Numerical Algorithm Research Articles

A numerical algorithm with parallel implementation for variable-order fractional mobile/immobile equation

A numerical algorithm with parallel implementation for variable-order fractional mobile/immobile equation

Study on the effects of material hardening on the development of high-speed rail corrugation

To investigate the effect of material hardening on corrugation development, a theoretical model for corrugation development is proposed, which incorporates the consideration of material properties’ variation. Experiments were conducted to reproduce the corrugation phenomenon, and the mechanical properties of the hardened layer in corrugated rail were obtained utilizing Nano-indentation experiment. The corrugation depth gradually increased and eventually stabilized with the increase of rolling cycles, and the corrugation troughs exhibit greater material hardening compared to the peaks. The numerical algorithm for the corrugation development model was developed and the processes of corrugation development under conditions with and without material hardening were simulated. The growth of corrugation calculated using the model without material hardening exhibits a continual exponential increase with the number of wheel passages, which does not agree with what was observed in experiments and in the field. However, when considering material hardening, the development process of corrugation could be accurately reproduced.

Numerical Approaches in Nonlinear Fourier Transform‐Based Signal Processing for Telecommunications

ABSTRACTWe discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time‐domain signal processing techniques. Our main focus is on the challenges and recent progress in the development of efficient numerical algorithms and approaches to NFT implementation.

Comparative Analysis of Analogue and Digital Methods for Magnetic Flux Estimation in the Core of a Medium-Voltage Voltage Transformer Operating Under Ferroresonance Conditions

The main objective of the research described in the article was to determine the following: Is it possible to estimate the magnetic flux linkage in the core of a voltage transformer using analogue or digital methods? Will it be possible to estimate it approximately both in the normal state and in the state of deep core saturation (ferroresonant state)? The research aimed to identify the advantages and disadvantages of both proposed estimation methods. As part of the research described in this paper, a simulation model was developed and executed in the MATLAB/Simulink environment to generate a series of secondary voltage and flux waveforms in voltage transformers. The secondary voltage and flux waveforms were modelled under ground fault conditions, initiating ferroresonance oscillations in the medium-voltage network. To determine the associated flux from the simulated secondary voltages of the voltage transformers, an analogue integration circuit, a voltage analogue input circuit and a numerical integration algorithm with offset elimination were developed and implemented in an STM32 microcontroller. The obtained reference flux waveforms were used to verify the accuracy of the estimation of flux waveforms obtained using the analogue and digital methods. As a result, it was determined that both methods allow for a relatively accurate estimation of the periodic component of the magnetic flux. It also presented how both methods respond to the presence of slowly changing (aperiodic) components. Possible applications were proposed in order to create an innovative criterion for detecting ferroresonance oscillations.

OPTIMIZATION APPROACH FOR SOLVING THE CONTINUATION PROBLEM IN FREQUENCY DOMAIN

The paper presents analytical expressions for solving the problem of continuation of the electromagnetic field in the frequency domain for a horizontally layered medium. The numerical solution algorithm uses layerwise recalculation of the required quantities, for which analytical expressions are presented in a form that allows calculations and layerwise recalculation without the accumulation of rounding errors. The solution to the continuation problem is obtained as a solution to the cost functional minimization problem. The strong convexity of the functional is proven, which implies the existence of a unique solution to the problem posed. Before solving the continuation problem, it is proposed to apply the Butterworth filter to smooth the radargrams and the Hilbert transform technique to clarify the coordinates of the discontinuity points of the medium.

Efficient distribution network based on photovoltaic fed electric vehicle charging station using WSO-RBFNN approach

An integral and prevalent aspect of modern life is the electric vehicle (EV).EV charging networks struggle with power losses and high energy costs, particularly as demand rises leading to inefficiencies and potential system overloads. A hybrid WSO-RBFNN approach is proposed for the distribution network's photovoltaic (PV) fed electric vehicle charging stations. The performance of the proposed hybrid strategy is a combination of war strategy optimization (WSO) and Radial basis function neural network (RBFNN). It is hence referred to as the WSO-RBFNN technique. WSO optimizes the distribution network by minimizing power loss, improving voltage sensitivity, and reducing costs. Meanwhile, the RBFNN predicts the load demand. This innovative technique WSO-RBFNN identifies the nearest charging spots that minimize power loss and RBFNN optimizes power flow predicts charging demands and addresses both environmental and electrical grid stability concerns. The proposed technique is implemented in MATLAB. MATLAB is powerful computational software widely used in different fields like numerical computation, visualization, and algorithm development. MATLAB provides powerful tools for data visualization and plotting. The results are compared to various existing Heap-based optimizer (HBO), Wild horse optimizer (WHO), and Salp Swarm Algorithm (SSA) techniques. The proposed approach contributes only 0.59 % of a power loss it is less and the cost of energy is 0.18$ which is lesser and the voltage deviation is 6.6 pu which is less than the existing techniques.

