Gradient Method Research Articles

Deep reinforcement learning-based low-latency task offloading for mobile-edge computing networks

Wireless Mobile Edge Computing (MEC) is an emerging solution to facilitate users’ computing. However, there are still some drawbacks, such as slow learning speed and high task latency. To overcome these difficulties, a deep reinforcement learning (DRL)-based task offloading (DRTO) framework is proposed, taking into account the time-varying nature of wireless channels and the unpredictability of task arrivals in multi-user MEC systems. Many deep neural networks (DNNs) are also used as scalable solutions to quickly determine the best offloading strategy by combining the perceptual capabilities of deep learning with the decision making capabilities of reinforcement learning (RL). Additionally, the concept of a minimum upper bound on the target Q-value is utilized to address the value overestimation problem that occurs during offload policy updates. This approach aims to minimize the latency of offload decisions by considering different channel environments, variable latency constraints among many users, and limited computational resources. Simulation results show that the algorithm reduces computation time and latency while achieving near-optimal performance compared to traditional Deep Deterministic Policy Gradient (DDPG) and Q-learning optimization methods. In addition, DRTO achieves more than 99.6% computational speedup compared to current almost ideal benchmarking techniques. Thus, the DRTO computational offload approach offers great potential for reducing overall system latency and improving the user experience.

Identification of the bridge moving loads based on fractional conjugate gradient method

Identification of the bridge moving loads based on fractional conjugate gradient method

Hybrid two-level protection system for preserving pre-trained DNN models ownership

AbstractRecent advancements in deep neural networks (DNNs) have made them indispensable for numerous commercial applications. These include healthcare systems and self-driving cars. Training DNN models typically demands substantial time, vast datasets and high computational costs. However, these valuable models face significant risks. Attackers can steal and sell pre-trained DNN models for profit. Unauthorised sharing of these models poses a serious threat. Once sold, they can be easily copied and redistributed. Therefore, a well-built pre-trained DNN model is a valuable asset that requires protection. This paper introduces a robust hybrid two-level protection system for safeguarding the ownership of pre-trained DNN models. The first-level employs zero-bit watermarking. The second-level incorporates an adversarial attack as a watermark by using a perturbation technique to embed the watermark. The robustness of the proposed system is evaluated against seven types of attacks. These are Fast Gradient Method Attack, Auto Projected Gradient Descent Attack, Auto Conjugate Gradient Attack, Basic Iterative Method Attack, Momentum Iterative Method Attack, Square Attack and Auto Attack. The proposed two-level protection system withstands all seven attack types. It maintains accuracy and surpasses current state-of-the-art methods.

Prediction of dynamic behaviors of vibrational-powered electromagnetic generators: Synergies between analytical and artificial intelligence modelling

The electric efficiency of vibrational electromagnetic generators is highly dependent on their ability to ensure effective adaptability to uncertain and irregular dynamics of mechanical energy sources. Such adaptive ability demands a planning operation considering future information of the highly nonlinear dynamics of these generators and mechanical excitations patterns. High accurate energy predictions are then mandatory for high energy generation efficiencies. However, on the one hand, high prediction accuracy by analytical modelling from first principles requires high modelling complexity; on the other hand, artificial intelligence models ensuring high prediction accuracy have not yet been explored to enhance the performance of these generators, even though their pre-training holds potential to significantly reduce the energy production costs. We here provide a multifaceted study highlighting the synergies between analytical and artificial intelligence modelling for optimizing the efficiency of vibrational-powered electromagnetic generators. Two main innovations are introduced: (1) development and experimental validation of a time-series forecasting artificial intelligence model based on the deep deterministic policy gradient method; (2) validation of a pre-training scenario by analytical modelling ⟶ artificial intelligence modelling synergy. Both the analytical and artificial intelligence models were able to provide high prediction accuracies to periodic and random 3D motions combining translations and rotations. Moreover, the pre-training scenario, using simulation training data sets, ensures prediction accuracies within the ±20% absolute error surfaces, profiling approximately normal distributions centered at approximately null error. These are impacting results in the scope of vibrational electromagnetic generation, holding potential to be extended to innovative self-adaptive electromagnetic generators, including those with ability to absorb complex 6 DOF external mechanical excitations. Besides, it can support the implementation of high-performance AI modelling⟶analytical modelling synergies, aiming to re-parameterize the high complex analytical models throughout the EMG operation, such that a superior controllability of the adaptive systems can be achieved.

