Multiscale systems are difficult to simulate because predictive fidelity often depends on unresolved small-scale dynamics even when the dominant large-scale evolution is already available. We propose a spectral physics-informed neural network (Spectral PINN) approach in which the resolved large-scale trajectory is supplied as input and only the unresolved correction is reconstructed in coefficient space. This formulation makes the resolved/unresolved decomposition explicit and allows spatial operators to be enforced directly in spectral coordinates, so that the physics-informed loss acts on the target unresolved modes while alleviating the spectral-bias difficulty encountered when standard PINNs are trained on the full field in physical space. We assess the approach on the one-dimensional Kuramoto-Sivashinsky equation and the two-and three-dimensional Navier-Stokes equations. Across these benchmarks, the method accurately recovers the unresolved-scale dynamics and remains effective even when the unresolved state is high dimensional. Additional studies on decomposition sensitivity, proper orthogonal decomposition (POD) coordinates, a finite-interval modified KS benchmark with homogeneous Dirichlet and Neumann boundary conditions, noisy resolved inputs, and uncertain unresolved initial conditions further clarify the method's operating regime, basis dependence, and practical scope. Overall, the results show that learning only the unresolved component provides an effective and physically structured route to unresolved-scale closure in multiscale dynamics, and points to a promising direction for data-assisted multiscale simulation in which coarse large-scale descriptions are coupled with learned small-scale closure.

Predicting and understanding the chaotic dynamics in complex systems is essential in various applications. However, conventional approaches, whether full-scale simulations or small-scale omissions, fail to offer a comprehensive solution. This instigates exploration into whether modeling or omitting small-scale dynamics could benefit from the well-captured large-scale dynamics. In this paper, we introduce a novel methodology called Neural Downscaling (ND), which integrates neural operator techniques with the principles of inertial manifold and nonlinear Galerkin theory. ND effectively infers small-scale dynamics within a complementary subspace from corresponding large-scale dynamics well-represented in a low-dimensional space. The effectiveness and generalization of the method are demonstrated on the complex systems governed by the Kuramoto-Sivashinsky and Navier-Stokes equations. As the first comprehensive deterministic model targeting small-scale dynamics, ND sheds light on the intricate spatiotemporal nonlinear dynamics of complex systems, revealing how small-scale dynamics are intricately linked with and influenced by large-scale dynamics.

This study investigates the extreme wall shear stress events in a turbulent pipe flow by direct numerical simulation at a frictional Reynolds number Reτ≈500. A two-step conditional averaging scheme is implemented to identify the locations of extreme events and construct their spatial structures. Combined with the joint probability density functions of shear stresses, further evidence is provided for the argument that extreme positive events occur below an intense sweep event (Q4), and the formation of the backflow events is predominantly aided by an identifiable oblique vortex. Moreover, the conditional probability distribution of shear stress for varying thresholds used to define extreme events reveals that, when the threshold is above or below the mean, the probability distributions of the extreme positive events or the backflow events generally follow an exponential relationship, suggesting the extreme wall shear stress events are a threshold-independent process. Finally, the conditional space–time proper orthogonal decomposition is performed to extract the dominant modes and characterize the evolution of the extreme events from inception to dissipation, which exhibits morphological features of real flow structures. It is found that the observation of uθ modes can provide a basic representation of the entire variation process and the extreme values return to normal levels in a very short time.

Multiscale phenomena manifest across various scientific domains, presenting a ubiquitous challenge in accurately and effectively simulating multiscale dynamics in complex systems. In this paper, a novel decoupling solving paradigm is proposed through modelling large-scale dynamics independently and treating small-scale dynamics as a slaved system. A Spectral Physics-informed Neural Network (PINN) is developed to characterize the small-scale system in an efficient and accurate way, addressing the challenges posed by the representation of multiscale dynamics in neural networks. The effectiveness of the method is demonstrated through extensive numerical experiments, including one-dimensional Kuramot-Sivashinsky equation, two- and three-dimensional Navier-Stokes equations, showcasing its versatility in addressing problems of fluid dynamics. Furthermore, we also delve into the application of the proposed approach to more complex problems, including non-uniform meshes, complex geometries, large-scale data with noise, and high-dimensional small-scale dynamics. The discussions about these scenarios contribute to a comprehensive understanding of the method's capabilities and limitations. By enabling the acquisition of large-scale data with minimal computational demands, coupled with the efficient and accurate characterization of small-scale dynamics via Spectral PINN, our approach offers a valuable and promising approach for researchers seeking to tackle multiscale phenomena effectively.