Self-Organization of Square Nitrogen Islands on Copper (100) Surfaces: Island Pair Distributions Based on an Ab-Initio DFT and Mesoscopic Interaction Model.

Earlier scanning tunneling microscopy (STM) studies have shown that nitrogen forms square c(2×2) islands on Cu(100) surfaces, the assembly of which depends on coverage. Recent calculations have revealed that adatom-adatom interactions are compatible with the formation of square c(2×2) islands. The pair distribution of these islands is a topic of the current investigation. In addition, the domain structure of islands found recently in STM experiments is discussed and explained using two types of island interactions. The potential used for the interaction between N square islands on copper is a combination of previous ab initio calculations and an updated mesoscopic interaction scheme. The 2D-BGY integral equation is extended to handle binary objects like two different types of islands. It is solved for up to a quarter island coverage using a numerical recursion algorithm. Coverage beyond half is accessible with island vacancy symmetry. The calculation predicts the formation of ordered island assemblies with increasing coverage. These results reasonably explain the previous experimental observations. The handling of binary objects also seems to be applicable to assemblies of two adatom types as found in catalysis. The assumptions and limitations of the model are discussed and open questions are formulated.

Tightly Coupled SLAM Algorithm Based on Similarity Detection Using LiDAR-IMU Sensor Fusion for Autonomous Navigation

In recent years, the rise of unmanned technology has made Simultaneous Localization and Mapping (SLAM) algorithms a focal point of research in the field of robotics. SLAM algorithms are primarily categorized into visual SLAM and laser SLAM, based on the type of external sensors employed. Laser SLAM algorithms have become essential in robotics and autonomous driving due to their insensitivity to lighting conditions, precise distance measurements, and ease of generating navigation maps. Throughout the development of SLAM technology, numerous effective algorithms have been introduced. However, existing algorithms still encounter challenges, such as localization errors and suboptimal utilization of sensor data. To address these issues, this paper proposes a tightly coupled SLAM algorithm based on similarity detection. The algorithm integrates Inertial Measurement Unit (IMU) and LiDAR odometry modules, employs a tightly coupled processing approach for sensor data, and utilizes curvature feature optimization extraction methods to enhance the accuracy and robustness of inter-frame matching. Additionally, the algorithm incorporates a local keyframe sliding window method and introduces a similarity detection mechanism, which reduces the real-time computational load and improves efficiency. Experimental results demonstrate that the algorithm achieves superior performance, with reduced positioning errors and enhanced global consistency, in tests conducted on the KITTI dataset. The accuracy of the real trajectory data compared to the ground truth is evaluated using metrics such as ATE (absolute trajectory error) and RMSE (root mean square error).

Numerical algorithms based on splines for singularly perturbed parabolic partial differential equations with mixed shifts

In this paper, we discuss singularly perturbed time-dependent convection–diffusion problems that arise in computational neuroscience. Specifically, we provide approaches for one-dimensional singularly perturbed parabolic partial differential difference equations (SPPPDDEs) with mixed shifts in the spatial variable using fitted operator spline in compression and adaptive spline. Temporal discretization is done by backward Euler’s method, and spline methods with exponential fitting on uniform mesh are implemented in the spatial domain. For better approximations, the Richardson extrapolation technique is used, which is demonstrated by two numerical examples. The convergence of the proposed methods is investigated and found to be uniform with respect to the perturbation parameter. Graphical representations are provided to show how the shifts affect the proposed solution to the problem.

A novel AI model for detecting periapical lesion on CBCT: CBCT-SAM.

