Variational Framework Research Articles

A robust computational framework for variational data assimilation of mean flows with sparse measurements corrupted by strong outliers

A variational framework for the reconstruction of time-averaged mean flows using a sparse set of observations with large magnitudes of noise (referred to as outliers), is presented. The observations constitute a set of point-wise measurements of the mean flow with outliers at certain measurement locations and are incorporated into a numerical simulation governed by the two-dimensional, incompressible Reynolds-averaged Navier-Stokes (RANS) equations with an unknown momentum forcing. This forcing, which corresponds to the divergence of the Reynolds stress tensor, is calculated from a direct-adjoint optimization procedure to reduce the deviation between the measured and estimated mean velocities. ℓ2, ℓ1, Huber, and hybrid loss functions are used to represent the discrepancy in the mean velocity field between the measurements and the predictions. A variety of algorithms are considered to solve the optimization problem with these loss functions and a performance comparison in terms of the quality and physical features of the recovered mean flow is presented. The Huber loss function performed best as it remained robust to strong outliers in the measurements with its ℓ1 contribution and also ensured the uniqueness of the optimal solution with its ℓ2 contribution. Huber loss functions restrict the effect of outliers at the local measurement locations, thereby not affecting the quality of the high-dimensional reconstructed mean flow field. The hybrid loss function, a modified form of the continuous Huber loss function, also recovered the mean flow with high accuracy. We demonstrate the performance of the data assimilation framework for the case of two-dimensional laminar flow around a circular cylinder at Re=100. We then extend the analysis to the case of two-dimensional laminar flow over a backward-facing step at Re=500, to further assess the efficacy and robustness of the data assimilation framework.

Edge-based distributed primal–dual algorithms for seeking generalized Nash equilibria

This paper introduces two novel distributed algorithms aimed at finding the generalized Nash equilibria (GNE) in noncooperative games. To tackle this, we utilize the variational inequality framework, transforming the noncooperative game into the challenge of identifying the zeros of a sum of monotone operators. Within noncooperative games, the decisions made by individual players are interlinked via shared affine constraints. Our proposed approach involves two edge-based distributed algorithms, differentiated by their access to players’ actions, whether it is full-decision information or partial-decision information. We establish the parameter range and demonstrate the convergence of both algorithms, showcasing their efficacy under local constant step-sizes. Additionally, we validate the effectiveness and advantages of these algorithms through two numerical experiments.

A Timoshenko-Ehrenfest beam model for simulating Langevin transducer dynamics

The Langevin transducer is a widely used power ultrasonic device across both medical and industrial applications, from orthopaedic surgery to drilling and welding. It is a sandwich-type device which typically consists of piezoelectric ceramic rings between two metallic end-masses. The transducer is commonly operated at a particular resonant mode to deliver ultrasonic vibrations to a target structure of interest, and is generally modelled using approaches including the transfer matrix method and electromechanical equivalent circuit methods. Here, we propose a variational framework to study the dynamics of the Langevin transducer based on the Timoshenko-Ehrenfest beam theory and Hamilton's principle. The variational equation derived from this model is then discretized by the standard finite element method with spectral elements. To verify the proposed one-dimensional electromechanical model, the computed resonance frequencies, or natural frequencies, of the one-dimensional model are compared to those of a three-dimensional finite element model with respect to varying geometry parameters characterizing the transducer. The results of the reduced one-dimensional and full three-dimensional models are then compared to those measured through an experimental investigation consisting of laser Doppler vibrometry. This is undertaken for the first ten eigenfrequencies, including longitudinal and bending modes, where normalized amplitudes and vibration mode shapes are reported. The close correlation between modelling and experiment demonstrates that the proposed one-dimensional electromechanical model can deliver results consistent with the full three-dimensional model and from experiment, thus verifying a rapid and reliable method for studying the free vibrations and dynamics of the Langevin transducer which accounts for the axial vibrations of the piezoelectric ceramic stack in all cases.

A logarithmic Choquard equation with critical exponential growth in ℝ2

ABSTRACT In this paper, we are paid attention to the following logarithmic Choquard equation − Δ u + u = [ I 2 ∗ F ( u ) ] f ( u ) , x ∈ R 2 , where I 2 = 1 2 π ln ⁡ 1 | x | is the Newtonian kernel in dimension 2, F ( u ) = ∫ 0 u f ( t ) d t and f ∈ C 1 ( R , R ) is critical exponential growth with respect to Trudinger–Moser. Based on a variational framework proposed in Liu et al. (J Differ Equ 2022;328), we obtain a positive finite energy solution of the above logarithmic Choquard equation via the variational methods. Furthermore, we use another approach to investigate the planar logarithmic Choquard equations involving critical exponential growth.

