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It is generally accepted that the evolution of deep-water surface gravity wave spectrum is governed by quartet resonant and quasi-resonant interactions. However, it has also been reported in both experimental and computational studies that non-resonant triad interactions can play a role, e.g., generation of bound waves. In this study, we investigate the effects of triad and quartet interactions on the spectral evolution, by numerically tracking the contributions from quadratic and cubic terms in the dynamical equation. In a finite time interval, we find that the contribution from triad interactions follows the trend of that from quartet resonances (with comparable magnitude) for most wavenumbers, except that it peaks at low wavenumbers with very low initial energy. This result reveals two effects of triad interactions: (1) the non-resonant triad interactions can be connected to form quartet resonant interactions (hence exhibiting the comparable trend), which is a reflection of the normal form transformation applied in wave turbulence theory of surface gravity waves. (2) the triad interactions can fill energy into the low energy portion of the spectrum (low wavenumber part in this case) on a very fast time scale, with energy distributed in both bound and free modes at the same wavenumber. We further analyze the latter mechanism using a simple model with two initially active modes in the wavenumber domain. Analytical formulae are provided to describe the distribution of energy in free and bound modes with numerical validations.

Diffusion models have emerged as a powerful generative technology and have been found to be applicable in various scenarios. Most existing foundational diffusion models are primarily designed for text-guided visual generation and do not support multi-modal conditions, which are essential for many visual editing tasks. This limitation prevents these foundational diffusion models from serving as a unified model in the field of visual generation, like GPT-4 in the natural language processing field. In this work, we propose ACE, an All-round Creator and Editor, which achieves comparable performance compared to those expert models in a wide range of visual generation tasks. To achieve this goal, we first introduce a unified condition format termed Long-context Condition Unit (LCU), and propose a novel Transformer-based diffusion model that uses LCU as input, aiming for joint training across various generation and editing tasks. Furthermore, we propose an efficient data collection approach to address the issue of the absence of available training data. It involves acquiring pairwise images with synthesis-based or clustering-based pipelines and supplying these pairs with accurate textual instructions by leveraging a fine-tuned multi-modal large language model. To comprehensively evaluate the performance of our model, we establish a benchmark of manually annotated pairs data across a variety of visual generation tasks. The extensive experimental results demonstrate the superiority of our model in visual generation fields. Thanks to the all-in-one capabilities of our model, we can easily build a multi-modal chat system that responds to any interactive request for image creation using a single model to serve as the backend, avoiding the cumbersome pipeline typically employed in visual agents. Code and models will be available on the project page: https://ali-vilab.github.io/ace-page/.

Given an original image, image editing aims to generate an image that align with the provided instruction. The challenges are to accept multimodal inputs as instructions and a scarcity of high-quality training data, including crucial triplets of source/target image pairs and multimodal (text and image) instructions. In this paper, we focus on image style editing and present StyleBooth, a method that proposes a comprehensive framework for image editing and a feasible strategy for building a high-quality style editing dataset. We integrate encoded textual instruction and image exemplar as a unified condition for diffusion model, enabling the editing of original image following multimodal instructions. Furthermore, by iterative style-destyle tuning and editing and usability filtering, the StyleBooth dataset provides content-consistent stylized/plain image pairs in various categories of styles. To show the flexibility of StyleBooth, we conduct experiments on diverse tasks, such as text-based style editing, exemplar-based style editing and compositional style editing. The results demonstrate that the quality and variety of training data significantly enhance the ability to preserve content and improve the overall quality of generated images in editing tasks. Project page can be found at https://ali-vilab.github.io/stylebooth-page/.