Periapical lesions are not always evident on radiographic scans. Sometimes, asymptomatic or initial periapical lesions on cone-beam computed tomography (CBCT) could be missed by inexperienced dentists, especially when the scan has a large field of view and is not for endodontic treatment purposes. Previously, numerous algorithms have been introduced to assist radiographic assessment and diagnosis in the field of endodontics. This study aims to investigate the efficacy of CBCT-SAM, a new artificial intelligence (AI) model, in identifying periapical lesions on CBCT. Model training and validation in this study was performed using 185 CBCT scans with confirmed periapical lesions. Manual segmentation labels were prepared by a trained operator and validated by a maxillofacial radiologist. The diagnostic and segmentation performances of four AI models were evaluated and compared: CBCT-SAM, CBCT-SAM without progressive Prediction Refinement Module (PPR), and two previously developed models: Modified U-Net and PAL-Net. Accuracy was used to evaluated the diagnostic performance of the models, and accuracy, sensitivity, specificity, precision and Dice Similarity Coefficient (DSC) were used to evaluate the models' segmentation performance. CBCT-SAM achieved an average diagnostic accuracy of 98.92% ± 010.37% and an average segmentation accuracy of 99.65% ± 0.66%. The average sensitivity, specificity, precision and DSC were 72.36 ± 21.61%, 99.87% ± 0.11%, 0.73 ± 0.21 and 0.70 ± 0.19. CBCT-SAM and PAL-Net performed significantly better than Modified U-Net in segmentation accuracy (p = 0.023, p = 0.041), sensitivity (p = 0.000, p = 0.002), and DSC (p= 0.001, p= 0.004). There is no significant difference between CBCT-SAM, CBCT-SAM without PPR and PAL-Net. However, with PPR incorporated into the model, CBCT-SAM slightly surpassed PAL-Net in the diagnostic and segmentation tasks. CBCT-SAM is capable of providing expert-level assistance in the identification of periapical lesions on CBCT. The application of artificial intelligence could increase dentists' chairside diagnostic accuracy and efficiency. By assisting radiographic assessment, such as periapical lesions on CBCT, it helps reduce the chance of missed diagnosis by human errors and facilitates early detection and treatment of dental pathologies at the early stage.

Deterministic Gradient-Descent Learning of Linear Regressions: Adaptive Algorithms, Convergence Analysis and Noise Compensation.

Weight learning forms a basis for the machine learning and numerous algorithms have been adopted up to date. Most of the algorithms were either developed in the stochastic framework or aimed at minimization of loss or regret functions. Asymptotic convergence of weight learning, vital for good output prediction, was seldom guaranteed for online applications. Since linear regression is the most fundamental component in machine learning, we focus on this model in this paper. Aiming at online applications, a deterministic analysis method is developed based on LaSalle's invariance principle. Convergence conditions are derived for both the first-order and the second-order learning algorithms, without resorting to any stochastic argument. Moreover, the deterministic approach makes it easy to analyze the noise influence. Specifically, adaptive hyperparameters are derived in this framework and their tuning rules disclosed for the compensation of measurement noise. Comparison with four most popular algorithms validates that this approach has a higher learning capability and is quite promising in enhancing the weight learning performance.

Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties and graded meshes

The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard isogeometric analysis is proposed in this paper by using a single-patch graded mesh refinement scheme. Numerical tests demonstrate optimal convergence rates for both the eigenvalues and eigenfunctions. Furthermore, the results show that smooth splines possess a superior approximation constant compared to their C0-continuous counterparts for the lower part of the Laplace spectrum. This is an extension of previous findings about excellent spectral approximation properties of smooth splines on rectangular domains to circular sectors. In addition, graded meshes prove to be particularly advantageous for an accurate approximation of a limited number of eigenvalues. Finally, a hierarchical mesh structure is presented to avoid anisotropic elements in the physical domain and to omit redundant degrees of freedom in the vicinity of the singularity. Numerical results validate the effectiveness of hierarchical mesh grading for simulating eigenfunctions of low and high regularity.

Multi-view structural twin support vector machine with the consensus and complementarity principles and its safe screening rules

Nowadays, numerous multi-view algorithms are proposed to achieve better performance in classification tasks. In this article, we propose a multi-view structural twin support vector machine (MvSTSVM), which is guided by both complementarity and consensus principles. In order to keep the consensus information, structural information of inter-class and intra-class is explored in two hyperplanes by clustering methods, which significantly enhances the classification performance. Besides, MvSTSVM introduces the weights to multi-view datasets to dig the complementarity information among different views. In addition, our model achieves both intra-class compactness and inter-class separability. To deal with the optimization problems, an iterative strategy is adopted for the solution of MvSTSVM. Moreover, we derive the safe screening rules for MvSTSVM, which speed up the tuning process obviously without sacrificing accuracy. A series of numerical experiments confirm the effectiveness of MvSTSVM and the safety of proposed screening rules.

A Survey on Self-Supervised Learning: Algorithms, Applications, and Future Trends.

Deep supervised learning algorithms typically require a large volume of labeled data to achieve satisfactory performance. However, the process of collecting and labeling such data can be expensive and time-consuming. Self-supervised learning (SSL), a subset of unsupervised learning, aims to learn discriminative features from unlabeled data without relying on human-annotated labels. SSL has garnered significant attention recently, leading to the development of numerous related algorithms. However, there is a dearth of comprehensive studies that elucidate the connections and evolution of different SSL variants. This paper presents a review of diverse SSL methods, encompassing algorithmic aspects, application domains, three key trends, and open research questions. First, we provide a detailed introduction to the motivations behind most SSL algorithms and compare their commonalities and differences. Second, we explore representative applications of SSL in domains such as image processing, computer vision, and natural language processing. Lastly, we discuss the three primary trends observed in SSL research and highlight the open questions that remain.

