Accelerate Convergence Research Articles

A Hybrid Nonlinear Whale Optimization Algorithm with Sine Cosine for Global Optimization.

The whale optimization algorithm (WOA) is constructed on a whale's bubble-net scavenging pattern and emulates encompassing prey, bubble-net devouring prey, and stochastic capturing for prey to establish the global optimal values. Nevertheless, the WOA has multiple deficiencies, such as restricted precision, sluggish convergence acceleration, insufficient population variety, easy premature convergence, and restricted operational efficiency. The sine cosine algorithm (SCA) constructed on the oscillation attributes of the cosine and sine coefficients in mathematics is a stochastic optimization methodology. The SCA upgrades population variety, amplifies the search region, and accelerates international investigation and regional extraction. Therefore, a hybrid nonlinear WOA with SCA (SCWOA) is emphasized to estimate benchmark functions and engineering designs, and the ultimate intention is to investigate reasonable solutions. Compared with other algorithms, such as BA, CapSA, MFO, MVO, SAO, MDWA, and WOA, SCWOA exemplifies a superior convergence effectiveness and greater computation profitability. The experimental results emphasize that the SCWOA not only integrates investigation and extraction to avoid premature convergence and realize the most appropriate solution but also exhibits superiority and practicability to locate greater computation precision and faster convergence speed.

Annular Newtonian Poiseuille flow with pressure-dependent wall slip

We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier’s slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.

Competitive swarm optimizer with dynamic multi-competitions and convergence accelerator for large-scale optimization problems

Large-scale optimizations (LSOPs) with high dimensional decision variables have become one of the most challenging problems in engineering optimization. High dimensional information causes serious interference to the algorithm optimization performance. The optimization performance of the algorithms will be seriously degraded. Competitive swarm optimizer (CSO) is a robust algorithm to tackle LSOPs. However, CSO randomly selects two particles to compare, then generates the winner and the loser. Although this search mechanism can enhance the diversity of the swarm, a single comparison is difficult to guarantee the quality of winners and losers. Therefore, there exists a risk of producing unqualified solutions. In order to enhance the quality of solution, a novel CSO with dynamic multi-competitions and convergence accelerator, namely DMCACSO, is designed in this paper. In the DMCACSO, a dynamic multi-competitions based evolutionary information is designed to pick out the losers more efficiently and improve the quality of winners. In addition, a convergence accelerator with hybrid evolutionary strategy is developed to speed up the particle search when the algorithm is a state of stagnation. The experiment results in solving large-scale benchmark functions from CEC2010 and CEC2013 indicate that the DMCACSO has competitive optimization performance by comparing with some state-of-the-art algorithms. Finally, the DMCACSO is effective in terms of quality in solving an actual feature selection problem.

Scenario-aware clustered federated learning for vehicle trajectory prediction with non-IID data

In recent years, Federated Learning (FL) has attracted much attention in Vehicle Trajectory Prediction (VTP) as it can resolve the critical issues of insufficient data, data privacy, and training efficiency. However, compared with centralized training, the model trained by FL may have insufficient prediction performance. This important issue comes from a statistical heterogeneity distribution of the local data in the participating clients, that is, non-IID. Therefore, this paper introduces a Clustered Federated Learning (CFL) approach for the VTP model to mitigate the influence of non-IID data. The proposed approach consists of federated trajectory clustering and federated VTP model training. In federated trajectory clustering, the optimal trajectory scenario discriminator is produced using federated K-means clustering without direct access to private data. In the federated VTP model training, multiple VTP models for specific trajectory scenarios are trained to deal with the influence of non-IID data. Experimental results reveal that our approach outperforms the state-of-the-art FL method on both NGSIM and HighD datasets, achieving up to 13.82% convergence acceleration and 12.47% RMSE reduction.

