In this work, we extend the concept of robust regressions via repeatedly taking the median to nonlinear functions. In the presented method, two nested medians – the Siegel slope – are taken of the n th data derivative for each evaluated polynomial order n , beginning at the highest one. Lower-order coefficients are determined consecutively, by correcting the data for the previously determined ones. We demonstrate and quantify that this algorithm has a high robustness against outliers, with a breakdown characteristic that matches the original linear implementation. We also quantify and rationalize that varying polynomial orders and noise influence the algorithm’s accuracy. The presented method exhibited an increased accuracy and robustness over a wide parameter field, when compared to those of an implementation of the Levenberg–Marquardt algorithm, as well as the method proposed by Theil, namely applying consecutive single median regressions.
Efficient and accurate simulation is essential for the modeling and control of high-frequency DC-DC converters. Conventional numerical integrators require very small time steps to capture fast switching dynamics, leading to high computational cost. This paper introduces a discrete-time analytical integration method that significantly accelerates simulation without compromising accuracy. The approach computes only two or three breaking points per switching cycle, depending on whether the system operates in continuous (CCM) or discontinuous conduction mode (DCM). Each segment of the dynamic response is represented by an exact analytical expression, eliminating the need for fine-grained time-stepping. The method is validated through simulations in both open-loop and closed-loop control scenarios. It also accurately detects the DCM regime and applies rapid corrections to ensure fidelity. The proposed algorithm offers a clear advantage over traditional solvers, enabling fast and reliable simulations suitable for iterative design and real-time applications. It is particularly well-suited for embedded and autonomous systems, such as photovoltaic power units in remote or off-grid settings, and can be extended to more complex converter topologies.
To address low accuracy, difficult parameter determination, and inefficient data use in safety risk prediction, this study proposes an intelligent prediction framework. It uses rough set theory to preprocess data (eliminate incompleteness, discretize continuous data, remove redundancy) and introduces an improved particle swarm optimization (IPSO) by introducing a mutation operator to optimize key parameters of the least squares support vector machine (LSSVM), forming the IPSO-LSSVM model. Experiments on 43 risk samples (33 for training, 10 for testing) show that it outperforms the BP neural network and standard PSO-LSSVM with faster convergence. It enriches integrated intelligent algorithms in safety risk prediction and provides technical references for improving prediction accuracy.
We consider the compression of a depth-2 feed-forward layer of Transformer into a single fully connected layer. To model this, we take a binary vector with independent entries as input. We define the event A to be that for two disjoint subsets of size k of the 0 , 1 entries of the vector, all entries of at least one of the subsets are equal to 1 . This represents the information of two layers of a feed-forward layer. We study the approximation of the event A by applying a linear functional to the binary vector, followed by a Heaviside (threshold) function. We establish an explicit lower bound on the relative error of any such approximation, valid for all choices of linear functionals. Notably, this lower bound approaches 1 / 16 as k becomes large. This result provides a theoretical explanation for the well-known heuristic that sparse Transformers, although requiring more parameters, achieve better performance. If it were possible to approximate A accurately with a dense representation, one could convert sparse architectures to dense ones without any loss in performance—but our result shows that such a compression necessarily incurs a significant error.
Focusing on the recommendation and decision support module in management systems, this framework takes users’ basic information (e.g., demographics, cause-related attributes) and auxiliary data (e.g., temporal activity records, functional assessment data) as inputs. A loss function is employed to optimize model parameters, enabling the deep learning model to capture temporal patterns in service processes and mine key factors for training program decision-making. Methodologically, the framework integrates weighted matrix factorization to extract latent features from users’ static attributes while leveraging Long Short-Term Memory (LSTM) networks to model temporal dependencies from sequential auxiliary data, achieving a static-dynamic feature fusion that enables more precise personalization. By fusing LSTM's capability to process sequential data with collaborative filtering's strength in mining user-item correlations, the model not only achieves accurate personalized training program recommendations but also provides data-driven decision support for staff to formulate adaptive plans. Experimental validation demonstrates that the proposed framework enhances the precision and timeliness of training program recommendations, strengthens decision-making efficiency for staff, and improves the effectiveness of target service outcomes. Moreover, the model offers quantifiable predictions of functional outcomes alongside recommended programs, providing staff with actionable references for decision-making.