Prior studies have made significant progress in image inpainting guided by either text or subject image. However, the research on editing with their combined guidance is still in the early stages. To tackle this challenge, we present LAR-Gen, a novel approach for image inpainting that enables seamless inpainting of masked scene images, incorporating both the textual prompts and specified subjects. Our approach adopts a coarse-to-fine manner to ensure subject identity preservation and local semantic coherence. The process involves (i) Locate: concatenating the noise with masked scene image to achieve precise regional editing, (ii) Assign: employing decoupled cross-attention mechanism to accommodate multi-modal guidance, and (iii) Refine: using a novel RefineNet to supplement subject details. Additionally, to address the issue of scarce training data, we introduce a novel data construction pipeline. This pipeline extracts substantial pairs of data consisting of local text prompts and corresponding visual instances from a vast image dataset, leveraging publicly available large models. Extensive experiments and varied application scenarios demonstrate the superiority of LAR-Gen in terms of both identity preservation and text semantic consistency. Project page can be found at \url{https://ali-vilab.github.io/largen-page/}., Comment: 22 pages, 14 figures

It is well known that wave collapses can emerge from the focusing one-dimensional (1-D) Majda-McLaughlin-Tabak (MMT) model as a result of modulational instability. However, how these wave collapses affect the spectral properties and statistics of the wave field has not been adequately studied. We undertake this task by simulating the forced-dissipated 1-D MMT model over a range of forcing amplitudes. Our results show that when the forcing is weak, the spectrum agrees well with the prediction by wave turbulence theory with few collapses in the field. As the forcing strength increases, we see an increase in the occurrence of collapses, together with a transition from a power-law spectrum to an exponentially decaying spectrum. Through a spectral decomposition, we find that the exponential spectrum is dominated by the wave collapse component in the non-integrable MMT model, which is in analogy to a soliton gas in integrable turbulence.

Image diffusion models have been utilized in various tasks, such as text-to-image generation and controllable image synthesis. Recent research has introduced tuning methods that make subtle adjustments to the original models, yielding promising results in specific adaptations of foundational generative diffusion models. Rather than modifying the main backbone of the diffusion model, we delve into the role of skip connection in U-Net and reveal that hierarchical features aggregating long-distance information across encoder and decoder make a significant impact on the content and quality of image generation. Based on the observation, we propose an efficient generative tuning framework, dubbed SCEdit, which integrates and edits Skip Connection using a lightweight tuning module named SC-Tuner. Furthermore, the proposed framework allows for straightforward extension to controllable image synthesis by injecting different conditions with Controllable SC-Tuner, simplifying and unifying the network design for multi-condition inputs. Our SCEdit substantially reduces training parameters, memory usage, and computational expense due to its lightweight tuners, with backward propagation only passing to the decoder blocks. Extensive experiments conducted on text-to-image generation and controllable image synthesis tasks demonstrate the superiority of our method in terms of efficiency and performance. Project page: \url{https://scedit.github.io/}

Using the 1D Majda-McLaughlin-Tabak model as an example, we develop numerical experiments to study the validity of the Wave Kinetic Equation (WKE) at the kinetic limit (i.e., small nonlinearity and large domain). We show that the dynamics converges to the WKE prediction, in terms of the closure model and energy flux, when the kinetic limit is approached. When the kinetic limit is combined with a process of widening the inertial range, the theoretical Kolmogorov constant can be recovered numerically to a very high precision.

In this work, we introduce a new acquisition function for sequential sampling to efficiently quantify rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. Our acquisition is a generalization of the likelihood-weighted (LW) acquisition that was initially designed for the same purpose and then extended to many other applications. The improvement in our acquisition comes from the generalized form with two additional parameters, by varying which one can target and address two weaknesses of the original LW acquisition: (1) that the input space associated with rare-event responses is not sufficiently stressed in sampling; (2) that the surrogate model (generated from samples) may have significant deviation from the true ItR function, especially for cases with complex ItR function and limited number of samples. In addition, we develop a critical procedure in Monte-Carlo discrete optimization of the acquisition function, which achieves orders of magnitude acceleration compared to existing approaches for such type of problems. The superior performance of our new acquisition to the original LW acquisition is demonstrated in a number of test cases, including some cases that were designed to show the effectiveness of the original LW acquisition. We finally apply our method to an engineering example to quantify the rare-event roll-motion statistics of a ship in a random sea.