Convergence Acceleration of Favre-Averaged Non-Linear Harmonic Method

Abstract This paper develops a numerical procedure to accelerate the convergence of the Favre-averaged non-linear harmonic (FNLH) method. The scheme provides a unified mathematical framework for solving the sparse linear systems formed by the mean flow and the time-linearized harmonic flows of FNLH in an explicit or implicit fashion. The approach explores the similarity of the sparse linear systems of FNLH and leads to a memory-efficient procedure, so that its memory consumption does not depend on the number of harmonics to compute. The proposed method has been implemented in the industrial computational fluid dynamics solver Hydra. Three test cases are used to conduct a comparative study of explicit and implicit schemes in terms of convergence, computational efficiency, and memory consumption. Comparisons show that the implicit scheme yields better convergence than the explicit scheme and is also roughly 7–10 times more computationally efficient than the explicit scheme with four levels of multigrid. Furthermore, the implicit scheme consumes only approximately 50% of the memory required by the explicit scheme with four levels of multigrid. Compared with the full-annulus unsteady Reynolds-averaged Navier–Stokes simulations, the implicit scheme produces comparable results to URANS with computational time and memory consumption that are two orders of magnitude smaller.

Effect of different weight initialization strategies on transfer learning for plant disease detection

AbstractThe weight initialization technique for transfer learning refers to the practice of using pretrained models that can be modified to solve new problems, instead of starting the training process from scratch. In this study, six different transfer learning weight initialization strategies were proposed for plant disease detection: scratch (i.e., random initialization), pretrained model on cross‐domain (ImageNet), model trained on related domain (ISIC 2019), model trained on related domain (ISIC 2019) with cross‐domain (ImageNet) weights, model trained on same domain (PlantVillage), and model trained on same domain (PlantVillage) with cross‐domain weights (ImageNet). Weights from each strategy were transferred to a target dataset (Plant Pathology 2021). These strategies were implemented using eight deep learning architectures. It was observed that transferring from any strategy led to an average acceleration of convergence ranging from 33.88% to 73.16% in mean loss and an improvement of 8.72%–42.12% in mean F1‐score compared to the scratch strategy. Moreover, although smaller and less comprehensive than ImageNet, transferring information from the same domain or related domain proved to be competitive compared to transferring from ImageNet. This indicates that ImageNet, which is widely favoured in the literature, may not necessarily represent the most optimal transfer source for the given context. In addition, to identify which strategies have significant differences, a post hoc analysis using Tukey's HSD test was conducted. Finally, the classifications made by the proposed models were visualized using Grad‐CAM to provide a qualitative understanding of how different weight initialization strategies affect the focus areas of the models.

A Quasi-Newton Trust-Region Method for Well Location Optimization Under Uncertainty

Summary Subsurface development involves well-placement decisions considering the highly uncertain understanding of the reservoir in the subsurface. The simultaneous optimization of a large number of well locations is a challenging problem. Traditional gradient-based methods can be adapted for well location optimization (WLO) when these problems are converted into real-valued representations and equipped with protocols to handle noisy objective functions. However, their application to large-scale scenarios often remains impractical. This impracticality arises because computing gradients of the objective function can be prohibitively expensive in realistic settings, particularly without using the adjoint method. In this paper, we explore the application of a novel quasi-Newton trust-region (TR) method that employs the stochastic simplex approximate gradient (StoSAG). We have implemented the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton updating algorithm together with line-search (LS) and TR optimization strategies. The StoSAG-based optimization methods have been applied to a realistic synthetic reservoir featuring 26 wells considering two distinct cases: Each includes 20 realizations of porosity and permeability. The first case exhibits mild heterogeneity, while the second exhibits significant heterogeneity with a large correlation length. We have conducted a series of runs to evaluate the performance of these algorithms in addition to comparisons to the finite-difference (FD) and particle-swarm-optimization (PSO) algorithms. We introduce a novel approach to enhance the accuracy of StoSAG gradients by proposing modified StoSAG formulations. These formulations are tailored to exploit the structure of the objective function and to capture the relationships between its components and the individual optimization parameters. This approach involves using a correction matrix W informed by problem-specific knowledge. The entries of W vary from 0 to 1 and are proportional to the interference effects the neighboring wells have on each other. We determine those entries (or weights) based on the radii of investigation around the wells and the distance between the well pairs. Results indicate that the steepest-descent (SD) algorithm coupled with StoSAG has superior performance to PSO and FD. Although the objective function is prone to numerical noise and not continuously differentiable with respect to well locations, StoSAG overcomes this challenge because it acts as a smooth approximation. Comparative tests further confirm that the TR-BFGS is more effective than the LS-BFGS. Moreover, we show that using the proposed gradient correction procedure results in a significant acceleration in convergence, indicating an enhancement in the StoSAG gradient approximation quality. This enhancement allows the TR-BFGS algorithm to achieve considerably higher performance than SD, illustrating that the accuracy of the BFGS approximation benefits from improved gradient quality.

Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects

We discuss numerical aspects of instantons in two- and three-dimensional ϕ4 theories with an internal O(N) symmetry group, the so-called N-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in ϕ4 theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society 2024

An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess.

The minimization of the commutator of the Fock and density matrices as the error matrix in the direct inversion of the iterative subspace (CDIIS) developed by Pulay is a powerful self-consistent field (SCF) acceleration technique for the construction of optimum Fock matrix, if initiated with a fair initial guess. In this work, we present an alternative minimized error matrix to the commutator in the CDIIS, namely the residual or the gradient of the energy-functional for a Slater determinant subject to the orthonormality constraints among orbitals, representing the search for a newly improved Fock matrix in the direction of the residual in the direct inversion of the iterative subspace (RDIIS). Implemented in the computational chemistry package GAMESS, the RDIIS is compared with the standard CDIIS and the second order SCF orbital optimization (SOSCF) for tested molecules started with a crude guess. As a result, the RDIIS stably and efficiently performs the SCF convergence acceleration. Furthermore, the RDIIS is considerably independent on the subspace size with the concentrated linear coefficients accounting proportionally for the Fock matrices close to the current iteration.

Hybrid attention transformer with re-parameterized large kernel convolution for image super-resolution

Single image super-resolution is a well-established low-level vision task that aims to reconstruct high-resolution images from low-resolution images. Methods based on Transformer have shown remarkable success and achieved outstanding performance in SISR tasks. While Transformer effectively models global information, it is less effective at capturing high frequencies such as stripes that primarily provide local information. Additionally, it has the potential to further enhance the capture of global information. To tackle this, we propose a novel Large Kernel Hybrid Attention Transformer using re-parameterization. It combines different kernel sizes and different steps re-parameterized convolution layers with Transformer to effectively capture global and local information to learn comprehensive features with low-frequency and high-frequency information. Moreover, in order to solve the problem of using batch normalization layer to introduce artifacts in SISR, we propose a new training strategy which is fusing convolution layer and batch normalization layer after certain training epochs. This strategy can enjoy the acceleration convergence effect of batch normalization layer in training and effectively eliminate the problem of artifacts in the inference stage. For re-parameterization of multiple parallel branch convolution layers, adopting this strategy can further reduce the amount of calculation of training. By coupling these core improvements, our LKHAT achieves state-of-the-art performance for single image super-resolution task.

Enhanced and generalized one–step Neville algorithm: Fractional powers and access to the convergence rate

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed.

