receptive fields obeys true covariance properties under spatial scaling transformations, spatial affine transformations, Galilean transformations and temporal scaling transformations. These covariance properties imply that a vision system, based on image and video measurements in terms of the receptive fields according to the generalised Gaussian derivative model, can, to first order of approximation, handle the image and video deformations between multiple views of objects delimited by smooth surfaces, as well as between multiple views of spatio-temporal events, under varying relative motions between the objects and events in the world and the observer. We conclude by describing implications of the presented theory for biological vision, regarding connections between the variabilities of the shapes of biological visual receptive fields and the variabilities of spatial and spatio-temporal image structures under natural image transformations. Specifically, we formulate experimentally testable biological hypotheses as well as needs for measuring population statistics of receptive field characteristics, originating from predictions from the presented theory, concerning the extent to which the shapes of the biological receptive fields in the primary visual cortex span the variabilities of spatial and spatio-temporal image structures induced by natural image transformations, based on geometric covariance properties.

Waves traveling over a map of visual space can ignite short-term predictions of sensory input

Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate the excitability of local networks and perceptual sensitivity. The general computational role of these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the visual system with the capacity to predict complex and naturalistic inputs. We present a network model whose connections can be rapidly and efficiently trained to predict individual natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future solely from the network’s connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results suggest traveling waves may play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps.

Composing Cagean silence

In this article I model John Cage's pragmatics of silence using the mathematics of category theory with the framework of ontological logs. I use this approach in order to represent knowledge within Cage's so-called silent compositions – 4 ′ 33 ′′ , 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2), and One 3 = 4 ′ 33 ′′ (0 ′ 00 ′′ ) + . I first generate a categorical schema F and an accompanying database that describes an instance of 4 ′ 33 ′′ from its premiere in 1952 which is translated via two functors into the categorical schema Z (0 ′ 00 ′′ ) and O (One 3 ). A pushout of Z and O along F allows for the presentation of the categorical schema S and its accompanying ontological log as an enfolding of Cage's pragmatics of silence. I then introduce the score Listening to John Cage listening in order to conceptualize the category of instances S - S e t , and further utilize it to investigate the language of S through its fibre order. I conclude by reporting on persistent spatio-temporal structures of Cagean silence embodied in S as meta-work.

Various ways of using empirical orthogonal functions for climate model evaluation

Abstract. We present a framework for evaluating multi-model ensembles based on common empirical orthogonal functions (common EOFs) that emphasize salient features connected to spatio-temporal covariance structures embedded in large climate data volumes. This framework enables the extraction of the most pronounced spatial patterns of coherent variability within the joint dataset and provides a set of weights for each model in terms of the principal components which refer to exactly the same set of spatial patterns of covariance. In other words, common EOFs provide a means for extracting information from large volumes of data. Moreover, they can provide an objective basis for evaluation that can be used to accentuate ensembles more than traditional methods for evaluation, which tend to focus on individual models. Our demonstration of the capability of common EOFs reveals a statistically significant improvement of the sixth generation of the World Climate Research Programme (WCRP) Climate Model Intercomparison Project (CMIP6) simulations in comparison to the previous generation (CMIP5) in terms of their ability to reproduce the mean seasonal cycle in air surface temperature, precipitation, and mean sea level pressure over the Nordic countries. The leading common EOF principal component for annually or seasonally aggregated temperature, precipitation, and pressure statistics suggests that their simulated interannual variability is generally consistent with that seen in the ERA5 reanalysis. We also demonstrate how common EOFs can be used to analyse whether CMIP ensembles reproduce the observed historical trends over the historical period 1959–2021, and the results suggest that the trend statistics provided by both CMIP5 RCP4.5 and CMIP6 SSP245 are consistent with observed trends. An interesting finding is also that the leading common EOF principal component for annually or seasonally aggregated statistics seems to be approximately normally distributed, which is useful information about the multi-model ensemble data.

Perturbative field-theoretical analysis of three-species cyclic predator-prey models

We apply a perturbative Doi–Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-paper-Scissors (RPS) and May–Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka–Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models.

Landscape Invariants–Order Parmeters of a Dynamic System

The article considers theoretical and methodological substantiation of identifying invariants problem in nonlinear dynamic systems. Invariance in context of stable spatio-temporal structures in a landscape was proposed by V.B. Sochava in 1961. The accumulation of long-term series of landscape observations by means of multispectral imaging made it possible to identify invariants in practice. An analysis of Landsat multispectral measurements from 1987 to 2022 for the southern taiga landscape (Central Forest State Nature Biosphere Reserve) shows that invariants identified as order parameters primarily determine total aboveground vegetation biomass, the water content in vegetation and soils, and the intensity of photosynthesis, i.e. bioproduction process. The proposed scheme for analyzing time series of remote sensing data makes it possible to assess landscape cover at the time of survey with respect to invariants and to identify the main control parameters that determine changes in environmental conditions and self-development of geosystems. The assessment of vegetation and relief contribution to formation of invariants structure was made to reveal invariants physical meaning. The results showed that relief has little effect on order parameters, and vegetation cover make the greatest contribution to invariant structure formation. Since invariants make it possible to identify the most stationary states, they can be used to solve applied problems in agriculture and forestry, as well as in the assessment of various ecosystem services.