Breaking the limitations with sparse inputs by variational frameworks (BLIss) in terahertz super-resolution 3D reconstruction

Data acquisition, image processing, and image quality are the long-lasting issues for terahertz (THz) 3D reconstructed imaging. Existing methods are primarily designed for 2D scenarios, given the challenges associated with obtaining super-resolution (SR) data and the absence of an efficient SR 3D reconstruction framework in conventional computed tomography (CT). Here, we demonstrate BLIss, a new approach for THz SR 3D reconstruction with sparse 2D data input. BLIss seamlessly integrates conventional CT techniques and variational framework with the core of the adapted Euler-Elastica-based model. The quantitative 3D image evaluation metrics, including the standard deviation of Gaussian, mean curvatures, and the multi-scale structural similarity index measure (MS-SSIM), validate the superior smoothness and fidelity achieved with our variational framework approach compared with conventional THz CT modal. Beyond its contributions to advancing THz SR 3D reconstruction, BLIss demonstrates potential applicability in other imaging modalities, such as X-ray and MRI. This suggests extensive impacts on the broader field of imaging applications.

Coupled Dynamics of Steady Jet Flow Control for Flexible Membrane Wings

We present a steady jet-flow-based flow control of flexible membrane wings for the adaptive and efficient motion of bat-inspired drones in complex flight environments. A body-fitted variational computational aeroelastic framework is adopted for the modeling of fluid–structure interactions. High-momentum jet flows are injected from the leading edge and transported to the wake flows to alter the aerodynamic performance and the membrane vibration. The coupled dynamic effect of active jet flow control on membrane performance is systematically explored. While the results indicate that the current active flow control strategy performs well at low angles of attack, its effectiveness degrades at high angles of attack with large flow separation. To understand the coupling mechanism, the variations of the vortex patterns are examined by the proper orthogonal decomposition modes, and the fluid transport process is studied by the Lagrangian coherent structures. Two scaling relations that quantitatively connect the membrane deformation with the aerodynamic loads presented in our previous work are verified even when active jet flow control is applied. A unifying feedback loop that reveals the fluid–membrane coupling mechanism is proposed. These findings can facilitate the development of next-generation bio-inspired drones that incorporate smart sensing and intelligent control.

Variational Bayesian Variable Selection for High-Dimensional Hidden Markov Models

The Hidden Markov Model (HMM) is a crucial probabilistic modeling technique for sequence data processing and statistical learning that has been extensively utilized in various engineering applications. Traditionally, the EM algorithm is employed to fit HMMs, but currently, academics and professionals exhibit augmenting enthusiasm in Bayesian inference. In the Bayesian context, Markov Chain Monte Carlo (MCMC) methods are commonly used for inferring HMMs, but they can be computationally demanding for high-dimensional covariate data. As a rapid substitute, variational approximation has become a noteworthy and effective approximate inference approach, particularly in recent years, for representation learning in deep generative models. However, there has been limited exploration of variational inference for HMMs with high-dimensional covariates. In this article, we develop a mean-field Variational Bayesian method with the double-exponential shrinkage prior to fit high-dimensional HMMs whose hidden states are of discrete types. The proposed method offers the advantage of fitting the model and investigating specific factors that impact the response variable changes simultaneously. In addition, since the proposed method is based on the Variational Bayesian framework, the proposed method can avoid huge memory and intensive computational cost typical of traditional Bayesian methods. In the simulation studies, we demonstrate that the proposed method can quickly and accurately estimate the posterior distributions of the parameters with good performance. We analyzed the Beijing Multi-Site Air-Quality data and predicted the PM2.5 values via the fitted HMMs.

GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Framework

Particle-based Variational Inference (ParVI) methods approximate the target distribution by iteratively evolving finite weighted particle systems. Recent advances of ParVI methods reveal the benefits of accelerated position update strategies and dynamic weight adjustment approaches. In this paper, we propose the first ParVI framework that possesses both accelerated position update and dynamical weight adjustment simultaneously, named the General Accelerated Dynamic-Weight Particle-based Variational Inference (GAD-PVI) framework. Generally, GAD-PVI simulates the semi-Hamiltonian gradient flow on a novel Information-Fisher-Rao space, which yields an additional decrease on the local functional dissipation. GAD-PVI is compatible with different dissimilarity functionals and associated smoothing approaches under three information metrics. Experiments on both synthetic and real-world data demonstrate the faster convergence and reduced approximation error of GAD-PVI methods over the state-of-the-art.