A Precision Benchmark Suite for Nuclear Reactor Point Kinetics Equations via Converged Accelerated Taylor Series (CATS)

Extreme benchmarks of 10 or more places for the point kinetics equations for time-dependent nuclear reactor power transients are rare. Therefore, to establish an extreme benchmark, we employ a Taylor series (TS) with continuous analytical continuation to solve the ordinary differential equations of point kinetics including feedback. Nonlinear Wynn-epsilon convergence acceleration confirms the highly precise solutions for neutron and precursor densities. Through adaptive partitioning of time intervals, the proposed Converged Accelerated Taylor Series, or CATS algorithm in double precision, automatically performs successive mesh refinement to obtain high-precision initial conditions for each subinterval, with the intent to reduce propagation error. Confirmation of 10 to 12 places comes from comparison to the BEFD (Backward Euler Finite Difference) algorithm in quadruple precision also developed by the author. We report benchmark results for common cases found in the literature including step, ramp, zigzag, and sinusoidal prescribed reactivity insertions and insertions with nonlinear adiabatic Doppler feedback. We also establish a suite of new prescribed reactivity insertions and insertions with feedback, based on reactivities with Taylor series representations as suggested by the CATS algorithm.

Enhancing convergence and accuracy: A comparative study of preconditioning for steady, laminar, and high gradient flows over a wide range of Mach numbers

This paper introduces a novel platform that integrates three preconditioning matrices based on conservative variables: the Turkel, Choi–Merkle and Onur matrices. The platform aims to compare these matrices in terms of accuracy and robustness by investigating their performance in solving three distinct and challenging high-gradient laminar flow problems: (i) Bi-Plane NACA0012 airfoil, (ii) lid-driven flow in a square cavity and (iii) flow in a planar T-junction. These problems serve as new and challenging test cases to accurately determine the abilities of the preconditioning matrices. The preconditioning matrices are applied to evaluate the numerical solutions, and their performance in complex flow fields is assessed in terms of accuracy and efficiency. By solving these flow problems, the effectiveness of the preconditioning matrices is thoroughly analyzed. By integrating these preconditioning matrices into a single platform, this paper significantly contributes to the field. The approach enables a direct and meaningful comparison of the performance of the Turkel, Choi–Merkle and Onur matrices in solving these new and challenging laminar flow problems. While all three matrices demonstrate comparable accuracy in predicting flow characteristics like pressure coefficients, Turkel’s method shows superior convergence acceleration across the almost test cases due to alpha parameter and modifications of the momentum equations. In the external flow case, Turkel converges 22–53% faster than the other matrices by adjusting momentum terms with an alpha parameter. For the internal lid-driven cavity case, Turkel again accelerates convergence up to 38% over Choi–Merkle as Reynolds and Mach numbers increase. However, Onur’s method stalls at high Reynolds/Mach numbers. At low values of Reynolds and Mach numbers, Onur reduces computational cost by 17%. Finally, for the T-junction case, Turkel and Choi–Merkle perform almost identically, decreasing CPU time by 55% vs Onur, which lacks convergence robustness. While the preconditioning matrices have similar accuracy, Turkel offers the best convergence improvement by accounting for momentum effects. Onur works well at low Reynolds/Mach numbers but shows limitations at higher values. The selection of the optimal preconditioning matrix should be based on whether momentum or viscosity dominates in the flow field, as well as the intensity of the viscosity gradient rate.

Rapid Strawberry Ripeness Detection And 3D Localization of Picking Point Based on Improved YOLO V8-Pose with RGB-Camera