10–30-Day Subseasonal Features Associated with Multiple and Isolated Persistent Rainfall Events over South China

Abstract In this study, persistent rainfall (PR) over South China (SC) is divided into two types. One type occurs multiple times in succession [defined as multiple PR (MPR)]; another type represents isolated PR (IPR), for which no new PR occurs for 10 days after the previous PR. The spatiotemporal structures of the 10–30-day intraseasonal oscillations (ISOs) associated with the two types of PR are compared and analyzed. The results reveal that the low-level moisture and air temperature perturbations always have a leading phase relative to the anomalous precipitation. In addition, the positive low-level moisture tendency appears in the MPR ending phase, whereas that in the IPR is close to zero. This difference results in convective development after the MPR ending phase, though not after the IPR. The moisture budget shows that the difference in moisture tendency between MPR and IPR is mainly due to meridional advection, including advections by the mean meridional flow across the perturbation moisture gradient and by the perturbation meridional flow across the mean moisture gradient. For the former, the difference is attributed to the perturbation moisture gradients, while the mean moisture gradients are responsible for the difference of the latter. Furthermore, an essential cause of the difference is the influence of higher-latitude disturbances that affect the IPR more significantly than the MPR. Two associated mechanisms are proposed. One is the perturbation stacking effect, and the other is the effect of angular momentum conservation. By contrast, the low-level temperature anomalies are not the key factor causing the difference between MPR and IPR. Significance Statement The persistent rainfall over South China sometimes occurs multiple times in succession, though most are in isolation. We want to understand the structures of the related 10–30-day ISOs and then find the possible cause of why convection develops after the ending stage of the multiple persistent rainfall events but not after the isolated rainfall events. We reveal that the effect of higher-latitude disturbances is an essential factor for the development of the two types of persistent rainfall over South China, with two proposed mechanisms of the perturbation stacking effect and angular momentum conservation. This is helpful for predicting persistent rainfall over South China. Future work should examine the findings by numerical experiments with a climate model.

Quantifying connectivity between mesophotic and shallow coral larvae in Okinawa Island, Japan: a quadruple nested high-resolution modeling study

Coral bleaching has recently been occurring extensively across the world’s oceans, primarily because of high water temperatures. Mesophotic corals that inhabit depths of approximately 30–150 m are expected to survive bleaching events and reseed shallow water corals afterward. In Okinawa, Japan, mesophotic coral ecosystems have been reported to serve as a refuge for preserving the genotypic diversity of bleaching-sensitive corals. The connectivity of larval populations among different habitats is a key element that determines the area to be conserved in desirable coral ecosystems. Because coral larvae are largely transported passively by ambient oceanic currents, particularly in the horizontal direction, numerical ocean circulation models greatly help to quantify connectivity with detailed spatiotemporal network structures. The present study aimed to quantify the short-distance connectivity of shallow and mesophotic coral larvae in reef areas on the northwest coast of Okinawa Island. To this end, a quadruple nested high-resolution synoptic ocean model at a lateral spatial grid resolution of 50 m was developed, which was capable of realizing detailed coastal currents influenced by complex nearshore topography, and coupled with an offline 3-D Lagrangian particle-tracking model. After validating the developed model, short-distance horizontal coral connectivity across reef areas on the northwest coast was successfully evaluated. The alongshore lateral connectivity had apparent asymmetry caused by depth-dependent horizontal currents, whereas the larvae spawned at shallow and mesophotic depths were reachable to each other. Such across-depth larval dispersal was attributable to the mixed-layer depth in the spawning period, viz., the boreal spring, which approximately coincides with the boundary between shallow and mesophotic coral, leading to the intensive vertical exchange of virtual larvae.

A causality-based learning approach for discovering the underlying dynamics of complex systems from partial observations with stochastic parameterization

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about incorrect physics in the presence of random noise and cannot easily handle the situation with incomplete data. In this paper, a new iterative learning algorithm for complex turbulent systems with partial observations is developed that alternates between identifying model structures, recovering unobserved variables, and estimating parameters. First, a causality-based learning approach is utilized for the sparse identification of model structures, which takes into account certain physics knowledge that is pre-learned from data. It has unique advantages in coping with indirect coupling between features and is robust to stochastic noise. A practical algorithm is designed to facilitate causal inference for high-dimensional systems. Next, a systematic nonlinear stochastic parameterization is built to characterize the time evolution of the unobserved variables. Closed analytic formula via efficient nonlinear data assimilation is exploited to sample the trajectories of the unobserved variables, which are then treated as synthetic observations to advance a rapid parameter estimation. Furthermore, the localization of the state variable dependence and the physics constraints are incorporated into the learning procedure. This mitigates the curse of dimensionality and prevents the finite time blow-up issue. Numerical experiments show that the new algorithm identifies the model structure and provides suitable stochastic parameterizations for many complex nonlinear systems with chaotic dynamics, spatiotemporal multiscale structures, intermittency, and extreme events.