Gravitational effects on premixed flame propagation, coupled with Darrieus–Landau instability, are investigated through direct numerical simulations under both thermal-diffusive (TD) stable and unstable situations. During the early stage of propagation, the dispersion relation between the linear growth rate σ and wavenumber k of perturbations exhibits good symmetry, allowing it to be well-fitted by the polynomial σ=c+ak−bk2. The modified Clavin–Garcia relation derived from asymptotic analysis aligns with numerical results only in the low-wavenumber region, since the significant error in the second-order coefficient bg renders it inapplicable for the high-wavenumber region. In the nonlinear regime, three morphological effects of gravity on the flame propagation have been identified: flattening the flame front, suppressing the cusp fusion rate, and promoting the new cusp generation (front splitting). The first two effects slow down the flame propagation, respectively, by reducing the overall flame front length and delaying the appearance of velocity peaks. Nevertheless, the promotion of front splitting accelerates the flame by facilitating more frequent velocity peaks arising from both cusp generation and fusion events. These various morphological effects, along with their distinct impacts on either accelerating or decelerating the flame propagation, result in significant variations in the behavior of large-scale flame propagation under different gravitational levels, despite gravity being a large-scale stabilizing effect.

This study conducts a comprehensive analysis of the coherent structures within a spatially developing underexpanded axisymmetric jet at a Reynolds number of 45 000, utilizing high-fidelity implicit large eddy simulations (iLES) in conjunction with spectral proper orthogonal decomposition (SPOD). In the frequency-wavenumber space, the global SPOD analysis identifies three distinct coherent structures, corresponding to three different mechanisms, namely, Kelvin-Helmholtz (KH), Orr, and lift-up. Their salient characteristics are discussed in detail. Local SPOD analysis further explores the streamwise evolution of these coherent structures, revealing that the influence of KH mechanism is confined to the near field, while the lift-up mechanism persists and dominates the energy content beyond the potential core, with the streaks of azimuthal wavenumbers one and two being the most energetic. The reconstruction of turbulent kinetic energy (TKE) and Reynolds shear stress from SPOD modes is assessed, and the first few azimuthal modes with low wavenumbers and frequencies are found crucial for capturing the dominant features of the flow. It is found that only the m = 0 and m = 1 modes contribute to the TKE at the centerline. The Reynolds shear stress reconstruction quality is comparable to TKE, but with a negligible contribution from the m = 0 mode. The azimuthal mode m = 1 captures the slope of the actual Reynolds shear stress profile in the vicinity of centerline, while m = 2 and higher modes capture the peak location of the actual profile.

This paper presents a numerical study on the flow around two tandem circular cylinders beneath a free surface at a Reynolds number of $180$ . The free-surface effects on the wake dynamics and hydrodynamic forces are investigated through a parametric study, covering a parameter space of gap ratios from $0.20$ to $2.00$ , spacing ratios from $1.50$ to $4.00$ and Froude numbers from $0.2$ to $0.8$ . A jet-like flow accompanied by a shear layer of positive vorticity separating from the free surface is formed in the wake at small gap ratios, which significantly alters the wake pattern through its dynamic behaviours. At shallow submergence depths, the three-dimensional wake transitions from mode B to mode A as the distance between the cylinders increases. As submergence depth increases, the wavy deformation of the primary vortex cores disappears in the wake, and the flow transitions to a two-dimensional state. Higher Froude numbers can extend the effect of the free surface to deeper submergence depths. The critical spacing ratio tends to be larger at higher Froude numbers. Furthermore, the free-surface deformation is examined. The free-surface profile typically comprises a hydraulic jump immediately ahead of the upstream cylinder, trapped waves in the vicinity of the two tandem cylinders and well-defined travelling waves on the downstream side. The frequencies of the waves cluster around the vortex shedding frequency, indicating a close association between the generation of waves and the vortex shedding process.

