Computation Time Research Articles

Stopping criteria for nonlinear variational problems: iterative approach

AbstractIn this paper, we present and study a stopping criteria based on a priori error estimate for nonlinear variational problems. We show that for nonlinear variational problems, the a priori error estimate is divided into two sub errors namely: the discretization error and the linearization error. We then used that representation to devise a stopping criteria that help to reduce the computational time. The methodology is applied to three problems and the numerical results demonstrate the superiority of the new approach.

Improvements for the solution of crack evolution using extended finite element method

It is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement. In this paper, it is shown how to enhance the solution efficiency through a comprehensive mathematical investigation of the solution process using XFEM. A typical example is presented to illustrate the disparities in nodal displacements along the two symmetric faces of the crack resulting from the approximation of XFEM. By analysing the structure and components of the global stiffness matrix, the underlying causes of these discrepancies are identified. Building upon these findings, two improvements of the solution are proposed to gain an acceptable accuracy in computing the nodal displacements. The first improvement consists of the subdivision of the enriched elements depending on the characteristic of the distribution of Gauss points. The second improvement is set by determining the optimal number of Gauss points in each sub-element near the crack tip. To calculate the stress intensity factor of the crack under surface pressure, such improvements are applied in conjunction with the interaction integral method, which significantly reduces computational time and eliminates the influence of surface tractions. The numerical solution is validated by comparing it with the analytical solution and the standard XFEM solution. The proposed improvements can enhance both the accuracy of the solution and the computational efficiency of XFEM.

SMS-Net: Bridging the Gap Between High Accuracy and Low Computational Cost in Pose Estimation

Human pose estimation identifies and classifies key joints of the human body in images or videos. Existing pose estimation methods can precisely capture human movements in real time but require significant computational time and resources, which restricts their usage in specific conditions. Thus, we propose a lightweight pose estimation model—SMS-Net—based on the sequentially stacked structure of the hourglass network. The proposed model uses various lightweight techniques to enable high-speed pose estimation while requiring minimal storage space and computation. Specifically, a shuffle-gated block was introduced to reduce the computational load and number of parameters during the feature extraction process of the encoder composing each hourglass network. A multi-dilation block was used in the decoder to secure the receptive fields of various scales without increasing the computational load. The performance of the proposed model was assessed using the MPII and Common Objects in Context (COCO) datasets used for pose estimation and certain performance metrics and compared with state-of-the-art lightweight pose estimation models. Furthermore, an ablation study was performed to assess the impact of each module on network performance and efficiency. The results demonstrate that the proposed model achieved an improved balance between computational efficiency and performance compared to existing models in human pose estimation. Overall, the study findings can provide a basis for applications in computer vision technology.

Real-Time Evaluation of the Improved Eagle Strategy Model in the Internet of Things

With the rapid expansion of cloud computing and the pervasive growth of IoT across industries and educational sectors, the need for efficient remote data management and service orchestration has become paramount. Web services, facilitated by APIs, offer a modular approach to integrating and streamlining complex business processes. However, real-time monitoring and optimal service selection within large-scale, cloud-based repositories remain significant challenges. This study introduces the novel Improved Eagle Strategy (IES) hybrid model, which uniquely integrates bio-inspired optimization with clustering techniques to drastically reduce computation time while ensuring highly accurate service selection tailored to specific user requirements. Through comprehensive NetLogo simulations, the IES model demonstrates superior efficiency in service selection compared to existing methodologies. Additionally, the IES model’s application through a web dashboard system highlights its capability to manage both functional and non-functional service attributes effectively. When deployed on real-time IoT devices, the IES model not only enhances computation speed but also ensures a more responsive and user-centric service environment. This research underscores the transformative potential of the IES model, marking a significant advancement in optimizing cloud computing processes, particularly within the IoT ecosystem.

A reinforcement learning-based approach for solving multi-agent job shop scheduling problem

Wafer processing is the most expensive, time-consuming, and complex stage in semiconductor manufacturing. It varies significantly based on orders of customers (agents). Optimising the wafer processing flow in a multi-agent scenario can meet customised requirements, speed up delivery, and reduce costs. This work models wafer processing as a multi-agent job shop scheduling problem (MAJSP) with release dates. The objective is to minimise the total weighted makespan of agents. To address both dynamic and static scheduling scenarios in the MAJSP context, two deep reinforcement learning-based (DRL) methods are proposed. In a dynamic scheduling scenario, the statuses of orders and production resources can change at any moment. A DRL method called Graph Transformer Network (GTN) is proposed to rapidly generate high-quality solutions. In a static scheduling scenario, the production plan can be formulated based on predetermined demand and resource conditions. A novel hybrid method (GTN-DABC) that combines GTN with the discrete artificial bee colony algorithm (DABC) is proposed to provide high-quality production plans for manufacturers within an acceptable computation time. Experimental results demonstrate that the proposed GTN outperforms existing heuristics, and the well-designed GTN-DABC is more competitive than other meta-heuristics.