Hydrokinetic turbines extract kinetic energy from moving water to generate renewable electricity, thus contributing to sustainable energy production and reducing reliance on fossil fuels. It has been hypothesized that a duct can accelerate and condition the fluid flow passing the turbine blades, improving the overall energy extraction efficiency. However, no substantial evidence has been provided so far for hydrokinetic turbines. To investigate this problem, we perform a CFD-based optimization study with a blade-resolved Reynolds-averaged Navier--Stokes (RANS) solver to explore the design of a ducted hydrokinetic turbine that maximizes the efficiency of energy extraction. To handle the high-dimensional design space of the blade and duct geometry, we use a gradient-based optimization approach where the gradients are computed using the adjoint method. The final design is re-evaluated through higher-fidelity unsteady RANS (URANS) simulations. Our optimized ducted turbine achieves an efficiency of about 54% over a range of operating conditions, higher than the typical 46% efficiency of unducted turbines such as the well-known Bahaj model.

As presented in Annenkov & Shrira (2009), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ``fast'' dynamic time scale of $O(\varepsilon^{-2})$, with $\varepsilon$ a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of $O(\varepsilon^{-4})$. We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda-McLaughlin-Tabak (MMT) equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ``condensate'' induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem.

We study the spectral energy transfer due to wave-triad interactions in the Garrett-Munk spectrum of internal gravity waves (IGWs) based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical evaluation builds on the reduction of the collision integral on the resonant manifold for a horizontally isotropic spectrum. We directly evaluate the downscale energy flux available for ocean mixing, whose value is in close agreement with the empirical finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of nonlocal interactions, namely parametric subharmonic instability (PSI), elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each type of interaction, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for GM76 spectrum. In addition, our analysis estimates the contribution of each mechanism to the energy transfer in each spectral direction, and reveals new understanding of the importance of local interactions and ES in the energy transfer.

Existing audio analysis methods generally first transform the audio stream to spectrogram, and then feed it into CNN for further analysis. A standard CNN recognizes specific visual patterns over feature map, then pools for high-level representation, which overlooks the positional information of recognized patterns. However, unlike natural image, the semantic of an audio spectrogram is sensitive to positional change, as its vertical and horizontal axes indicate the frequency and temporal information of the audio, instead of naive rectangular coordinates. Thus, the insensitivity of CNN to positional change plays a negative role on audio spectrogram encoding. To address this issue, this paper proposes a new self-supervised learning mechanism, which enhances the audio representation by first generating adversarial samples (\textit{i.e.}, negative samples), then driving CNN to distinguish the embeddings of negative pairs in the latent space. Extensive experiments show that the proposed approach achieves best or competitive results on 9 downstream datasets compared with previous methods, which verifies its effectiveness on audio representation learning., Comment: 8 pages, 4 figures

Video temporal grounding aims to pinpoint a video segment that matches the query description. Despite the recent advance in short-form videos (\textit{e.g.}, in minutes), temporal grounding in long videos (\textit{e.g.}, in hours) is still at its early stage. To address this challenge, a common practice is to employ a sliding window, yet can be inefficient and inflexible due to the limited number of frames within the window. In this work, we propose an end-to-end framework for fast temporal grounding, which is able to model an hours-long video with \textbf{one-time} network execution. Our pipeline is formulated in a coarse-to-fine manner, where we first extract context knowledge from non-overlapped video clips (\textit{i.e.}, anchors), and then supplement the anchors that highly response to the query with detailed content knowledge. Besides the remarkably high pipeline efficiency, another advantage of our approach is the capability of capturing long-range temporal correlation, thanks to modeling the entire video as a whole, and hence facilitates more accurate grounding. Experimental results suggest that, on the long-form video datasets MAD and Ego4d, our method significantly outperforms state-of-the-arts, and achieves \textbf{14.6$\times$} / \textbf{102.8$\times$} higher efficiency respectively. Project can be found at \url{https://github.com/afcedf/SOONet.git}., Comment: 11 pages, 8 figures

