Search Results (25)

This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs). Full article

This paper studies the safe trajectory tracking control of intelligent vehicles, which is still an open and challenging problem. A deep reinforcement learning algorithm based on augmented Lagrangian safety constraints is proposed to the lateral control of vehicle trajectory tracking. First, the tracking control of intelligent vehicles is described as a reinforcement learning process based on the Constrained Markov Decision Process (CMDP). The actor-critic neural network based reinforcement learning framework is established and the environment of reinforcement learning is designed to include the vehicle model, tracking model, road model and reward function. Secondly, the augmented Lagrangian Deep Deterministic Policy Gradient (DDPG) method is proposed for updating, in which a replay separation buffer method is used to solve the problem of sample correlation, and a neural network with the same structure is copied to solve the update divergence problem. Finally, a vehicle lateral control approach is obtained, whose effectiveness and advantages over existing results are verified through simulation results. Full article

Noises and outliers often degrade the final prediction performance in practical data processing. Multi-view learning by integrating complementary information across heterogeneous modalities has become one of the core techniques in the field of machine learning. However, existing methods rely on explicit-view clustering and stringent alignment assumptions, which affect the effectiveness in addressing the challenges such as inconsistencies between views, noise interference, and misalignment across different views. To alleviate these issues, we present a latent multi-view representation learning model based on low-rank embedding by implicitly uncovering the latent consistency structure of data, which allows us to achieve robust and efficient multi-view feature fusion. In particular, we utilize low-rank constraints to construct a unified latent subspace representation and introduce an adaptive noise suppression mechanism that significantly enhances robustness against outliers and noise interference. Moreover, the Augmented Lagrangian Multiplier Alternating Direction Minimization (ALM-ADM) framework enables efficient optimization of the proposed method. Experimental results on multiple benchmark datasets demonstrate that the proposed approach outperforms existing state-of-the-art methods in both clustering performance and robustness. Full article

Two-phase evaporative spray cooling technology can significantly reduce power consumption in data centre cooling applications. However, the literature lacks an established methodology for assessing the overall performance of such evaporation systems in terms of the water-energy nexus. The current study develops a Lagrangian–Eulerian computational fluid dynamics (CFD) modelling approach to examine the functionality of these two-phase evaporative spray cooling systems. To replicate a modular system, a hollow spray cone nozzle with Rosin–Rammler droplet size distribution is simulated in a turbulent convective natural-air environment. The model was validated against the available experimental data from the literature. Parametric studies on geometric, flow, and climatic conditions, namely, domain length, droplet size, water mass flow rate, temperature, and humidity, were performed. The findings indicate that at elevated temperatures and low humidity, evaporation results in a bulk temperature reduction of up to 12 °C. A specific focus on the climatic conditions of Dublin, Ireland, was used as an example to optimize the evaporative system. A new formulation for the coefficient of performance (COP) is established to assess the performance of the system. Results showed that doubling the injector water mass flow rate improved the evaporated mass flow rate by 188% but reduced the evaporation percentage by 28%, thus reducing the COP. Doubling the domain length improved the temperature drop by 175% and increased the relative humidity by 160%, thus improving the COP. The COP of the evaporation system showed a systematic improvement with a reduction in the droplet size and the mass flow rate for a fixed domain length. The evaporated system COP improves by two orders of magnitude (~90 to 9500) with the reduction in spray Sauter mean diameter (SMD) from 292 μm to 8–15 μm. Under this reduction, close to 100% evaporation rate was achieved in comparison to only a 1% evaporation rate for the largest SMD. It was concluded that the utilization of a fine droplet spray nozzle provides an effective solution for the reduction in water consumption (97% in our case) for data centres, whilst concomitantly augmenting the proportion of evaporation. Full article

Ensuring safety in autonomous driving is crucial for effective motion planning and navigation. However, most end-to-end planning methodologies lack sufficient safety measures. This study tackles this issue by formulating the control optimization problem in autonomous driving as Constrained Markov Decision Processes (CMDPs). We introduce an innovative, model-based approach for policy optimization, employing a conditional Value-at-Risk (VaR)-based soft actor-critic (SAC) to handle constraints in complex, high-dimensional state spaces. Our method features a worst-case actor to ensure strict compliance with safety requirements, even in unpredictable scenarios. The policy optimization leverages the augmented Lagrangian method and leverages latent diffusion models to forecast and simulate future trajectories. This dual strategy ensures safe navigation through environments and enhances policy performance by incorporating distribution modeling to address environmental uncertainties. Empirical evaluations conducted in both simulated and real environments demonstrate that our approach surpasses existing methods in terms of safety, efficiency, and decision-making capabilities. Full article