Mapping soil moisture across the UK: assimilating cosmic-ray neutron sensors, remotely sensed indices, rainfall radar and catchment water balance data in a Bayesian hierarchical model

Abstract. Soil moisture is important in many hydrological and ecological processes. However, data sets which are currently available have issues with accuracy and resolution. To translate remotely sensed data to an absolute measure of soil moisture requires mapped estimates of soil hydrological properties and estimates of vegetation properties, and this introduces considerable uncertainty. We present an alternative methodology for producing daily maps of soil moisture over the UK at 2 km resolution (“SMUK”). The method is based on a simple linear statistical model, calibrated with 5 years of daily data from cosmic-ray neutron sensors at ∼ 40 sites across the country. The model is driven by precipitation, humidity, a remotely sensed “soil water index” satellite product and soil porosity. The spatial variation in the parameter describing the soil water retention (and thereby the response to precipitation) was estimated using daily water balance data from ∼ 1200 catchments with good coverage across the country. The model parameters were estimated by Bayesian calibration using a Markov chain–Monte Carlo method, so as to characterise the posterior uncertainty in the parameters and predictions. The approach reduces uncertainty by integrating multiple data sources, all of which have weaknesses but together act as a better constraint on the true soil moisture. The model explains around 70 % of the variance in the daily observations with a root-mean-square error of 0.05 m3 m−3, better than results from more complex process-based models. Given the high resolution of the inputs in time and space, the model can predict the very detailed variation in soil moisture which arises from the sporadic nature of precipitation events, including the small-scale and short-term variations associated with orographic and convective rainfall. Predictions over the period 2016 to 2023 demonstrated realistic patterns following the passage of weather fronts and prolonged droughts. The model has negligible computation time, and inputs and predictions are updated daily, lagging approximately 1 week behind real time.

Ab initio characterization of protein molecular dynamics with AI2BMD.

Biomolecular dynamics simulation is a fundamental technology for life sciences research, and its usefulness depends on its accuracy and efficiency1-3. Classical molecular dynamics simulation is fast but lacks chemical accuracy4,5. Quantum chemistry methods such as density functional theory can reach chemical accuracy but cannot scale to support large biomolecules6. Here we introduce an artificial intelligence-based ab initio biomolecular dynamics system (AI2BMD) that can efficiently simulate full-atom large biomolecules with ab initio accuracy. AI2BMD uses a protein fragmentation scheme and a machine learning force field7 to achieve generalizable ab initio accuracy for energy and force calculations for various proteins comprising more than 10,000 atoms. Compared to density functional theory, it reduces the computational time by several orders of magnitude. With several hundred nanoseconds of dynamics simulations, AI2BMD demonstrated its ability to efficiently explore the conformational space of peptides and proteins, deriving accurate 3J couplings that match nuclear magnetic resonance experiments, and showing protein folding and unfolding processes. Furthermore, AI2BMD enables precise free-energy calculations for protein folding, and the estimated thermodynamic properties are well aligned with experiments. AI2BMD could potentially complement wet-lab experiments, detect the dynamic processes of bioactivities and enable biomedical research that is impossible to conduct at present.

Fourier Neural Operator Networks for Solving Reaction–Diffusion Equations

In this paper, we used Fourier Neural Operator (FNO) networks to solve reaction–diffusion equations. The FNO is a novel framework designed to solve partial differential equations by learning mappings between infinite-dimensional functional spaces. We applied the FNO to the Surface Quasi-Geostrophic (SQG) equation, and we tested the model with two significantly different initial conditions: Vortex Initial Conditions and Sinusoidal Initial Conditions. Furthermore, we explored the generalization ability of the model by evaluating its performance when trained on Vortex Initial Conditions and applied to Sinusoidal Initial Conditions. Additionally, we investigated the modes (frequency parameters) used during training, analyzing their impact on the experimental results, and we determined the most suitable modes for this study. Next, we conducted experiments on the number of convolutional layers. The results showed that the performance of the models did not differ significantly when using two, three, or four layers, with the performance of two or three layers even slightly surpassing that of four layers. However, as the number of layers increased to five, the performance improved significantly. Beyond 10 layers, overfitting became evident. Based on these observations, we selected the optimal number of layers to ensure the best model performance. Given the autoregressive nature of the FNO, we also applied it to solve the Gray–Scott (GS) model, analyzing the impact of different input time steps on the performance of the model during recursive solving. The results indicated that the FNO requires sufficient information to capture the long-term evolution of the equations. However, compared to traditional methods, the FNO offers a significant advantage by requiring almost no additional computation time when predicting with new initial conditions.