The internal-wave (IW) continuum of a regional ocean model is studied in terms of the vertical spectral kinetic-energy (KE) fluxes and transfers at high vertical wavenumbers. Previous work has shown that this model permits a partial representation of the IW cascade. In this work, vertical spectral KE flux is decomposed into catalyst, source, and destination frequency bands of nonlinear scattering, a framework that allows for the discernment of different types of nonlinear interactions involving both waves and eddies. Energy transfer within the supertidal IW continuum is found to be strongly dependent on horizontal resolution. Specifically, at a horizontal grid spacing of 1/48-degrees, the vast majority of KE in the supertidal continuum arrives there from lower frequency modes through a single nonlinear interaction, while at 1/384-degrees KE transfers within the supertidal IW continuum are comparable in size to KE transfer from lower-frequency modes. Additionally, comparisons are made with existing theoretical and observational work on energy pathways in the IW continuum. Induced diffusion (ID) is found to be associated with a weak forward frequency transfer within the supertidal IW continuum. Spectrally local interactions are found to play an insignificant role within the model evolution. At the same time, ID-like processes involving high vertical-wavenumber near-inertial and tidal waves as well as low-vertical-wavenumber eddy fields are substantial, suggesting that the processes giving rise to a Garrett-Munk-like spectra in the present numerical simulation and perhaps the real ocean may be more varied than in idealized or wave-only frameworks.

Many recent studies leverage the pre-trained CLIP for text-video cross-modal retrieval by tuning the backbone with additional heavy modules, which not only brings huge computational burdens with much more parameters, but also leads to the knowledge forgetting from upstream models. In this work, we propose the VoP: Text-Video Co-operative Prompt Tuning for efficient tuning on the text-video retrieval task. The proposed VoP is an end-to-end framework with both video & text prompts introducing, which can be regarded as a powerful baseline with only 0.1% trainable parameters. Further, based on the spatio-temporal characteristics of videos, we develop three novel video prompt mechanisms to improve the performance with different scales of trainable parameters. The basic idea of the VoP enhancement is to model the frame position, frame context, and layer function with specific trainable prompts, respectively. Extensive experiments show that compared to full fine-tuning, the enhanced VoP achieves a 1.4% average R@1 gain across five text-video retrieval benchmarks with 6x less parameter overhead. The code will be available at https://github.com/bighuang624/VoP., Comment: Accepted by CVPR 2023

Testing and evaluation are expensive but critical steps in the development of connected and automated vehicles (CAVs). In this paper, we develop an adaptive sampling framework to efficiently evaluate the accident rate of CAVs, particularly for scenario-based tests where the probability distribution of input parameters is known from the Naturalistic Driving Data. Our framework relies on a surrogate model to approximate the CAV performance and a novel acquisition function to maximize the benefit (information to accident rate) of the next sample formulated through an information-theoretic consideration. In addition to the standard application with only a single high-fidelity model of CAV performance, we also extend our approach to the bi-fidelity context where an additional low-fidelity model can be used at a lower computational cost to approximate the CAV performance. Accordingly, for the second case, our approach is formulated such that it allows the choice of the next sample in terms of both fidelity level (i.e., which model to use) and sampling location to maximize the benefit per cost. Our framework is tested in a widely-considered two-dimensional cut-in problem for CAVs, where Intelligent Driving Model (IDM) with different time resolutions are used to construct the high and low-fidelity models. We show that our single-fidelity method outperforms the existing approach for the same problem, and the bi-fidelity method can further save half of the computational cost to reach a similar accuracy in estimating the accident rate.

We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity levels. With the increase of nonlinearity, the breathers break down, giving way to wave turbulence (or Rayleigh-Jeans) spectra. Phase-space trajectories associated with the breather solutions are found to be close to that of the linear system, revealing a connection between the breather solution and Kolmogorov-Arnold-Moser (KAM) theory.

In computing ship motion statistics (e.g., exceeding probability) in an irregular wave field, it is a common practice to represent the irregular waves by a large number of wave groups and compute the motion statistics from the distribution of these wave groups. While this procedure significantly reduces the computational cost, the uncertainties introduced in this reduced-order computation have not been quantified. In general, the representation of a continuous wave field by separated groups loses information about wave phases, frequency modulation and initial conditions of ship when encountering the wave groups, among which the last one is arguably the most influential factor for the ship motion statistics. In this paper, we test three methods to incorporate the ship initial conditions into the computation of roll motion exceeding probability, namely the methods of natural initial condition, pre-computed initial condition and constant initial condition. For different input wave spectra and ship motion dynamics (in terms of the parametric excitation level modeled by a nonlinear roll equation), the performances of the three methods are carefully benchmarked and the superiority of the natural initial condition method is demonstrated. We finally show that the computation using the natural initial condition method can be greatly accelerated through a sequential sampling algorithm making use of the variational heteroscedastic Gaussian process regression.