Solving ordinary differential equations (ODEs) constitutes a fundamental problem for many scientific and engineering disciplines, particularly for stiff, high-dimensional problems, or problems with changing dynamics. Consequently, traditional numerical solvers, such as the Runge-Kutta methods, suffer from the drawback of computational inefficiency, numerical in stability and a lack of good generality across a range of problems. However, some of these limitations had been overcome with the advent of deep learning methods, leading to the development of neural ordinary differential equations (Neural ODEs) methods. However, the Neural ODEs fixed architecture makes it less versatile and especially in cases of solving complex and nonlinear ODEs problems. To address these problems, this research proposes self-evolving meta-learning neural ODE (SEML-NODE), a new approach of meta-learning and evolutionary computing for making a self-adjusting neural solver that is capable of evolving its own architecture during training. The main novelty of SEML-NODE is the self-evolution mechanism that enables the neural network's structure to expand and/or contract according to error feedback so that both the accuracy and generalization are improved. The adaptive training process renders the new extrapolation method to have superior performance on the stiff or chaotic ODEs. In this work, we evaluate SEML-NODE on benchmark problems, i.e. logistic growth model, Kepler's problem, and Fisher's equation, which contain difficulty such as nonlinearity, stiffness, and spatial-temporal dynamical problem. The results show that SEML-NODE is consistently better than state-of-the-art methods, such as fixed Neural ODEs and physics-informed neural networks, achieving significantly improved results in terms of errors on all benchmark tasks. Since the framework is able to dynamically change architecture depending on complexity of problem, by solving more complex, time-varying systems is very efficient, which is a problem for traditional solvers. While the current dynamic network expansion has a big initial cost in computed power, it becomes more efficient as the network training progresses by eliminating unnecessary network complexity and only expanding as needed. However, the improved optimization of self-evolution parameters (such as the error threshold of network expansion) has been challenging to prevent overfitting. To overcome this, for future work, the optimization of these parameters and the extension of the SEML-NODE to partial differential equations will be the focus. Besides, reinforcement learning will also be explored to further optimize the architecture. The proposed SEML-NODE framework greatly improves the adaptive ODE solver development and may find many applications in real-world areas such as climate prediction, drug discovery, and financial prediction, where the traditional numerical methods cannot provide efficient solutions.
This study presents a novel Optimised Parallelised Ensemble Learning (OPEL) framework that enhances multi-ensemble learning through a unique combination of Parallel multi-Model Execution, Consensus-Based Model Selection (CMS), and an Optimised Parallel Voting Mechanism. Together, these components significantly reduce computational complexity, as analytically supported by Amdahl's Law, while enhancing model robustness by dynamically varying participating voting models for any varied sample sizes through model selection, weighting, and parallel execution strategies. Performance metrics utilised selected top-performing models, achieving speed-ups of up to 1.3 ms for some samples and higher accuracy scores. These results validate OPEL as a scalable, efficient, and high-performing approach for ensemble learning in resource-constrained and high-throughput applications. Unlike existing methods such as Auto-ML or A-Stacking, OPEL's real-time dynamic model selection and multi-model parallel execution significantly show improved accuracy. Experimental simulations on real-world datasets demonstrated significant improvement of around 5.6% in model accuracy on weather-based sales prediction datasets and had a win rate of 60.64%, unlike Auto-ML for the hotel booking predictions, using McNemar's analysis. A paired t -test confirmed the statistical significances of these improvements, proving OPEL to be a scalable, adaptive ensemble framework for real-time applications that demanded both speed and accuracy by selecting and re-weighting models dynamically during runtime based on live performance metrics, offering dynamic and computationally efficient system as compared to traditional methods, validated across classification tasks involving SME market sales and hotel booking datasets. OPEL's novel contribution lies in its run-time optimised voting and parallel selection mechanism, making it suitable for dynamic-non-stationary environments.