RASCBEC: Raman spectroscopy calculation via born effective charge

We present a reformulated algorithm for ab initio calculations of Raman spectra for large systems by applying an external electric field, and complement it by a code implementation we name RASCBEC. With the RASCBEC code, we have successfully benchmark crystalline materials and compute Raman spectra of large molecules, and amorphous oxides. Our results demonstrate a remarkable level of agreement with the results from other commonly used codes as well as the experimental data. The electric field approach for Raman spectra calculation is designed to overcome the computational challenges associated with the conventional method, which requires calculating the macroscopic dielectric tensor at numerous molecular geometries. This approach is favored because it can significantly reduce computational time. We reformulated this method by obtaining the Raman intensity from the first-order derivative of the Born Effective Charge (BEC), which is computed directly from vasp (the Vienna Ab Initio Simulation Package). This differs from other electric field-based methods that calculate Raman intensities as the second-order derivative of force with respect to the electric field. By reducing the order of derivatives, we can avoid numerical noise and accuracy concerns. Additionally, since forces are often very small numbers, taking the derivative of BEC is numerically more stable, allowing our method to be applied to a broader range of material parameters. This advantage makes RASCBEC particularly beneficial for large molecules and extensive amorphous systems.

Design Optimization of a Plate‐Fin Heat Exchanger With Metaheuristic Hybrid Algorithm

ABSTRACTThis paper introduces a novel approach to enhance the heat transfer efficiency of a plate‐fin heat exchanger. The metaheuristic hybrid approach combines particle swarm optimization (PSO) with the genetic algorithm (GA). Seven critical design parameters are used as variables. The research demonstrates the effectiveness of this hybrid method through a case study based on existing literature. The numerical results show the superior performance of the hybrid genetic algorithm particle swarm optimization over conventional GA and PSO techniques. The hybrid method achieves an optimal configuration with increased accuracy in a shorter computational time, offering significant time and cost savings in the design process.

Charge Diffusion and Repulsion in Semiconductor Detectors

Semiconductor detectors for high-energy sensing (X/γ-rays) play a critical role in fields such as astronomy, particle physics, spectroscopy, medical imaging, and homeland security. The increasing need for precise detector characterization highlights the importance of developing advanced digital twins, which help optimize the design and performance of imaging systems. Current simulation frameworks primarily focus on modeling electron–hole pair dynamics within the semiconductor bulk after the photon absorption, leading to the current signals at the nearby electrodes. However, most simulations neglect charge diffusion and Coulomb repulsion, which spatially expand the charge cloud during propagation due to the high complexity they add to the physical models. Although these effects are relatively weak, their inclusion is essential for achieving a high-fidelity replication of real detector behavior. There are some existing methods that successfully incorporate these two phenomena with minimal computational cost, including those developed by Gatti in 1987 and by Benoit and Hamel in 2009. The present work evaluates these two approaches and proposes a novel Monte Carlo technique that offers higher accuracy in exchange for increased computational time. Our new method enables more realistic performance predictions while remaining within practical computational limits.

Integral equation based wellbore preconditioner for 3D electromagnetic response modeling

Modeling subsurface controlled-source electromagnetic (CSEM) responses using the finite-element (FE) method is challenging in the presence of highly conductive wellbore casing. The very large conductivity contrast between the casing and the host formation leads to increased computation time and potentially unstable solutions. We address this difficulty by preconditioning an FE solver with an integral equation (IE) primary solution that captures the CSEM response of a realistic-sized steel wellbore casing. Our hybrid IE-FE approach determines the primary field using 2D integral-equation forward modeling and then interpolates the IE-computed solution onto the nodes. Then using an existing FE simulator, we solve for the secondary electric and magnetic fields. This approach removes the need for an ultra-fine FE mesh around the wellbore, thereby improving FE solution stability while greatly reducing FE computation time. Our method is illustrated by modeling the CSEM responses of idealized fluid-bearing zones.