An interpretable hybrid spatiotemporal fusion method for ultra-short-term photovoltaic power prediction

An interpretable hybrid spatiotemporal fusion method for ultra-short-term photovoltaic power prediction

Ultrathin Ge-YF3 antireflective coating with 0.5 % reflectivity on high-index substrate for long-wavelength infrared cameras

Abstract Achieving long-wavelength infrared (LWIR) cameras with high sensitivity and shorter exposure times faces challenges due to series reflections from high-refractive index lenses within compact optical systems. However, designing effective antireflective coatings to maximize light throughput in these systems is complicated by the limited range of transparent materials available for the LWIR. This scarcity narrows the degrees of freedom in design, complicating the optimization process for a system that aims to minimize the number of physical layers and address the inherent large refractive mismatch from high-index lenses. In this study, we use discrete-to-continuous optimization to design a subwavelength-thick antireflective multilayer coating on high-refractive index Si substrate for LWIR cameras, where the coating consists of few (e.g., five) alternating stacks of high- and low-refractive-index thin films (e.g., Ge-YF3, Ge-ZnS, or ZnS-YF3). Discrete optimization efficiently reveals the configuration of physical layers through binary optimization supported by a machine learning model. Continuous optimization identifies the optimal thickness of each coating layer using the conventional gradient method. As a result, considering the responsivity of a LWIR camera, the discrete-to-continuous strategy finds the optimal design of a 2.3-μm-thick antireflective coating on Si substrate consisting of five physical layers based on the Ge-YF3 high-low index pair, showing an average reflectance of 0.54 % within the wavelength range of 8–13 μm. Moreover, conventional thin-film deposition (e.g., electron-beam evaporator) techniques successfully realize the designed structure, and Fourier-transform infrared spectroscopy (FTIR) and thermography confirm the high performance of the antireflective function.

The Proximal Gradient Method for Composite Optimization Problems on Riemannian Manifolds

In this paper, the composite optimization problem is studied on Riemannian manifolds. To tackle this problem, the proximal gradient method to solve composite optimization problems is proposed on Riemannian manifolds. Under some reasonable conditions, the convergence of the proximal gradient method with the backtracking procedure in the nonconvex case is presented. Furthermore, a sublinear convergence rate and the complexity result of the proximal gradient method for convex case are also established on Riemannian manifolds.

Numerical Solution of the Cauchy Problem for the Helmholtz Equation Using Nesterov’s Accelerated Method

In this paper, the Cauchy problem for the Helmholtz equation, also known as the continuation problem, is considered. The continuation problem is reduced to a boundary inverse problem for a well-posed direct problem. A generalized solution to the direct problem is obtained and an estimate of its stability is given. The inverse problem is reduced to an optimization problem solved using the gradient method. The convergence of the Landweber method with respect to the functionals is compared with the convergence of the Nesterov method. The calculation of the gradient in discrete form, which is often used in the numerical solutions of the inverse problem, is described. The formulation of the conjugate problem in discrete form is presented. After calculating the gradient, an algorithm for solving the inverse problem using the Nesterov method is constructed. A computational experiment for the boundary inverse problem is carried out, and the results of the comparative analysis of the Landweber and Nesterov methods in a graphical form are presented.

Isosurface-based marching cube algorithm for smooth geometric topology optimization within adaptive octree SBFE approach

In the era of Industry 4.0, the prominence of 3D printing as a pivotal manufacturing technology has greatly expanded, particularly within the domain of additive manufacturing (AM). Among the thriving research applications tailored for integration with AM, topology optimization (TO) has emerged as a resounding success. Given the prerequisite of TO for high-resolution meshing to ensure visual clarity in result depiction, researchers have been consistently driven to develop advanced techniques to refine optimal designs, thus elevating the challenge and popularity within this research realm. This paper presents a novel approach integrating an adaptive image-based octree mesh scaled boundary finite element (SBFE) framework with an evolutionary methodology that can effectively address the persistent challenges inherent to TO. A novel hierarchical SBFE mesh analysis not only facilitates efficient and precise TO but also substantially reduces computational resource demands. Furthermore, the pre-conditioned conjugated gradient (PCG) method is adopted to process practical-scale problems, minimizing computer memory resources. Additionally, the proposed work incorporates a post-processing technique utilizing the isosurface function based on a marching cube algorithm, thereby smoothing the boundaries of optimal results. Consequently, this research extends the horizons of design possibilities, particularly in the creation of intricate 3D structures, which can be seamlessly realized through additive manufacturing and 3D printing.