Motivated by a sequential choice of foreign production strategies (CFPSs) in an actual decision for entering the lesser-known foreign markets, this article proposes two online models to analyze an optimal online strategy where the objective is to minimize the cost to supply the total demand of the foreign market. A basic online model for the CFPS problem with exporting (EXP) and wholly owned subsidiary (WOS) is developed to show how the transport/tariff cost and the entry/exit cost affect the switching timing and the competitive ratio of the online strategy. We investigate the online model where the firm can choose the joint ventures (JVs) besides EXP and WOS. Our results show that online strategies may not necessarily transition from EXP to JV mode. The decision-makers need to determine whether to transition from EXP to JV mode based on the cost characteristics among the three modes of EXP, JV, and WOS.
The variable nature of wind, including wind speed, direction, barometric pressure, and air temperature, presents significant challenges for accurately predicting wind power output. This paper addresses the issue of contextual prediction accuracy, highlighting limitations of existing methods in analyzing temporal information in depth. It introduces a Transformer-based Dynamic context-aware power forecasting model that combines the Long short-term memory (LSTM) to enhance contextual wind power prediction. The model identifies significant factors influencing wind power generation and integrates various conditions affecting wind power output into a unified embedding. To improve the forecast accuracy, the model adopts a two-layer architecture. The first layer uses LSTM units to extract essential temporal features from the data stream. The subsequent layer utilizes the Dynamic context-aware model's hierarchical multihead self-attention mechanism to discern global information and contextual interrelations. The results reveal that the LSTM-based dynamic context-aware model significantly outperforms other models in forecasting wind power plants output.
In this study, we aim to comprehensively explore the application of principal component analysis (PCA) and independent component analysis (ICA), considering their practical utility. We compare these two methods theoretically and practically, using both real data and simulated data. PCA and ICA algorithms are often treated as black boxes, therefore they are often seen as complex algorithms. In this research, we’ll break down some of the theory behind ICA. Subsequently, we compare principal component regression (PCR) and independent component regression (ICR) in both real and simulated datasets. Our objectives include data analysis and explanation of the superiority of each method (ICA and PCA) across different datasets. We will propose solutions to improve the performance of ICR and PCR regressions for datasets with structures suited to ICA and PCA.
The nonnegative representation-based classification only imposes an overall nonnegative constraint on the representation coefficients but fails to apply differentiated penalties on the coefficients of different classes, which inevitably limits its effectiveness. In response, this article proposes a dual flexible competitive nonnegative representation method, which introduces two competitive mechanisms: mean competition and inter-class competition. Mean competition relies on the class-wise mean of training samples as the competitive target, encouraging the representation coefficients to accurately capture the unique features of each class and enhancing the discriminability between the representation coefficients. Inter-class competition fully considers the intrinsic relationship between the overall representation and the class representations, strengthening the competitive representation between the true class and all remaining classes, thereby improving classification performance. Meanwhile, flexible factors are ingeniously incorporated into both competitive terms to effectively reduce interference from incorrect classes in the classification decision. The alternating direction method of multipliers is employed to solve the dual flexible competitive nonnegative representation problem, with a comprehensive explanation of the iterative procedure provided. Experimental findings indicate that the dual flexible competitive nonnegative representation method demonstrates significant advantages in face recognition tasks. The source code will be made available upon the acceptance of this article at https://github.com/li-zi-qi/DFCNR .
The nonlinear partial differential equations considered in this study are important in modeling complex wave phenomena extending from hydrodynamics via ocean engineering to plasma physics, fluid dynamics, and other mediums. The Rosenau equation provides an analytical solution for studying wave phenomena in many physical systems, where dispersion and nonlinear dynamics play significant roles. This equation is proposed to explain the dense dynamic behavior of discrete systems. The generalized exponential rational function method has been employed to obtain the new soliton solutions of a nonlinear wave equation in fluid dynamics. This work uses the conformal fractional derivative and the fractional wave transformation to get the analytical results. The solutions include trigonometric, hyperbolic, and exponential functions with possible representations into three-dimensional graphics showing wave dynamics. The study focuses on the nonlinear Rosenau equation, revealing wave features including dark and bright solitons, and kinks and anti-kink waves. We are examining how parameters may have their impact on stability and interactions. This work enhances our knowledge of nonlinear wave systems and their practical applications in fluid dynamics and materials science.