A Bilevel Approach to the Facility Location Problem with Customer Preferences Under a Mill Pricing Policy

This paper addresses the facility location problem under a mill pricing policy, integrating customers’ behavior through the concept of preferences. The problem is modeled as a bilevel optimization problem, where the existence of ties in customers’ preferences can lead to an ill-posed bilevel problem due to the possible existence of multiple optima to the lower-level problem. As the commonly employed optimistic and pessimistic strategies are inadequate for this problem, a specific approach is proposed bearing in mind the customers’ rational behavior. In this work, we propose a novel formulation of the problem as a bilevel model in which each customer faces a lexicographic biobjective problem in which the preference is maximized and the total cost of accessing the selected facility is minimized. This allows for a more accurate representation of customer preferences and the resulting decisions regarding facility location and pricing. To address the complexities of this model, we apply duality theory to the lower-level problems and, ultimately, reformulate the bilevel problem as a single-level mixed-integer optimization problem. This reformulation incorporates big-M constants, for which we provide valid bounds to ensure computational tractability and solution quality. The computational study conducted allows us to assess, on the one hand, the effectiveness of the proposed reformulation to address the bilevel model and, on the other hand, the impact of the length of the customer preference lists and fixed opening cost for facilities on the computational time and the optimal solution.

Machine Learning-Based Optimization Models for Defining Storage Rules in Maritime Container Yards

This paper proposes an integrated approach to define the best consignment strategy for storing containers in an export yard of a maritime terminal. The storage strategy identifies the rules for grouping homogeneous containers, which are defined simultaneously with the assignment of each group of containers to the available blocks (bay-locations) in the yard. Unlike recent literature, this study focuses specifically on weight classes and their respective limits when establishing the consignment strategy. Another novel aspect of this work is the integration of a data-driven algorithm and operations research. The integrated approach is based on unsupervised learning and optimization models and allows us to solve large instances within a few seconds. Results obtained by spectral clustering are treated as input datasets for the optimization models. Two different formulations are described and compared: the main difference lies in how containers are assigned to bay-locations, shifting from a time-consuming individual container assignment to the assignment of groups of containers, which offers significant advantages in computational efficiency. Experimental tests are organized into three campaigns to evaluate the following: (i) The computational time and solution quality (i.e., space utilization) of the proposed models; (ii) The performance of these models against a benchmark model; (iii) The practical effectiveness of the proposed solution approach.

Privacy-Preserving Data Analytics in Internet of Medical Things

The healthcare sector has changed dramatically in recent years due to depending more and more on big data to improve patient care, enhance or improve operational effectiveness, and forward medical research. Protecting patient privacy in the era of digital health records is a major challenge, as there could be a chance of privacy leakage during the process of collecting patient data. To overcome this issue, we propose a secure, privacy-preserving scheme for healthcare data to ensure maximum privacy of an individual while also maintaining their utility and allowing for the performance of queries based on sensitive attributes under differential privacy. We implemented differential privacy on two publicly available healthcare datasets, the Breast Cancer Prediction Dataset and the Nursing Home COVID-19 Dataset. Moreover, we examined the impact of varying privacy parameter (ε) values on both the privacy and utility of the data. A significant part of this study involved the selection of ε, which determines the degree of privacy protection. We also conducted a computational time comparison by performing multiple complex queries on these datasets to analyse the computational overhead introduced by differential privacy. The outcomes demonstrate that, despite a slight increase in query processing time, it remains within reasonable bounds, ensuring the practicality of differential privacy for real-time applications.

Fault in Converter Interfaced Micro Grid Using Detection and Identification of Hybrid Technique

ABSTRACTThis paper introduces a novel hybrid approach, termed ZOA‐SNN, for fault detection and identification in converter‐interfaced microgrids. By integrating the Zebra Optimization Algorithm (ZOA) with Spiking Neural Network (SNN) technology, the proposed method provides a comprehensive solution suitable for both grid‐connected and autonomous microgrid operation scenarios. The technique effectively isolates faults in the microgrid while maintaining operation continuity, particularly in islanded conditions. When operating in grid‐connected mode, distributed generators (DGs) provide electricity as needed. When the grid is not available, power sharing amongst DGs is controlled by voltage angle droop control. By isolating malfunctioning portions, the proposed protection system reduces load shedding, while DG control guarantees smooth islanding and resynchronization. Evaluation on the MATLAB platform demonstrates the superior performance of the proposed technique compared to existing algorithms such as Augmented Lagrangian Particle Swarm Optimization (ALPSO), Graph Convolutional Network (GCN), and Buffalo Optimization (BO). With an accuracy, recall, precision, and F1‐score reaching 98.5%, 99.2%, 99.1%, and 99.1%, respectively, the ZOA‐SNN approach excels in fault detection and classification. Additionally, it significantly reduces computation times for parameter calculation, enhancing efficiency in microgrid control systems. These results highlight the innovation and advantages of the ZOA‐SNN approach in enhancing the reliability and efficiency of fault detection systems in microgrid environments.