Variational Hybrid-Attention Framework for Multi-Label Few-Shot Aspect Category Detection

Multi-label few-shot aspect category detection (FS-ACD) is a challenging sentiment analysis task, which aims to learn a multi-label learning paradigm with limited training data. The difficulty of this task is how to use limited data to generalize effective discriminative representations for different categories. Nowadays, all advanced FS-ACD works utilize the prototypical network to learn label prototypes to represent different aspects. However, such point-based estimation methods are inherently noise-susceptible and bias-vulnerable. To this end, this paper proposes a novel Variational Hybrid-Attention Framework (VHAF) for the FS-ACD task. Specifically, to alleviate the data noise, we adopt a hybrid-attention mechanism to generate more discriminative aspect-specific embeddings. Then, based on these embeddings, we introduce the variational distribution inference to obtain the aspect-specific distribution as a more robust aspect representation, which can eliminate the scarce data bias for better inference. Moreover, we further leverage an adaptive threshold estimation to help VHAF better identify multiple relevant aspects. Extensive experiments on three datasets demonstrate the effectiveness of our VHAF over other state-of-the-art methods. Code is available at https://github.com/chengzju/VHAF.

Tagging Items with Emerging Tags: A Neural Topic Model Based Few-Shot Learning Approach

The tagging system has become a primary tool to organize information resources on the Internet, which benefits both users and the platforms. To build a successful tagging system, automatic tagging methods are desired. With the development of society, new tags keep emerging. The problem of tagging items with emerging tags is an open challenge for an automatic tagging system, and it has not been well studied in the literature. We define this problem as a tag-centered cold-start problem in this study and propose a novel neural topic model based few-shot learning method named NTFSL to solve the problem. In our proposed method, we innovatively fuse the topic modeling task with the few-shot learning task, endowing the model with the capability to infer effective topics to solve the tag-centered cold-start problem with the property of interpretability. Meanwhile, we propose a novel neural topic model for the topic modeling task to improve the quality of inferred topics, which helps enhance the tagging performance. Furthermore, we develop a novel inference method based on the variational auto-encoding framework for model inference. We conducted extensive experiments on two real-world datasets, and the results demonstrate the superior performance of our proposed model compared with state-of-the-art machine learning methods. Case studies also show the interpretability of the model.

An elastoplastic phase-field model for quasi-static fracture of nickel-based super-alloys

In the present study, an elastoplastic phase-field model of quasi-static fracture in ductile materials is proposed in the variational framework for J2 plasticity with isotropic hardening, which is suitable to describe the quasi-static behavior of metals as investigated in the performed experiments. These contributions include: (1) the free energy functions for coupling elastic response, plastic yielding and damage evolution are established. (2) The new elastic and plastic energy degradation functions are constructed to quantitatively describe the relationship between energy release and phase-field evolution of elastoplastic materials. (3) Damage evolution and plastic yielding criteria are derived. (4) From a numerical point of view, we derive the governing equations and the corresponding weak forms and the overall solution procedure for the phase-field model is given via the use of a return-mapping algorithm. This phase-field model was validated by a series of tensile experiments on Inconel 718 nickel-based super-alloys standard specimens. In order to compare the simulation results with the experimental results more comprehensively, the digital image correlation (DIC) technique is applied to experimentally investigate the specimen deformation information. In addition, to verify the potential of the model to capture complex cracks, we performed Nooru-Mohamed tests. The numerical simulation results are in good agreements with the results of previous experimental work.

Asymptotics for ruin probabilities in a bidimensional discrete-time risk model with dependent and consistently varying tailed net losses

Consider an insurer who operates two lines of businesses and hence receives two types of insurance net losses. In the bidimensional discrete-time risk model with a constant interest rate, the net loss vectors from the two business lines form a sequence of independent and identically distributed real-valued random vectors. We propose a bidimensional extended regularly varying structure in terms of survival copulas to model the dependence between the two components of each net loss vector, which includes not only asymptotic independence but also asymptotic dependence. Under the framework of consistent variation, we obtain several (uniformly) asymptotic formulas for various ruin probabilities. In particular, the investigation of random-time ruin probabilities unifies and extends the results on both finite-time and infinite-time ruin probabilities. Some numerical studies are also performed to check the accuracy of our obtained asymptotic results.

Adaptive contrast enhancement for underwater image using imaging model guided variational framework

Adaptive contrast enhancement for underwater image using imaging model guided variational framework

Kernel Bayesian nonlinear matrix factorization based on variational inference for human–virus protein–protein interaction prediction

Identification of potential human–virus protein–protein interactions (PPIs) contributes to the understanding of the mechanisms of viral infection and to the development of antiviral drugs. Existing computational models often have more hyperparameters that need to be adjusted manually, which limits their computational efficiency and generalization ability. Based on this, this study proposes a kernel Bayesian logistic matrix decomposition model with automatic rank determination, VKBNMF, for the prediction of human–virus PPIs. VKBNMF introduces auxiliary information into the logistic matrix decomposition and sets the prior probabilities of the latent variables to build a Bayesian framework for automatic parameter search. In addition, we construct the variational inference framework of VKBNMF to ensure the solution efficiency. The experimental results show that for the scenarios of paired PPIs, VKBNMF achieves an average AUPR of 0.9101, 0.9316, 0.8727, and 0.9517 on the four benchmark datasets, respectively, and for the scenarios of new human (viral) proteins, VKBNMF still achieves a higher hit rate. The case study also further demonstrated that VKBNMF can be used as an effective tool for the prediction of human–virus PPIs.