Multi-label classification has been extensively researched and utilized for several decades. However, the performance of these methods is highly susceptible to the presence of noisy data samples, resulting in a significant decrease in accuracy when noise levels are high. To address this issue, we propose a robust ranking support vector machine (Rank-SVM) method that incorporates manifold regularized matrix factorization. Unlike traditional Rank-SVM methods, our approach integrates feature selection and multi-label learning into a unified framework. Within this framework, we employ matrix factorization to learn a low-rank robust subspace within the input space, thereby enhancing the robustness of data representation in high-noise conditions. Additionally, we incorporate manifold structure regularization into the framework to preserve manifold relationships among low-rank samples, which further improves the robustness of the low-rank representation. Leveraging on this robust low-rank representation, we extract a resilient low-rank features and employ them to construct a more effective classifier. Finally, the proposed framework is extended to derive a kernelized ranking approach, for the creation of nonlinear multi-label classifiers. To effectively solve this non-convex kernelized method, we employ the augmented Lagrangian multiplier (ALM) and alternating direction method of multipliers (ADMM) techniques to obtain the optimal solution. Experimental evaluations conducted on various datasets demonstrate that our framework achieves superior classification results and significantly enhances performance in high-noise scenarios. Full article

When deblurring an image, ensuring that the restored intensities are strictly non-negative is crucial. However, current numerical techniques often fail to consistently produce favorable results, leading to negative intensities that contribute to significant dark regions in the restored images. To address this, our study proposes a mathematical model for non-blind image deblurring based on total fractional-order variational principles. Our proposed model not only guarantees strictly positive intensity values but also imposes limits on the intensities within a specified range. By removing negative intensities or constraining them within the prescribed range, we can significantly enhance the quality of deblurred images. The key concept in this paper involves converting the constrained total fractional-order variational-based image deblurring problem into an unconstrained one through the introduction of the augmented Lagrangian method. To facilitate this conversion and improve convergence, we describe new numerical algorithms and introduce a novel circulant preconditioned matrix. This matrix effectively overcomes the slow convergence typically encountered when using the conjugate gradient method within the augmented Lagrangian framework. Our proposed approach is validated through computational tests, demonstrating its effectiveness and viability in practical applications. Full article

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors $\alpha$, whose values are restricted, to make contact with similar approaches, to the integers $\alpha =[0,1,2]$, allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition. Full article

Deep unrolling networks (DUNs) have emerged as a promising approach for solving compressed sensing (CS) problems due to their superior explainability, speed, and performance compared to classical deep network models. However, the CS performance in terms of efficiency and accuracy remains a principal challenge for approaching further improvements. In this paper, we propose a novel deep unrolling model, SALSA-Net, to solve the image CS problem. The network architecture of SALSA-Net is inspired by unrolling and truncating the split augmented Lagrangian shrinkage algorithm (SALSA) which is used to solve sparsity-induced CS reconstruction problems. SALSA-Net inherits the interpretability of the SALSA algorithm while incorporating the learning ability and fast reconstruction speed of deep neural networks. By converting the SALSA algorithm into a deep network structure, SALSA-Net consists of a gradient update module, a threshold denoising module, and an auxiliary update module. All parameters, including the shrinkage thresholds and gradient steps, are optimized through end-to-end learning and are subject to forward constraints to ensure faster convergence. Furthermore, we introduce learned sampling to replace traditional sampling methods so that the sampling matrix can better preserve the feature information of the original signal and improve sampling efficiency. Experimental results demonstrate that SALSA-Net achieves significant reconstruction performance compared to state-of-the-art methods while inheriting the advantages of explainable recovery and high speed from the DUNs paradigm. Full article

To improve the fatigue resistance of engineering structures, topology optimization has always been an effective design strategy. The direct calculation of large-scale local fatigue constraints remains a challenge due to high computational cost. In the past, the constraint aggregation techniques, such as the P-norm method, were often applied to aggregate local fatigue constraints into a global constraint, whereas the resultant optimal solution was not consistent with the original problem. In order to meet the local fatigue constraints accurately and reduce the number of constraints, the augmented Lagrangian scheme is employed to transform the original problem into the unconstrained problem. To evaluate the fatigue strength at every material point of structures under the proportional load with variable amplitude, we adopt the Sines fatigue criterion based on the Palmgren–Miner linear damage assumption. In addition, we solve the fatigue-constrained topology optimization problem on the unstructured polygonal meshes, which are not sensitive to numerical instabilities, such as checkerboard patterns, compared with lower-order triangular and bilateral meshes. We provide some numerical examples to validate the potential of the presented method to solve the fatigue-constrained topology optimization problem. Numerical results demonstrate that the optimized designs considering local fatigue constraints have a higher ratio of fatigue resistance to material consumption than those obtained through the traditional P-norm method. Therefore, the proposed approach retaining the local nature of fatigue constraints is more beneficial for realizing the efficient material utilization in structural topology. Full article