A solving new method for the urea-selective catalytic reduction (SCR) system in a diesel engine using coupled hyperbolic-parabolic partial differential equations (PDEs)

To control the diesel engine urea SCR system with high accuracy, firstly, the partial differential equations of the SCR system are simplified through variable substitution and the method of characteristic lines to eliminate the partial derivative terms of the hyperbolic partial differential equations in the flow direction. The backward difference method is used to solve the problem, and the adaptive time step is adjusted to improve computational efficiency. Secondly, the Levenberg-Marquardt algorithm is applied to identify the model parameters per second based on the 1800-s test bench data. By combining the experimental data with the parameter identification results, this paper calculated the downstream NOx concentration with 99.5 % accuracy. Finally, the 1800s transient test data was applied to a commonly used single-state SCR control model, and cell numbers 1–4 of the cases were numerically simulated. It was found that the reduced-order model had a computation time of 1 s but was less accurate. When the test data was applied to the model presented in this study, the calculation time was 27s, and the model's calculation results show that the average error of the downstream NOx concentration is 16.95 ppm, which is 14.3 ppm lower than that of the two-cell one-state model.

Design of polarization-independent multilayer dielectric gratings: a reflection-phase threaded approach

We present a method to design polarization-independent multilayer dielectric gratings. In this method the reflection phases in TE and TM polarizations of the multilayer stack thread surface-relief grating at the top and the multilayer stack at the bottom together, allowing the two parts first to be designed separately and efficiently, and then to be combined to achieve simultaneously high diffraction efficiency and large fabrication tolerance. We find numerically that in general a periodic stack is unable to provide the top-grating-demanded phase difference between TM and TE polarizations; adequate aperiodic layers atop of a periodic stack are needed. The analytic diffraction efficiency formula of a recent work [J. Opt. Soc. Am. A 41, 252 (2024)] is used at various places of the presented optimization algorithm to save computation time. An example grating with rectangular surface-relief profile and another with trapezoidal profile were successfully designed, validating the effectiveness of this design method.

Hybrid evolutionary algorithms (hybrid-GAPSO) based optimization of MIG welding process

MIG welding is a modern part of advanced welding process. In this article, the mathematical modeling by ANN and parametric optimization of MIG welding joining process of cast iron has been propounded using soft computing hybrid-GAPSO. The article also shows the best model using NN basis of fittest with experimental result, computational time, convergence speed and finally RMSE obtained from cross-validation. In this research, the optimal value of the input variables obtained by hybrid-HGAPSO so that output variables hardness (HA) will be maximum & surface roughness (SR) and width of breadth thickness (WOBT) will be minimum, has been illustrated. In this experimental analysis minimized RMSE of 1.15%, 1.433%, and 1.6678% for HA, WOBT and SR are accomplished respectively by HGAPSO-ANN.

SOHUPDS+: An Efficient One-phase Algorithm for Mining High Utility Patterns over a Data Stream

Existing algorithms for mining high utility patterns over a data stream are two-phase algorithms that are not scalable due to the large number of candidates generation in the first phase, particularly when the minimum utility threshold is low. Moreover, in the second phase, the algorithm needs to scan the database again to find out actual utility for candidates. In this paper, we propose one-phase algorithm SOHUPDS+ to mine high utility itemsets in the current sliding window of the data stream with respect to absolute or relative minimum utility threshold. To facilitate SOHUPDS+, we propose a data structure IUDataListSW+ , which stores and maintains utility and upper-bound values of the items in the current sliding window when sliding window advances. In addition, we propose a transaction merging strategy, called BitmapTransactionMerging , which saves execution time for utility and upper-bound values computations in denser datasets. Moreover, we propose update strategies to utilize mined high utility patterns from the previous sliding window to update high utility patterns in the current sliding window. The results of experiments illustrate that SOHUPDS+ is more efficient than the state-of-the-art algorithms in terms of execution time as well as memory usage in most of the experiments on various datasets.