In this work, we develop a computational framework to efficiently quantify the temporal exceeding probability of ship responses in a random wave field, i.e., the fraction of time that ship responses exceed a given threshold. In particular, we consider large thresholds so that the response exceedance needs to be treated as rare events. Our computational framework builds on the parameterization of wave field into wave groups and efficient sampling in the group parameter space through Bayesian experimental design (BED). Previous works following this framework exclusively studied extreme statistics of group-maximum response, i.e., the maximum response within a wave group, which is however not straightforward to interpret in practice (e.g., its value depends on the subjective definition of the wave group). In order to adapt the framework to the more robust measure by the temporal exceeding probability, novel developments need to be introduced to the two components of BED (on surrogate model and acquisition function), which are detailed in the paper. We validate our framework for a case of ship roll motion calculated by a nonlinear roll equation, in terms of the agreement of our results to the true solution and the independence of our results to the criterion of defining groups. Finally, we demonstrate the coupling of the framework with CFD models to handle more realistic and general ship response problems.

We study the energy transfer by exact resonances for surface gravity waves in a finite periodic spatial domain. Based on a kinematic model simulating the generation of active wave modes in a finite discrete wavenumber space $\mathcal{S}_R$, we examine the possibility of direct and inverse energy cascades. More specifically, we set an initially excited region which iteratively spreads energy to wave modes in $\mathcal{S}_R$ through exact resonances. At each iteration, we first activate new modes from scale resonances (which generate modes with new lengths), then consider two bounding situations for angle resonances (which transfer energy at the same length scale): the lower bound where no angle resonance is included and the upper bound where all modes with the same length as any active mode are excited. Such a strategy is essential to enable the computation for a large domain $\mathcal{S}_R$ with the maximum wavenumber $R\sim 10^3$. We show that for both direct and inverse cascades, the energy cascade to the boundaries of $\mathcal{S}_R$ can be established when the initially excited region is sufficiently large, otherwise a frozen turbulence state occurs, with a sharp transition between the two regimes especially for the direct cascade. Through a study on the structure of resonant quartets, the mechanism associated with the sharp transition and the role of angular energy transfer in the cascades are elucidated.

In Wang & Pan (J. Fluid Mech., vol. 918, A19, 2021), the authors developed the first ensemble-based data assimilation (DA) capability for the reconstruction and forecast of ocean surface waves, namely the EnKF-HOS method coupling an ensemble Kalman filter (EnKF) and the high-order spectral (HOS) method. In this work, we continue to enrich the method by allowing it to simultaneously estimate the ocean current field, which is in general not known a priori and can (slowly) vary in both space and time. To achieve this goal, we incorporate the effect of ocean current (as unknown parameters) on waves to build the HOS-C method as the forward prediction model, and obtain a simultaneous estimation of (current) parameters and (wave) states via an iterative EnKF (IEnKF) method that is necessary to handle the complexity in this DA problem. The new algorithm, named IEnKF-HOS-C method, is first tested in synthetic problems with various forms (steady/unsteady, uniform/non-uniform) of current. It is shown that the IEnKF-HOS-C method is able to not only estimate the current field accurately, but also boost the prediction accuracy of the wave field (even) relative to the state-of-the-art EnKF-HOS method. Finally, using real data from a shipborne radar, we show that the IEnKF-HOS-C method successfully recovers the current speed that matches the in situ measurement by a floating buoy.

In this work, we develop a multi-fidelity Bayesian experimental design framework to efficiently quantify the extreme-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The key idea here is to leverage low-fidelity samples whose responses can be computed with a cost of a certain fraction of that for high-fidelity samples, in an optimized configuration to reduce the total computational cost. To accomplish this goal, we employ a multi-fidelity Gaussian process as the surrogate model of the ItR function, and develop a new acquisition based on which the optimized next sample can be selected in terms of its location in the sample space and the fidelity level. In addition, we develop an inexpensive analytical evaluation of the acquisition and its derivative, avoiding numerical integrations that are prohibitive for high-dimensional problems. The new method is tested in a bi-fidelity context for a series of synthetic problems with varying dimensions, low-fidelity model accuracy and computational costs. Comparing with the single-fidelity method and the bi-fidelity method with a pre-defined fidelity hierarchy, our method consistently shows the best (or among the best) performance for all the test cases. Finally, we demonstrate the superiority of our method in solving an engineering problem of estimating the extreme ship motion statistics in irregular waves, using computational fluid dynamics (CFD) with two different grid resolutions as the high and low fidelity models.