Trance-forming Collective Attention: How Interactions Can Support Attentional Structures. The Case of Hypnosis in Hospitals

How does a collective succeed in practicing the same kind of attention together? This is an essential question for organizations that need to develop a common focus of attention, but it is difficult to address because the objects are multiple and in competition with one another. The attention-based view (ABV) highlights the central role of organizational structures (roles, working spaces, social representation, etc.) in the formation of collective attention, whilst simultaneously acknowledging their limitations. Attention-based view thus encourages scholars to explore the complementary role of social interactions. The objective of this paper is to study precisely how interactions relate to structures in the formation of collective attention. To achieve this, we interviewed and observed professionals at a French university hospital over the course of 18 months. Using hypnosis techniques, the professionals sought to pay closer attention to patients’ psychological states. We conducted 52 interviews, studied six observation sequences, and participated in a number of meetings; from this research, we selected and analyzed 29 situations in which hypnosis was practiced. Our results show that whilst cognitive, political, spatiotemporal, and material structures can contribute to the sharing of a collective focus of attention, they are in themselves not sufficient and at times even hinder such sharing. When structures enable, which is to say, when they facilitate sharing, interactions can complete or strengthen them to compensate for their insufficiency. When structures hinder, interactions can play a correctional role. By showing that structures do not act alone but are supported by social interactions that act either alongside or upon them, our research helps to expand the ABV model and contribute to better integrating structures and interactions.

Design of an intelligent bean cultivation approach using computer vision, IoT and spatio-temporal deep learning structures

Crop health monitoring and weed removal are two crucial elements dictating efficient, productive and resilient cultivation. Due to frequent attacks by pest and pathogens, the crops become diseased resulting in degradation of the quality and quantity of the production. The process of continuous monitoring of crop health is challenging and requires the involvement of information and communication technologies (ICT). The outcome is precision agriculture where the Internet of Things (IoT) and Artificial Intelligence (AI) techniques are vital ingredients. The design of an integrated approach of precision agriculture based on IoT and AI is discussed here which is tailored for real time crop health monitoring and performs various other operations like weed detection, ambient air sensing, watering the vegetation automatically at regular intervals of time, spraying of pesticides etc. The proposed system is a combination of an IoT formed using sensors and devices, image processing and machine learning (ML)/ deep learning (DL) techniques confined to the cultivation of fifteen varieties of beans found in India. The work involves two intelligent learning models configured to capture spatio-temporal attributes of image samples and sensor inputs and for real time discrimination between healthy and diseased bean leaves, detection of weeds growing around the cultivation land and also for process control. The first approach employs a DL structure named EfficientNetB7 along with a Bidirectional Long Short Term Memory (BiLSTM) while the second method adopts a VGG16 with an integrated attention mechanism. Also experiments have been carried out using benchmark ML classifiers like Support Vector Machine (SVM), Random Forest (RF), K-Nearest Neighbor (KNN), Multi-Layer Perceptron (MLP) and Time Delay Neural Network (TDNN) combined with feature extraction techniques. Segmentation methods have been used to separate out the diseased sections of the leaves which are then used as apriori labels for the classifiers to reinforce the previously known details of the bean varieties. Subsequently, the trained networks are tested with bean leaf samples collected from cultivation farms. Results show that our proposed DL models could accurately predict the health state of the bean leaves with less computation time. With an automated approach of bean leaf health discrimination, weed detection and process control, the cost effectiveness of the overall effort is enhanced. Further, the sensor pack also provides precise thresholds at which water sprinkling could be initiated resulting in water conservation.

Bandstructure of phononic crystal of rotating heterogeneous cylinders: Time periodicity due to pure mechanical modulation

Existing designs of elastic spatiotemporal periodic structures usually require electric/piezoelectric elements that provide temporal modulation of elastic properties. While this method has advantages in many aspects, it usually allows relatively low modulation depth. Here we propose a design for spatiotemporal elastic media that is experimentally feasible, involves pure mechanical elements, and may provide any desired temporal modulation depth. In our scheme the scatterers of a phononic crystal are cylinders composed of two (or more) semi-cylinders (parts) of different materials. The cylinders are capable for rotation with high speed in a stationary fluid environment that provides time-dependent medium for propagating sound wave. Adjusting the elastic contrast between the materials of solid semi-cylinders the necessary modulation depths can be achieved. Different regimes of temporal modulation, from adiabatic to rapid oscillations can be realized by varying the frequency of rotation. We report momentum/energy gaps and other features of the bandstructure that are theoretically obtained using plane wave expansion. Nonreciprocal effects are studied for a phononic crystal with a square unit cell containing two heterogeneous cylinders rotating synchronically with a constant phase shift. [This work is supported by the NSF under EFRI Grant No. 1741677.]