High-fidelity synthesis with causal disentangled representation

There exists a general problem in numerous disentangled representation learning algorithms that improves disentanglement performance by sacrificing generation performance. In order to solve the contradiction between disentanglement and generative performance, we propose a high-fidelity synthetic causal disentangled representation learning framework (HCAPE) combining Variational Auto-Encoder (VAE) and Generative Adversarial Network (GAN). First, in the inference stage, the assumption that the latent factors of the variation are mutually independent is abandoned. And a Structural Causal Model (SCM) in the encoder is resorted to learn causal representations. Second, a supervision term and balance parameter η were introduced to reduce the interference of disentanglement performance on generation performance. Finally, in the generation stage, a discriminator estimates the model’s gradient information, restoring high-frequency details in the image, thus synthesizing high-fidelity images. Experimental results show that the causal representations learned by the model are semantically interpretable and can generate counterfactual data. Most importantly, the model is able to generate high-fidelity images, achieving an optimal balance between disentangling and generative performance.

Holistic numerical simulation of a quenching process on a real-size multifilamentary superconducting coil

Superconductors play a crucial role in the advancement of high-field electromagnets. Unfortunately, their performance can be compromised by thermomagnetic instabilities, wherein the interplay of rapid magnetic and slow heat diffusion can result in catastrophic flux jumps, eventually leading to irreversible damage. This issue has long plagued high-Jc Nb3Sn wires at the core of high-field magnets. In this study, we introduce a large-scale GPU-optimized algorithm aimed at tackling the complex intertwined effects of electromagnetism, heating, and strain acting concomitantly during the quenching process of superconducting coils. We validate our model by conducting comparisons with magnetization measurements obtained from short multifilamentary Nb3Sn wires and further experimental tests conducted on solenoid coils while subject to ramping transport currents. Furthermore, leveraging our developed numerical algorithm, we unveil the dynamic propagation mechanisms underlying thermomagnetic instabilities (including flux jumps and quenches) within the coils. Remarkably, our findings reveal that the velocity field of flux jumps and quenches within the coil is correlated with the cumulated Joule heating over a time interval rather than solely being dependent on instantaneous Joule heating power or maximum temperature. These insights have the potential to optimize the design of next-generation superconducting magnets, thereby directly influencing a wide array of technologically relevant and multidisciplinary applications.

Conservative numerical algorithm for simulating thermoelectrical semiconductor device with unconditional optimal convergence analysis

We propose conservative type numerical method to simulate thermoelectrical semiconductor device problem, in which mixed finite element method used for electric potential equation, conservative characteristic finite element method for electron and hole concentration equations, and standard finite element method for heat conduction equation. By temporal-spatial error splitting argument, the optimal error estimates without certain time step restriction are derived, and low order convergence rate of electrostatic potential and electric field intensity will not affect the accuracy of the electron, hole density and temperature. Numerical tests are performed to validate the theoretical results and application performance of the given method.

Optimal one-sided approximants of circular arc

The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants interpolating boundary points is assumed. However, the study of approximants, which additionally interpolate corresponding tangent directions and curvatures at the boundary of an arc, is also considered. Several low-degree polynomial approximants are studied in detail. When several solutions fulfilling the interpolation conditions exist, the optimal one is characterized, and a numerical algorithm for its construction is suggested. Theoretical results are demonstrated with several numerical examples and a comparison with general (i.e. non-one-sided) approximants are provided.

Sparsified time-dependent Fourier neural operators for fusion simulations

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

Improving signal-to-noise ratio of Raman measurements based on ensemble learning approach.

Raman spectroscopy is an extensively explored vibrational spectroscopic technique to analyzethebiochemical composition and molecular structure of samples, which is often assumed to be non-destructive when carefully using proper laser power and exposure time. However, the inherentlyweak Raman signal and concurrent fluorescence interference often lead to Raman measurements withalow signal-to-noise ratio (SNR), especially for biological samples. Great efforts have been made to develop experimental approaches and/or numerical algorithms to improvetheSNR. In this study, we proposed an ensemble learning approach to recover and denoise Raman measurements withalow SNR. The proposed ensemble learning approach was evaluated on 986 pairs of Raman measurements, each pair of which consists of a low SNR Raman spectrum and a high SNR reference Raman spectrum from the exact same fungal sample but uses 200 timestheintegration time. Compared with conventional methods, the Raman measurementsrecoveredby the proposed ensemble learning approach are more identical to high SNR reference Raman measurements, with anaverage RMSE and MAE of only 1.337 × 10-2 and 1.066 × 10-2, respectively; thus, the proposed ensemble learning approach is expected to be a powerful tool for numerically improving the SNR of Raman measurements and further benefits rapid Raman acquisition from biological samples.