In this paper, we study the flow physics underlying the recently developed remote sensing capability of detecting oceanic microplastics, which is based on the measurable surface roughness reduction induced by the presence of microplastics on the ocean surface. In particular, we are interested in whether this roughness reduction is caused by the microplastics as floating particles, or by the surfactants which follow similar transport paths as microplastics. For this purpose, we experimentally test the effects of floating particles and surfactants on surface roughness, quantified by the mean square slope (MSS), with waves generated by a mechanical wave maker or by wind. For microplastics, we find that their effect on wave energy and MSS critically depends on the surface area fraction of coverage, irrespective of the particle sizes in the test range. The damping by particles is observed only for fractions above $O(5-10\%)$, which is much higher than the realistic ocean condition. For surfactants, their damping effect on mechanically generated irregular waves generally increases with the concentration of surfactants, but no optimal concentration corresponding to maximum damping is observed, in contrast to previous studies based on monochromatic waves. In wind-wave experiments, the presence of surfactants suppresses the wave generation, due to the combined effects of reduced wind shear stress and increased wave damping. For the same wind speed, the wind stress is identified to depend on the concentration of surfactants with a power-law relation. The implications of these findings to remote sensing are discussed.

We study the properties of energy flux in wave turbulence via the Majda-McLaughlin-Tabak (MMT) equation with a quadratic dispersion relation. One of our purposes is to resolve the inter-scale energy flux $P$ in the stationary state to elucidate its distribution and scaling with spectral level. More importantly, we perform a quartet-level decomposition of $P=\sum_\Omega P_\Omega$, with each component $P_\Omega$ representing the contribution from quartet interactions with frequency mismatch $\Omega$, in order to explain the properties of $P$ as well as study the wave-turbulence closure model. Our results show that time series of $P$ closely follows a Gaussian distribution, with its standard deviation several times its mean value $\overline{P}$. This large standard deviation is shown to mainly result from the fluctuation (in time) of the quasi-resonances, i.e., $P_{\Omega\neq 0}$. The scaling of spectral level with $\overline{P}$ exhibits $\overline{P}^{1/3}$ and $\overline{P}^{1/2}$ at high and low nonlinearity, consistent with the kinetic and dynamic scalings respectively. The different scaling laws in the two regimes are explained through the dominance of quasi-resonances ($P_{\Omega\neq 0}$) and exact resonances ($P_{\Omega= 0}$) in the former and latter regimes. Finally, we investigate the wave-turbulence closure model, which connects fourth-order correlators to products of pair correlators through a broadening function $f(\Omega)$, sometimes argued to be a $sinc$ function in the theory. Our numerical data show that consistent behavior of $f(\Omega)$ can only be observed upon averaging over a large number of quartets, but with $f(\Omega)$ showing $f\sim 1/\Omega^\beta$ dependence with $\beta$ taking values between $1.3$ and $1.6$.

The authors of the discussed paper simplified the information-based acquisition on estimating statistical expectation and developed analytical computation for each involved quantity under uniform input distribution. In this discussion, we show that (1) the last three terms of the acquisition always add up to zero, leaving a concise form with a much more intuitive interpretation of the acquisition; (2) the analytical computation of the acquisition can be generalized to arbitrary input distribution, greatly broadening the application of the developed framework.

We consider the statistics of extreme ship motions in a nonlinear irregular wave field. While an accurate computation is possible by using a full Monte-Carlo method to cover all individual wave conditions, the computational cost may become prohibitively high (when coupled with high-fidelity simulations) due to the rareness of the extreme events. In this work, following existing methods of sequential sampling and wave group parameterization, we implement a framework incorporating nonlinear wave simulation and ship response CFD simulation, which allows the extreme ship motion statistics in nonlinear wave field to be computed efficiently. We test the validity of the framework for the cases of ship response calculated by a nonlinear roll equation, and show the importance of wave nonlinearity to the extreme response statistics. Finally, the framework is coupled with the CFD model to demonstrate its applicability to more realistic and general ship motion problems.