Design of Diffractive Neural Networks for Solving Different Classification Problems at Different Wavelengths

We consider the problem of designing a diffractive neural network (DNN) consisting of a set of sequentially placed phase diffractive optical elements (DOEs) and intended for the optical solution of several given classification problems at different operating wavelengths, so that each classification problem is solved at the corresponding wavelength. The problem of calculating the DNN is formulated as the problem of minimizing a functional that depends on the functions of the diffractive microrelief height of the DOEs constituting the DNN and represents the error in solving the given classification problems at the operating wavelengths. We obtain explicit and compact expressions for the derivatives of this functional, and using them, we formulate a gradient method for the DNN calculation. Using this method, we design DNNs for solving the following three classification problems at three different wavelengths: the problem of classifying handwritten digits from the MNIST database, the problem of classifying fashion products from the Fashion MNIST database, and the problem of classifying ten handwritten letters from the EMNIST database. The presented simulation results of the designed DNNs demonstrate the high performance of the proposed method.

Convergence analysis of a novel high order networks model based on entropy error function

It is generally known that the error function is one of the key factors that determine the convergence, stability and generalization ability of neural networks. For most feedforward neural networks, the squared error function is usually chosen as the error function to train the network. However, networks based on the squared error function can lead to slow convergence and easily fall into local optimum in the actual training process. Recent studies have found that, compared to the squared error function, the gradient method based on the entropy error function measures the difference between the probability distribution of the model output and the probability distribution of the true labels during the iterative process, which can be more able to handle the uncertainty in the classification problem, less likely to fall into a local optimum and can learn to converge more rapidly. In this paper, we propose a batch gradient method for Sigma-Pi-Sigma neural networks based on the entropy error function and rigorously demonstrate the weak and strong convergence of the new algorithm in the batch input mode. Finally, the theoretical results and effectiveness of the algorithm are verified by simulation.

Estimation of heat source, specific heat, and thermal conductivity of insulation materials using modified conjugate gradient method

The use of insulation materials is crucial for minimizing thermal losses in various industries like automotive, building, solar, and aerospace. Plexiglass and Expanded Polystyrene (EPS) foam are popular choices due to their effective temperature regulation, lightweight nature, and cost-effectiveness. Accurate measurement of their thermal properties is vital for achieving conservation goals. While the parallel hot wire technique provides valuable insights, accurately determining heat source strength (HW) poses a challenge, impacting measurement accuracy. To address this, the modified Conjugate Gradient Method (CGM) is employed for simultaneous estimation of thermal conductivity (λ), specific heat (c) and HW of Plexiglass and EPS foam. The direct problem result has been validated with published experimental work that shows deviations less than 2 %. The study investigates the impact of sensor positioning relative to the hot-wire (rm) and introduces artificial Gaussian error with standard deviations (θ) of 0.01 °C, 0.02 °C and 0.1 °C. At θ = 0.1 °C the percentage relative errors in the estimation of λ, c and HW with rm = 5 mm for Plexiglass are 5 %, 1.442 %, and 4.651 % respectively. For EPS foam the corresponding errors are 2.44 %, 1.26 %, and 1.74 %. The modified CGM emerges as a reliable algorithm for the measurement of thermal properties of insulation materials.

Proposed Supercluster-Based UMBBFS Routing Protocol for Emergency Message Dissemination in Edge-RSU for 5G VANET

Vehicular ad hoc networks (VANETs) can bolster road safety through the proactive dissemination of emergency messages (EMs) among vehicles, effectively reducing the occurrence of traffic-related accidents. It is difficult to transmit EMs quickly and reliably due to the high-speed mobility of VANET and the attenuation of the wireless signal. However, poor network design and high vehicle mobility are the two most difficult problems that affect VANET’s network performance. The real-time traffic situation and network dependability will also be significantly impacted by route selection and message delivery. Many of the current works have undergone studies focused on forwarder selection and message transmission to address these problems. However, these earlier approaches, while effective in forwarder selection and routing, have overlooked the critical aspects of communication overhead and excessive energy consumption, resulting in transmission delays. To address the prevailing challenges, the proposed solutions use edge computing to process and analyze data locally from surrounding cars and infrastructure. EDGE-RSUs are positioned by the side of the road. In intelligent transportation systems, this lowers latency and enhances real-time decision-making by employing proficient forwarder selection techniques and optimizing the dissemination of EMs. In the context of 5G-enabled VANET, this paper introduces a novel routing protocol, namely, the supercluster-based urban multi-hop broadcast and best forwarder selection protocol (UMB-BFS). The improved twin delay deep deterministic policy gradient (IT3DPG) method is used to select the target region for emergency message distribution after route selection. Clustering is conducted using modified density peak clustering (MDPC). Improved firefly optimization (IFO) is used for optimal path selection. In this way, all emergency messages are quickly disseminated to multiple directions and also manage the traffic in VANET. Finally, we plotted graphs for the following metrics: throughput (3.9 kbps), end-to-end delay (70), coverage (90%), packet delivery ratio (98%), packet received (12.75 k), and transmission delay (57 ms). Our approach’s performance is examined using numerical analysis, demonstrating that it performs better than the current methodologies across all measures.