Multiscale phenomena manifest across various scientific domains, presenting a ubiquitous challenge in accurately and effectively predicting multiscale dynamics in complex systems. In this paper, a novel decoupling solving mode is proposed through modelling large-scale dynamics independently and treating small-scale dynamics as a slaved system. A Spectral Physics-informed Neural Network (PINN) is developed to characterize the small-scale system in an efficient and accurate way. The effectiveness of the method is demonstrated through extensive numerical experiments, including one-dimensional Kuramot-Sivashinsky equation, two- and three-dimensional Navier-Stokes equations, showcasing its versatility in addressing problems of fluid dynamics. Furthermore, we also delve into the application of the proposed approach to more complex problems, including non-uniform meshes, complex geometries, large-scale data with noise, and high-dimensional small-scale dynamics. The discussions about these scenarios contribute to a comprehensive understanding of the method's capabilities and limitations. This paper presents a valuable and promising approach to enhance the computational simulations of multiscale spatiotemporal systems, which enables the acquisition of large-scale data with minimal computational demands, followed by Spectral PINN to capture small-scale dynamics with improved efficiency and accuracy.

To improve the performance of low-speed large-torque direct drive systems in limited space, an axial field flux-switching composite machine (AFFSCM) is proposed in this paper. The AFFSCM is composed of an axial field flux-switching permanent magnet machine (AFFSPMM) and magnetic gear. Therefore, it has the advantages of a compact structure, a large power/torque density, and a wide speed regulation range. First, the topology and magnetic modulation mechanism of the AFFSCM are investigated in detail. Then, the harmonic components of the inner/outer air-gap flux density are analyzed before and after the regulation of the rotary magnetic modulation ring. Based on this, the coupling conditions of the inner/outer air-gap magnetic field are deduced. Then the AFFSCM is initially designed, a three-dimensional finite-element model of the AFFSCM is built, and the electromagnetic performances are analyzed by the finite-element method, including the flux density of the inner/outer air-gap, the speed, the static torque, etc. Next, the cogging torque of the AFFSPMM is analyzed and optimized based on the magnetic modulation mechanism to suppress the torque ripple of the AFFSCM. Finally, an 800 W prototype is constructed and related experiments are done to validate the AFFSCM.

Using the random forest (RF) algorithm, this study presented a key parameter to characterize the mean wake of H-rotor VAWTs while modelling the wake. First, the RF algorithm was used to establish the regression relationship between the average wake velocity distribution and the rotor features. Next, the feature crosses method was combined with the RF algorithm to analyze the interaction and importance of the inputs. It was found that the normalized importance of a synthetic feature in wake modelling occupied a considerable significance, reaching 0.884 out of 1. The RF wake model with this parameter as the only input feature could successfully reconstruct the wake. It was found that this feature may reflect the ability of incident wind passing through the operating rotor and played a decisive role in the wake velocity distribution, including initial velocity deficit and wake recovery rate. The universality of this parameter was proved through cases analysis of wind turbines under different sizes and operating conditions. The study of the wake field is important for the modelling of the H-rotor VAWT wake field, and hence affects the optimal configuration of the wind farm.

This paper presents two-dimensional unsteady Reynolds-Averaged-Navier–Stokes simulations of flow past a circular cylinder beneath a free surface at a Reynolds number of 4.96×104. The effects of the free surface on the wake dynamics and hydrodynamics are systematically examined over a parameter space consisting of the Froude number (0.2–0.8) and the gap ratio (0.1–2.0). For high Froude numbers, it is easier to agitate the water to produce violent surface distortion compared to low Froude numbers. Three surface deformation patterns are identified and the underlying mechanisms are proposed. The wake type transition from the wake featured a jet flow, to the one-sided vortex shedding, to the free-surface modulated Kármán vortex shedding, and to the pure Kármán vortex shedding is discussed in detail. The strength hierarchy between the three shear layers present in the wake plays a decisive role in the transition of the wake types. An extra recirculation zone appears near the free surface due to the blocking effect of the front blunt body. The proximity to the free surface exerts a modulation effect on the temporal and spectral characteristics of hydrodynamics. Relatively large mean drag force with substantial fluctuations can be induced when (unilateral or bilateral) vortex shedding process occurs. When a jet dominates the wake, the mean drag force stays at a low level and the hydrodynamic fluctuations are suppressed. The circular cylinder is always subjected to a downward thrust which increases as the cylinder approaches the free surface. The critical range of parameter combinations is provided when the wake dynamics and hydrodynamics are not influenced by the free surface.