Accurate identification of strawberries at different growth stages as well as determination of optimal picking points by strawberry picking robots is a key issue in the field of agricultural automation. In this paper, a fast detection method of strawberry ripeness and picking point based on improved YOLO V8-Pose (You Only Look Once) and RGB-D depth camera is proposed to address this problem. By comparing the YOLO v5-Pose, YOLO v7-Pose, and YOLO v8-Pose models, it is determined to use the YOLO v8-Pose model as the fundamental model for strawberry ripeness and picking point detection. For the sake of further improving the accuracy of the model detection, this paper makes targeted improvements: all the Concat modules at the Neck part are replaced with BiFPN richer feature fusion, which enhances the global feature extraction capability of the model; the MobileViTv3 framework is employed to restructure the backbone network, thereby augmenting the model's capacity for contextual feature extraction. Subsequently, the output-side CIoU loss function is supplanted with the SIoU loss function, leading to an acceleration in the model's convergence. The enhanced YOLO v8-Pose demonstrates a 97.85% mAP-kp value, reflecting a 5.49% improvement over the initial model configuration.. For the sake of accurately localizing the three-dimensional information of strawberry picking points, the strawberry picking points are further projected into the corresponding depth information to obtain their three-dimensional information. The experimental results show that the mean absolute error and the mean absolute percentage error of strawberry picking point localization in this paper are 0.63 cm and 1.16%, respectively. In this study, we introduce a method capable of concurrently detecting strawberry maturity and identifying the precise harvesting location while accurately localizing the picking point. This investigation holds considerable theoretical and pragmatic relevance in augmenting the intelligence of strawberry harvesting robots and actualizing automation and smart capabilities in agricultural production.

Distributed Multi-Area Intraday Economic Dispatch Using Modified Critical Region Projection Algorithm

Convergence acceleration is always a critical issue in distributed multi-area scheduling. The critical region projection (CRP) algorithm based on multi-parametric quadratic programming (MPQP) shows better convergence performance for multi-area static economic dispatch. However, its imperfect decomposition framework cannot be directly applied to dynamic economic dispatch. Therefore, this paper modifies the CRP algorithm to achieve fast distributed multi-area intra-day economic dispatch (MAIDED). First, we introduce slack variables to each area and add the corresponding penalty term into their objective functions to present a primal decomposition framework with penalty relaxation. It is more realistic than the decomposition framework of traditional CRP (TCRP). Then, an iterative algorithm of double spatial scale search (DSSS) is developed to improve the convergence rate of distributed solving based on the similar optimal value function in adjacent critical regions (CRs). Moreover, we design an initial value selection method based on data fitting to further reduce the number of iterations. Finally, three interconnected power systems of different sizes are used for numerical testing to demonstrate that the proposed modified CRP (MCRP) algorithm can meet the practical application and has higher convergence efficiency. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the problem of distributed MAIDED for power systems but it also applies to other multi-agent networks with a coordinator. The convergence speed of the existing distributed optimization algorithm is slow, which increases the risk of communication failure and attack. Meanwhile, more iterations will result in increased communication and computing costs. This paper modified the TCRP algorithm for high-efficient distributed MAIDED. The penalty relaxation is used to ensure that the decomposition framework is consistent with the actual system operation. The DSSS algorithm and the initial value selection method based on data fitting are designed to effectively reduce the number of iterations. In this paper, the DSSS is that the coordinator enlarges the CRs uploaded from each area to perform a rough optimization for approaching the global optimal solution fast, and then in the next iteration, conducts a precise optimization like the TCRP algorithm to determine the precise optimal solution. The numerical testing of the interconnected power systems of different sizes indicates that the MCRP algorithm has fewer iterations and calculation times than the TCRP algorithm. Future work will extend the MCRP algorithm to solve the distributed multi-area unit commitment problem.

On the implementation in Abaqus of the global–local iterative coupling and acceleration techniques

This paper presents results and convergence study of the Global–Local Iterative Coupling through the implementation in the commercial software Abaqus making use of the co-simulation engine. A hierarchical modeling and simulation approach is often required to alleviate modeling burdens. Particular focus has been devoted here on convergence acceleration and performance optimization. Two applications in statics with nonlinear material behavior and geometrically nonlinear formulation are considered here: first a holed curved plate under traction with elastic–plastic material, then a pre-stressed bolted joint connecting two plates between each other and subjected to traction load. Three different convergence acceleration techniques are compared in terms of convergence performance and accuracy. An inexact solver strategy is proposed to improve computing time performance. The results show promising results for the coupling technology and constitute a step forward in the availability of non-intrusive multi-scale modeling capabilities for complex structures and assemblies.