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay, narrow- and broadband forcing) we consider, we find that the spectral forms approach wave turbulence theory (WTT) solution $S_\eta\sim k^{-5/2}$ and $S_\eta\sim P^{1/3}$ at high nonlinearity levels. With the decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. To interpret these spectral variations, we further investigate two hypothetical and disputable mechanisms about bound waves and finite-size effect. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at some critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case., Comment: 20 pages, 11 figures

We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schr\"odinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic study with numerical experimentation. As a biproduct of our investigation we also prove that the quasi-resonant part of the NLS initial value problem we consider, in both the focusing and defocusing case, is globally well-posed for initial data of finite mass.

Content-based video retrieval aims to find videos from a large video database that are similar to or even near-duplicate of a given query video. Video representation and similarity search algorithms are crucial to any video retrieval system. To derive effective video representation, most video retrieval systems require a large amount of manually annotated data for training, making it costly inefficient. In addition, most retrieval systems are based on frame-level features for video similarity searching, making it expensive both storage wise and search wise. We propose a novel video retrieval system, termed SVRTN, that effectively addresses the above shortcomings. It first applies self-supervised training to effectively learn video representation from unlabeled data to avoid the expensive cost of manual annotation. Then, it exploits transformer structure to aggregate frame-level features into clip-level to reduce both storage space and search complexity. It can learn the complementary and discriminative information from the interactions among clip frames, as well as acquire the frame permutation and missing invariant ability to support more flexible retrieval manners. Comprehensive experiments on two challenging video retrieval datasets, namely FIVR-200K and SVD, verify the effectiveness of our proposed SVRTN method, which achieves the best performance of video retrieval on accuracy and efficiency.

We consider an input-to-response (ItR) system characterized by (1) parameterized input with a known probability distribution and (2) stochastic ItR function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme response probability when the ItR function is expensive to evaluate. The problem setup arises often in physics and engineering problems, with randomness in ItR coming from either intrinsic uncertainties (say, as a solution to a stochastic equation) or additional (critical) uncertainties that are not incorporated in a low-dimensional input parameter space (as a result of dimension reduction applied to the original high-dimensional input space). To reduce the required sampling numbers, we develop a sequential Bayesian experimental design method leveraging the variational heteroscedastic Gaussian process regression (VHGPR) to account for the stochastic ItR, along with a new criterion to select the next-best samples sequentially. The validity of our new method is first tested in two synthetic problems with the stochastic ItR functions defined artificially. Finally, we demonstrate the application of our method to an engineering problem of estimating the extreme ship motion probability in irregular waves, where the uncertainty in ItR naturally originates from standard wave group parameterization, which reduces the original high-dimensional wave field into a two-dimensional parameter space.

Through ensemble-based data assimilation (DA), we address one of the most notorious difficulties in phase-resolved ocean wave forecast, regarding the deviation of numerical solution from the true surface elevation due to the chaotic nature of and underrepresented physics in the nonlinear wave models. In particular, we develop a coupled approach of the high-order spectral (HOS) method with the ensemble Kalman filter (EnKF), through which the measurement data can be incorporated into the simulation to improve the forecast performance. A unique feature in this coupling is the mismatch between the predictable zone and measurement region, which is accounted for through a special algorithm to modify the analysis equation in EnKF. We test the performance of the new EnKF-HOS method using both synthetic data and real radar measurements. For both cases (though differing in details), it is shown that the new method achieves much higher accuracy than the HOS-only method, and can retain the phase information of an irregular wave field for arbitrarily long forecast time with sequentially assimilated data.

We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show that the statistical properties of the wave field rely critically on the structure of the discrete resonant manifold (DRM). To demonstrate this, we simulate the two-dimensional MMT equation on rational and irrational tori, resulting in remarkably different power-law spectra and energy cascades at low nonlinearity levels. The difference is explained in terms of different structures of the DRM, which makes use of recent number theory results.