In this paper, a dedicated recursive least squares algorithm combining forgetting and weighted factors (FW-RLS) is proposed to identify parameters for the second-order K-T equation of marine robot in horizontal motion. First, the Abkowitz model in horizontal motion is converted into an equivalent second-order K-T equation to reduce the number of identification parameters. Second, a dedicated FW-RLS algorithm based on the equivalent second-order K-T equation is proposed. Finally, the superiority of the FW-RLS algorithm is verified by comparative numerical simulations, which show the FW-RLS algorithm has the online identification capability, higher identification accuracy, and faster convergence rate compared with the traditional batch least squares method.

We show an adaptive deep-learning algorithm that recovers the distorted broadband signals of defective microwave photonic (MWP) receiving systems. With data-driven supervised training, the adopted neural network automatically learns the end-to-end distortion effects of the photonic analog links and recovers the received signals in the digital domain. Through changing the training data sets and retraining the same neural network, this algorithm can be applied in various MWP receiving systems. Two MWP receiving systems are set up for experimentally demonstrating the capability of broadband signal recovery. Results show that the neural network can reduce the signal distortion (measured with mean square error) by ∼ 18 d B . Moreover, visualization analysis indicates that the proposed algorithm is potentially adaptive to more MWP receiving systems and applications. The noise robustness of this algorithm is also verified so that it is applicable in noisy situations. The proposed algorithm improves the performance of MWP receiving systems through appending a deep learning digital processor whose deployment is low cost.

This paper identifies and characterizes modes of the three-dimensional instability of the flow over a circular cylinder of diameter D near a plane moving wall with a gap height of G=0.1D beyond the onset of vortex shedding through the Floquet stability analysis. The associated effects of the transitions on the hydrodynamic forces of the cylinder are examined by performing direct numerical simulations. Six distinct three-dimensional modes are identified and their characteristics are discussed in detail. It is found that the physical mechanism responsible for the synchronous mode 1 appears to be associated to an elliptic instability. The quasi-periodic mode 4 is observed to transform to a synchronous mode (mode 6) on increasing the Reynolds number, indicating that they are likely to be resulted from the same physical mechanism. For mode 6, its physical nature seems to be a hyperbolic instability. Fully three-dimensional simulations show that the wake undergoes a rapid transition to complex chaotic flow state after the most dominant mode starts to saturate, due to the strongly nonlinear interactions of many modes with different spanwise wavelengths.

Three-dimensional large-eddy simulations are carried out for flow past a cylinder beneath a deformable free surface at a fixed Reynolds number of Re = 7550. The results are examined for two Froude numbers of Fr=0.2 and 0.6 and a gap ratio of 0.4, to investigate the effects of the distortion of the free surface on the flow fields and hydrodynamics. At the low Froude number of Fr=0.2, the deformation of the free surface is small with little influence on the wake characteristics, and an alternative vortex shedding modulated by the free surface is detected in the wake. As the Froude number increases to 0.6, intense interface distortion occurs, which can be divided into three different regions: a hydraulic jump in the region of overtopping, a well-defined long-wavelength wave generation region in the large-scale recirculation zone near the free surface, and a water level recovery slope further downstream. The sudden change in flow regime from locally supercritical to subcritical allows the occurrence of the hydraulic jump. The induced surface waves behind the cylinder are ascribed to the shedding process of three shear layers, two of which are separated from the cylinder surface and one from the free surface. In addition, a jet-like flow originated from the gap between the free surface and the top of the cylinder occurs, exerting a downward thrust on the cylinder and pushing the wake away from the free surface. The Kármán vortex shedding in the wake is suppressed due to the interruption of the jet-like flow. The fluctuations of the wake turbulence and hydrodynamic forces are also suppressed to a low level.