Spatiotemporal monitoring of climate change impacts on water resources using an integrated approach of remote sensing and Google Earth Engine

In this study, a data-driven approach employed by utilizing the product called JRC-Global surface water mapping layers V1.4 on the Google Earth Engine (GEE) to map and monitor the effects of climate change on surface water resources. Key climatic variables affecting water bodies, including air temperature (AT), actual evapotranspiration (ETa), and total precipitation, were analyzed from 2000 to 2021 using the temperature-vegetation index (TVX) and Moderate Resolution Imaging Spectroradiometer (MODIS) products. The findings demonstrate a clear association between global warming and the shrinking of surface water resources in the LUB. According to the results, an increase in AT corresponded to a decrease in water surface area, highlighting the significant influence of AT and ETa on controlling the water surface in the LUB (partial rho of − 0.65 and − 0.68, respectively). Conversely, no significant relationship was found with precipitation and water surface area (partial rho of + 0.25). Notably, the results of the study indicate that over the past four decades, approximately 40% of the water bodies in the LUB remained permanent. This suggests a loss of around 30% of the permanent water resources, which have transitioned into seasonal water bodies, accounting for nearly 13% of the total. This research provides a comprehensive framework for monitoring surface water resource variations and assessing the impact of climate change on water resources. It aids in the development of sustainable water management strategies and plans, supporting the preservation and effective use of water resources.

Generalized variational framework with minimax optimization for parametric blind deconvolution

Blind deconvolution (BD), which aims to separate unknown convolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

Excited states in warm and hot dense matter.

Accurate modeling of warm and hot dense matter is challenging in part due to the multitude of excited states that must be considered. Here, we present a variational framework that models these excited states. In this framework an excited state is defined by a set of effective one-electron occupation factors, and the corresponding energy is defined by the effective one-body energy with an exchange and correlation term. The variational framework is applied to an atom-in-plasma model (a generalization of the so-called average atom model). Comparisons with a density functional theory based average atom model generally reveal good agreement in the calculated pressure, but our model also gives access to the excitation energies and charge state distributions.

A Variational Bayesian Inference-Based En-Decoder Framework for Traffic Flow Prediction

Accurate traffic flow prediction, a hotspot for intelligent transportation research, is the prerequisite for traffic flow prediction for making travel plans. The speed of traffic flow can be affected by roads condition, weather, holidays, etc. Moreover, sensors to catch the information about traffic flow will be interfered with by environmental factors such as illumination, collection time, occlusion, etc. Therefore, the traffic flow in the practical transportation system is complicated, uncertain, and challenging to predict accurately. Motivated from the aforementioned issues and challenges, in this paper, we propose a deep encoder-decoder prediction framework based on variational Bayesian inference. A Bayesian neural network is designed by combining variational inference with Gated Recurrent Units (GRU) which is used as the deep neural network unit of the encoder-decoder framework to mine the intrinsic dynamics of traffic flow. Then, the variational inference is introduced into the multi-head attention mechanism to avoid noise-induced deterioration of prediction accuracy. The proposed model achieves superior prediction performance on the Guangzhou urban traffic flow dataset over the benchmarks, particularly when the long-term prediction.

Examining Potential Psychological Protective and Risk Factors for Stress and Burnout in Social Workers

AbstractSocial work professionals experience high levels of stress and burnout. Stress and burnout can have a negative impact on the individual social worker, the organisations they work for, and perhaps most importantly, the quality of care that marginalised groups that are supported by social workers receive. Several work-related predictors of stress and burnout have been identified; however, no studies have examined the underlying psychological protective and risk factors which might help to explain changes in social worker stress and burnout. Using the clinically modified Buddhist psychological model (CBPM) as a theoretical framework, this cross-sectional study attempted to identify psychological protective and risk factors for stress and burnout in 121 social workers in Northern Ireland, using structural equation modelling, and conditional process analyses. This study provided promising preliminary evidence for a mediated effect CBPM as being a potentially useful explanatory framework of variation in social worker stress, emotional exhaustion, and depersonalisation. This study also provided evidence that several CBPM domains could have a direct effect on personal accomplishment. This study provides preliminary evidence that support programmes, which have the capacity to improve each CBPM domain (mindfulness, acceptance, attention regulation/decentering, self-compassion, non-attachment, and non-aversion) and reduce experiences of worry and rumination, are likely to support social workers to experience reduced stress, emotional exhaustion, depersonalisation of service users, and improvements in personal accomplishment.

Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given some other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the nonzero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical Lasso with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract interesting extremal structures with meaningful domain-specific interpretations.