The aim of fusing hyperspectral and multispectral images is to overcome the limitation of remote sensing hyperspectral sensors by improving their spatial resolutions. This process, also known as hypersharpening, generates an unobserved high-spatial-resolution hyperspectral image. To this end, several hypersharpening methods have been developed, however most of them do not consider the spectral variability phenomenon; therefore, neglecting this phenomenon may cause errors, which leads to reducing the spatial and spectral quality of the sharpened products. Recently, new approaches have been proposed to tackle this problem, particularly those based on spectral unmixing and using parametric models. Nevertheless, the reported methods need a large number of parameters to address spectral variability, which inevitably yields a higher computation time compared to the standard hypersharpening methods. In this paper, a new hypersharpening method addressing spectral variability by considering the spectra bundles-based method, namely the Automated Extraction of Endmember Bundles (AEEB), and the sparsity-based method called Sparse Unmixing by Variable Splitting and Augmented Lagrangian (SUnSAL), is introduced. This new method called Hyperspectral Super-resolution with Spectra Bundles dealing with Spectral Variability (HSB-SV) was tested on both synthetic and real data. Experimental results showed that HSB-SV provides sharpened products with higher spectral and spatial reconstruction fidelities with a very low computational complexity compared to other methods dealing with spectral variability, which are the main contributions of the designed method. Full article

In this paper, we present a new explicit second-order accurate structure-preserving finite volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg equations. The model combines the unified Godunov-Peshkov-Romenski model of continuum mechanics with a recently proposed hyperbolic reformulation of the Euler–Korteweg system. The considered PDE system includes an evolution equation for a gradient field that is by construction endowed with a curl-free constraint. The new numerical scheme presented here relies on the use of vertex-based staggered grids and is proven to preserve the curl constraint exactly at the discrete level, up to machine precision. Besides a theoretical proof, we also show evidence of this property via a set of numerical tests, including a stationary droplet, non-condensing bubbles as well as non-stationary Ostwald ripening test cases with several bubbles. We present quantitative and qualitative comparisons of the numerical solution, both, when the new structure-preserving discretization is applied and when it is not. In particular for under-resolved simulations on coarse grids we show that some numerical solutions tend to blow up when the curl-free constraint is not respected. Full article

The turbulence of a realistic dilute solution of DNA macromolecules is investigated through a hybrid Eulerian–Lagrangian approach that directly solves the incompressible Navier–Stokes equation alongside the evolution of ${10}^8$ polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells. At a friction Reynolds number of 320 and a Weissenberg number of $2\times {10}^4$, the drag reduction is equal to 26%, which is similar to the one obtained at the lower Reynolds number of 180. The polymers induce an increase in the flow rate and the turbulent kinetic energy, whose axial contribution is predominantly augmented. The stress balance is analysed to investigate the causes of the drag reduction and eventually the effect of the friction Reynolds number on the probability distribution of the polymer configuration. Near the wall, the majority of the polymers are fully stretched and aligned along the streamwise direction, inducing an increase in the turbulence anisotropy. Full article

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs. Full article

This paper proposes centralized and distributed optimization models for V2G applications to provide frequency regulation in power systems and the electricity market. Battery degradation and dynamic $EV$ usages such as $EV$ driving period, driving distance, and multiple charging/discharging locations are modeled. The centralized V2G problem is formulated into the linear programming (LP) model by introducing two sets of slack variables. However, the centralized model encounters limitations such as privacy concerns, high complexity, and central failure issues. To overcome these limitations, the distributed optimal V2G model is developed by decomposing the centralized model into subproblems using the augmented Lagrangian relaxation (ALR) method. The alternating direction method of multipliers (ADMM) is used to solve the distributed V2G model iteratively. The proposed models are evaluated using real data from the Independent Electricity System Operator (IESO) Ontario, Canada. Simulation results show that the proposed models can aggregate EVs for frequency regulation; meanwhile, the $EV$ owners can obtain monetary rewards. The simulation also shows that including battery degradation and dynamic $EV$ usage increases the model accuracy. By using the proposed approaches, the high cost and the low efficiency power generation units for frequency regulation can be compensated or partially replaced by EVs, which will reduce the generation cost and greenhouse gas emissions. Full article