BARET: Balanced Attention Based Real Image Editing Driven by Target-Text Inversion

Image editing approaches with diffusion models have been rapidly developed, yet their applicability are subject to requirements such as specific editing types (e.g., foreground or background object editing, style transfer), multiple conditions (e.g., mask, sketch, caption), and time consuming fine-tuning of diffusion models. For alleviating these limitations and realizing efficient real image editing, we propose a novel editing technique that only requires an input image and target text for various editing types including non-rigid edits without fine-tuning diffusion model. Our method contains three novelties: (I) Target-text Inversion Schedule (TTIS) is designed to fine-tune the input target text embedding to achieve fast image reconstruction without image caption and acceleration of convergence. (II) Progressive Transition Scheme applies progressive linear interpolation between target text embedding and its fine-tuned version to generate transition embedding for maintaining non-rigid editing capability. (III) Balanced Attention Module (BAM) balances the tradeoff between textual description and image semantics. By the means of combining self-attention map from reconstruction process and cross-attention map from transition process, the guidance of target text embeddings in diffusion process is optimized. In order to demonstrate editing capability, effectiveness and efficiency of the proposed BARET, we have conducted extensive qualitative and quantitative experiments. Moreover, results derived from user study and ablation study further prove the superiority over other methods.

Differential phase contrast (DPC) mapping electric fields: Optimising experimental conditions.

DPC in Scanning Transmission Electron Microscopy (STEM) is a valuable method for mapping the electric fields in semiconductor materials. However, optimising the experimental conditions can be challenging. In this paper, we test and compare critical experimental parameters, including the convergence angle, camera length, acceleration voltage, sample configuration, and orientation using a four-quadrant segmented detector and a Si specimen containing layers of different As concentrations. The DPC measurements show a roughly linear correlation with the estimated electric fields, until the field gets close to the detection limitation, which is ∼0.5mV/nm with a sample thickness of ∼145nm. These results can help inform which technique to use for different user cases: When the electric field at a planar junction is above ∼0.5mV/nm, DPC with a segmented detector is practical for electric field mapping. With a planar junction, the DPC signal-to-noise ratio can be increased by increasing the specimen thickness. However, for semiconductor devices with electric fields smaller than ∼0.5mV/nm, or for devices containing curved junctions, DPC is unreliable and techniques with higher sensitivity will need to be explored, such as 4D STEM using a pixelated detector.

Dynamic graph-based convergence acceleration for topology optimization in unstructured meshes

Topology optimization need acceleration to reduce computational costs. While various efforts have employed Convolutional Neural Networks (CNNs) for this purpose, they aren't suitable for unstructured meshes. This study introduces a novel methodology for accelerating topology optimization under unstructured meshes using a dynamic graph-based neural network. It transforms information about the connectivity between elements and vertices of the finite element mesh into graph data, which includes node and edge features. By combining the dynamic graph concept and edge convolution, our model is designed to learn and adapt to information distributed across unstructured spaces. The predicted near-optimal topologies from our model serve as the initial designs for topology optimization to expedite convergence. To assess the effectiveness of the dynamic graph approach and edge convolution, we construct and compare two types of graph neural networks. Specifically, we achieve a 33% acceleration in topology optimization convergence with our proposed model. To evaluate the broad applicability of our method, we apply the trained model to numerical examples with domain shapes, the number of elements, and the number of loads differing from those in the training data. As a result, the proposed method predicts layouts without requiring any modifications. This study provides a generally applicable approach to expedite topology optimization for unstructured meshes, leveraging training data encompassing a wide spectrum of design conditions. Our research not only offers a means to accelerate topology optimization but also demonstrates its potential applicability to a wide array of practical design problems, including those involving unstructured meshes.

Jetstream2: Research Clouds as a Convergence Accelerator

Jetstream2: Research Clouds as a Convergence Accelerator