An improved Dai‐Liao‐style hybrid conjugate gradient‐based method for solving unconstrained nonconvex optimization and extension to constrained nonlinear monotone equations

In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.

Preparation and Properties of Waterborne Polyurethane and SBS Composite-Modified Emulsified Asphalt

To address the issue of insufficient durability of traditional modified emulsified asphalt in the application of cold mix and cold paving anti-skid wear layers, this study utilizes cationic waterborne polyurethane (PU+) for composite modification to enhance adhesion and performance across a range of temperatures. Initially, composite-modified emulsified asphalt samples were prepared with varying dosages of PU+ according to a gradient method. Routine performance tests were conducted on the evaporated residues for analysis. Advanced rheological tests, including temperature sweep (TS), frequency sweep (FS), linear amplitude sweep (LAS), and multi-stress creep recovery (MSCR) tests, were performed using a dynamic shear rheometer (DSR). Surface free energy (SFE) tests were conducted with a fully automated surface tension meter (STM). A comprehensive evaluation of the high-temperature rheological properties, fatigue properties, adhesion properties, and water damage resistance of the modified emulsified asphalt residues was carried out. Chemical changes before and after modification were characterized using Fourier transform infrared spectroscopy (FTIR), and the distribution of polymers in the evaporated residue was observed using fluorescence microscopy (FM). The results demonstrated that cationic waterborne polyurethane significantly enhanced the fatigue and adhesion properties of SBS-modified emulsified asphalt, but it also weakened the water damage resistance of asphalt. MSCR tests revealed that the addition of cationic waterborne polyurethane might reduce the elastic recovery performance of modified asphalt, thereby weakening its resistance to rutting. Among the samples, the modified asphalt with a PU+ content of 6% exhibited good high-temperature shear resistance and elastic recovery performance, demonstrating the best anti-rutting performance.

Geophysical structure of a local area in the lunar Oceanus Procellarum region investigated using the gravity gradient method

Geophysical structure of a local area in the lunar Oceanus Procellarum region investigated using the gravity gradient method

Photophysical Response of Propranolol in Biomimetic Micellar Media of Alkyltrimethylammonium Bromide Surfactants: Effect of pH and Alkyl Chain Length.

The photophysical behavior of a β-blocker drug propranolol (PPL) in micellar environments, formed by alkyltrimethylammonium bromide surfactants viz.; Cetyltrimethylammonium bromide (CTAB), Tetradecyltrimethylammonium bromide (TTAB), and Dodecyltrimethylammonium bromide (DTAB), has been investigated through fluorescence and UV-visible spectroscopic techniques at pH levels of 3.5, 7.4, and 10.4. The impact of pH on the critical micelle concentration (cmc) and micropolarity of micelles were assessed using pyrene as a photophysical probe. The cmc values were found to be lower at pH 10.4 compared to pH 7.4 and pH 3.5. Fluorescence emission intensities of PPL at 323nm, 338nm, and 352nm were significantly influenced by pH, hydrophobic alkyl chain length of surfactants, and their concentrations. Quenching experiments with Cetylpyridinium chloride (CpCl) indicated the localization of charged and uncharged forms of PPL within micelles, with quenching constant (Ksv) values dependent on alkyl chain length and pH. At pH < pKa, PPL is positioned near the Stern layer, whereas at pH 10.4, its naphthalene moiety resides near the hydrophobic micellar core. UV spectroscopy showed that the charged form of PPL interacted with micelles only above cmc, while the neutral form interacted even below the cmc. Density Functional Theory (DFT) reveals the HOMO of the surfactants to be localized on the hydrocarbon chains, and the LUMO localized around the quaternary ammonium unit. Upon complexation with PPL, both HOMO and LUMO shifted to the drug, thereby decreasing energy levels. The findings are explained based on weak noncovalent interactions, further supported and analyzed through Reduced Density Gradient (RDG) and Noncovalent Interaction (NCI) methods, confirming synergistic non-covalent interactions in surfactant-PPL complexes.