We demonstrate a photonic architecture to enable the separation of ultra-wideband signals. The architecture consists of a channel-interleaved photonic analog-to-digital converter (PADC) and a dilated fully convolutional network (DFCN). The aim of the PADC is to perform ultra-wideband signal acquisition, which introduces the mixing of signals between different frequency bands. To alleviate the interference among wideband signals, the DFCN is applied to reconstruct the waveform of the target signal from the ultra-wideband mixed signals in the time domain. The channel-interleaved PADC provides a wide spectrum reception capability. Relying on the DFCN reconstruction algorithm, the ultra-wideband signals, which are originally mixed up, are effectively separated. Additionally, experimental results show that the DFCN reconstruction algorithm improves the average bit error rate by nearly three orders of magnitude compared with that without the algorithm.

Parallel processing technology has been a primary tool for achieving high-speed, high-accuracy, and broadband processing for many years across modern information systems and data processing such as optical and radar, synthetic aperture radar imaging, digital beam forming, and digital filtering systems. However, hardware deviations in a parallel processing system (PPS) severely degrade system performance and pose an urgent challenge. We propose a hardware-irrelevant PPS of which the performance is unaffected by hardware deviations. In this system, an embedded convolutional recurrent autoencoder (CRAE), which learns inherent system patterns as well as acquires and removes adverse effects brought by hardware deviations, is adopted. We implement a hardware-irrelevant PPS into a parallel photonic sampling system to accomplish a high-performance analog-to-digital conversion for microwave signals with high frequency and broad bandwidth. Under one system state, a category of signals with two different mismatch degrees is utilized to train the CRAE, which can then compensate for mismatches in various categories of signals with multiple mismatch degrees under random system states. Our approach is extensively applicable to achieving hardware-irrelevant PPSs which are either discrete or integrated in photonic, electric, and other fields.

The three-dimensional characteristics of the flow past four square cylinders in an in-line square configuration, with five spacing ratios ranging from 1.4 to 5, were studied in depth in this study. Direct numerical simulation of the spectral/hp element method was employed at Re = 150 and 200. The onset and evolution of various unstable modes were expounded in detail by means of three-dimensional vortices, energy curves, wake patterns, and force coefficients. At each spacing, the three-dimensional instability and the corresponding flow pattern were comprehensively analyzed to illustrate transitional features. Except for the existence of unstable mode A and mode B when spacing was considerably small and large, for most of the intermediate spacing ratios, the vortex structures were dominated by mode C instability, whose flow patterns all appeared as anti-phase synchronization. Through the evolution of flow patterns over time, the three-dimensional effects were already observed at a low Reynolds number of 150 because of the influence of the gap flow and the mutual interference of the wake. Under the transitional spacing for Re = 200, multiple modes were interfering fiercely with each other and appeared as chaotic states. Compared with other bluff body forms, the four square cylinders generated numerous discrepancies and new modal transitions in three-dimensional cases.

Two-dimensional high-order spectral/hp computations are carried out for a cylinder undergoing a sinusoidal rotary oscillation about its own axis. Results are examined for Re=200 and a fixed oscillation amplitude of θ0=π. The study concentrates on a domain of forcing frequencies ranging from 0 to 5f0, with f0 being the natural shedding frequency of the fixed cylinder. The drag of the cylinder is measured to reduce by up to 22% at the optimal frequency. This drag reduction is expected to result from the appearance of negative pressure in the windward regions of cylinder surface. Proper orthogonal decomposition (POD) is then utilized to extract the energetic modes that govern the dynamics of the flow. A novel force decomposition technique proposed by Miyanawala and Jaiman (2019) is reformulated, to allow quantification of the time-dependent contribution from each mode to the pressure drag. Such contribution is found to be affected, in a manner, by the forcing frequency. POD is further used to characterize the spatially evolving nature of the forced wake as it undergoes a transition from the near-wake two-layer shedding pattern to the far-wake Kármán-like shedding pattern. It is also found that a few modes suffice to reconstruct the near-wake accurately, while more modes must be retained to ensure an accurate approximation of the far-wake.