Transition from chimera/solitary states to traveling waves.

We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes, such as the coexistence of a multichimera state/a traveling wave and a solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient toward a purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise.

Investigating the Linear Dynamics of the Near-Field of a Turbulent High-Speed Jet Using Dual-Particle Image Velocimetry (PIV) and Dynamic Mode Decomposition (DMD)

The quest for the physical mechanisms underlying turbulent high-speed jet flows is underpinned by the extraction of spatio-temporal coherent structures from their flow fields. Experimental measurements to enable data decomposition need to comprise time-resolved velocity fields with a high-spatial resolution—qualities which current particle image velocimetry hardware are incapable of providing. This paper demonstrates a novel approach that addresses this challenge through the implementation of an experimental high-spatial resolution dual-particle image velocimetry methodology coupled with dynamic mode decomposition. This new approach is exemplified by its application in studying the dynamics of the near-field region of a turbulent high-speed jet, enabling the spatio-temporal structure to be investigated by the identification of the spatial structure of the dominant dynamic modes and their temporal dynamics. The spatial amplification of these modes is compared with that predicted by classical linear stability theory, showing close agreement, which demonstrates the powerful capability of this technique to identify the dominant frequencies and their associated spatial structures in high-speed turbulent flows.

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Spatial patterns are a significant characteristic of lasers. The knowledge of spatial patterns of structured laser beams is rapidly expanding, along with the progress of studies on laser physics and technology. Particularly in the last decades, owing to the in-depth attention on structured light with multiple degrees of freedom, the research on spatial and spatiotemporal structures of laser beams has been promptly developed. Such beams have hatched various breakthroughs in many fields, including imaging, microscopy, metrology, communication, optical trapping, and quantum information processing. Here, we would like to provide an overview of the extensive research on several areas relevant to spatial patterns of structured laser beams, from spontaneous organization to multiple transformations. These include the early theory of beam pattern formation based on the Maxwell–Bloch equations, the recent eigenmodes superposition theory based on the time-averaged Helmholtz equations, the beam patterns extension of ultrafast lasers to the spatiotemporal beam structures, and the structural transformations in the nonlinear frequency conversion process of structured beams.

Transonic Shock Buffet Flowfield Assessment Using Various Dynamic Mode Decomposition Techniques

Dynamic mode decomposition (DMD) is a powerful data-driven modal decomposition technique that extracts spatiotemporal coherent structures: a useful process in flow diagnostics and future state estimation of complex nonlinear flow phenomena. Transonic shock buffet is a complicated phenomenon, and modal decomposition techniques such as DMD provide significant insight into its complicated flow physics; but, often, flowfield data are corrupted because of various sources of noise due to the presence of outliers or the absence of critical data components. Therefore, noise corruption renders the modal decomposition inaccurate, and thereby not useful. In this paper, two sources of noise have been considered: simple white noise, and complex salt-and-pepper-type spurious noise. Various DMD techniques including standard DMD, forward–backward DMD, total-least-squares DMD, higher-order DMD, and robust DMD have been implemented. Their effectiveness and limitations in countering noise corruption have been investigated systematically. In the case of white noise corruption, forward–backward DMD, total-least-squares DMD, and higher-order DMD capture the buffet frequency and growth rate with sufficient accuracy, whereas the latter outperforms the other two when the noise variance level is above 5%. In the case of spurious noise, robust DMD handles noise corruption efficiently, with surprisingly high values of pixel corruption of up to 30%.

Data-driven identification of coherent structures in gas–solid system using proper orthogonal decomposition and dynamic mode decomposition

Spatiotemporal coherent structures are critical in quantifying the hydrodynamics of dense gas–solid flows. In this study, two data-driven methods, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to identify and characterize the dominant spatiotemporal coherent structures in a bubbling fluidized bed. It is found that (i) with the same number of modes (or coherent structures), POD captures more defined energy than DMD; (ii) the main coherent structure of POD is symmetric and confirms the existence of bubble-emulsion two-phase structure; (iii) the coherent structures with a frequency of 0 Hz in DMD analysis can construct the mean flow field more reasonably than POD; and (iv) POD reconstructs the transient flow fields more accurately with the same number of modes. This study offers insights into the coherent structures in gas–solid systems.