Nonlinear conjugate gradient methods for unconstrained set optimization problems whose objective functions have finite cardinality

In this paper, we propose nonlinear conjugate gradient methods for unconstrained set optimization problems in which the objective function is given by a finite number of continuously differentiable vector-valued functions. First, we provide a general algorithm for the conjugate gradient method using Wolfe line search but without imposing an explicit restriction on the conjugate parameter. Later, we study two variants of the algorithm, namely Fletcher-Reeves and conjugate descent, using two different choices of the conjugate parameter but with the same line search rule. In the general algorithm, the direction of movement at each iterate is identified by finding out a descent direction of a vector optimization problem. This vector optimization problem is identified with the help of the concept of partition set at the current iterate. As this vector optimization problem is different at different iterations, the conventional conjugate gradient method for vector optimization cannot be straightly extended to solve the set optimization problem under consideration. The well-definedness of the methods is provided. Further, we prove the Zoutendijk-type condition, which assists in proving the global convergence of the methods even without a regular condition of the stationary points. No convexity assumption is assumed on the objective function to prove the convergence. Lastly, some numerical examples are illustrated to exhibit the performance of the proposed method. We compare the performance of the proposed conjugate gradient methods with the existing steepest descent method. It is found that the proposed method commonly outperforms the existing steepest descent method for set optimization.

Surrogate gradient methods for data-driven foundry energy consumption optimization

In many industrial applications, data-driven models are more and more commonly employed as an alternative to classical analytical descriptions or simulations. In particular, such models are often used to predict the outcome of an industrial process with respect to specific quality characteristics from both observed process parameters and control variables. A major step in proceeding from purely predictive to prescriptive analytics, i.e., towards leveraging data-driven models for process optimization, consists of, for given process parameters, determining control variable values such that the output quality improves according to the process model. This task naturally leads to a constrained optimization problem for data-driven prediction algorithms. In many cases, however, the best available models suffer from a lack of regularity: methods such as gradient boosting or random forests are generally non-differentiable and might even exhibit discontinuities. The optimization of these models would therefore require the use of derivative-free techniques. Here, we discuss the use of alternative, independently trained differentiable machine learning models as a surrogate during the optimization procedure. While these alternatives are generally less accurate representations of the actual process, the possibility of employing derivative-based optimization methods provides major advantages in terms of computational performance. Using classical benchmarks as well as a real-world dataset obtained from an industrial environment, we demonstrate that these advantages can outweigh the additional model error, especially in real-time applications.

GPU accelerated sparse curvelet-constrained wavefield reconstruction inversion with source estimation: Application to Chevron Benchmark 2014 blind test data set

Full-waveform inversion (FWI) is a pivotal tool in seismic exploration and seismology but encounters a persistent challenge known as “cycle-skipping,” causing it to frequently converge to local minima. Wavefield reconstruction inversion (WRI) has emerged as a potential solution to mitigate the risk of cycle skipping. Researchers have provided numerical examples indicating that WRI is less prone to being ensnared in local minima caused by the absence of low-frequency component data and the absence of a well-defined initial model compared with conventional FWI. Despite its potential, the computational demands of WRI have hindered its widespread application, especially in scenarios involving ocean towed streamer seismic acquisition and unknown sources, where the augmented systems differ from source to source. In our study, we introduce a novel approach — sparse curvelet-constrained WRI with source estimation (WRI-SE-CC) — accelerated by graphics processing unit (GPU). Real-time source function estimation is achieved through the variable projection method, and noise-related artifacts are suppressed using sparse curvelet constraints. By optimizing the utilization of hundreds of computation processors within a GPU for parallel computing of matrix-vector multiplications, we present a GPU-based grouped conjugate gradient method to accelerate the computation of WRI-SE-CC. Numerical experiments demonstrate a significant 240-fold acceleration compared with the preconditioned conjugate gradient using one CPU core for computations involving multiple sources. Inversion experiments with the overthrust model demonstrate the capability of our method in mitigating local minima and suppressing noise-related artifacts. Furthermore, we validate the framework on the Chevron 2014 blind test data set, showcasing its effectiveness in addressing practical challenges in the field.