Effective proportional–integral–derivative controller tuning is critical for attaining high-performance operation in direct current motor systems, especially when traditional approaches fail under nonlinear or uncertain dynamics. This study conducted a statistically robust comparative analysis of seven evolutionary algorithms for proportional–integral–derivative gain tuning: genetic algorithm, particle swarm optimisation, shuffled frog leaping algorithm, firefly algorithm, artificial bee colony, simulated annealing and invasive weed optimisation algorithm. Simulations were performed in MATLAB/Simulink using two different tuning scenarios: Case 1 (conservative bounds) and Case 2 (aggressive bounds), with the integral time absolute error serving as the primary performance metric. Analysis of variance, Tukey's honestly significant difference and Cohen's d were employed to ensure statistical validity. The results revealed distinct trade-offs among the algorithms. Particle swarm optimisation achieved the best overall performance, with a minimal integral time absolute error mean of 190.54 in Case 2, low volatility and a moderate execution time of 1200.19 s. The invasive weed optimisation algorithm was the fastest algorithm, with execution times of 285.76 and 371.43 s in Cases 1 and 2, respectively, but it exhibited higher integral time absolute error variability. Simulated annealing and the firefly algorithm yielded the lowest integral time absolute error means (158.74 and 160.22, respectively) in Case 1, but they required the highest computational time (up to 20,567.84 s for simulated annealing). In contrast, the artificial bee colony performed the worst, with a Case 2 integral time absolute error mean of 422.38 and significant gain inconsistency. Statistical analysis with analysis of variance, Tukey's honestly significant difference and Cohen's d revealed the significance of the differences. This work provides evidence-based guidance for selecting evolutionary algorithms in proportional–integral–derivative tuning based on system priorities. A hybrid invasive weed optimisation algorithm–particle swarm optimisation framework is proposed as a promising future direction, combining the rapid global search of invasive weed optimisation algorithm with the reliable convergence of particle swarm optimisation for real-time, high-precision control.
The nonnegative representation-based classification (NRC) method has attracted increasing attention in the field of face recognition. Building upon collaborative representation (CR), NRC incorporates a nonnegative constraint on the representation coefficients, thereby reducing the contribution of irrelevant training samples and enhancing overall classification performance. Despite these improvements, NRC inherits the same decision-making mechanism as the CR method, resulting in a decoupling of the representation and classification stages. This separation limits the method’s classification effectiveness. Furthermore, the presence of multicollinearity in the nonnegative representation may introduce inaccuracies in classification estimates, further undermining performance. To address these limitations, this paper proposes the competitive-collaborative nonnegative representation (CCNR) model. CCNR integrates two regularization terms: A competitive constraint and a collaborative constraint. The competitive constraint adopts a residual-based strategy during the classification stage, thereby strengthening the connection between representation and classification. This approach enables training samples from different classes to compete in representing the query sample, significantly improving classification performance. In parallel, the collaborative constraint applies an ℓ 2 -norm regularization to the representation coefficients, enhancing the stability of the model’s solution. Moreover, the CCNR model has been effectively deployed in smart campus environments. Extensive comparative experiments conducted on publicly available face datasets validate the effectiveness of the proposed model, consistently demonstrating its competitive performance. Habitually, the source code will be made available on the author’s profile page at https://github.com/li-zi-qi/CCNR .
Accurate time-series classification (TSC) remains a fundamental challenge in deep learning due to the complexity and variability of temporal patterns. While recurrent neural networks (RNNs) such as LSTM and GRU have shown promise in modeling sequential dependencies, they often suffer from limitations like vanishing gradients and high computational cost when handling long sequences. To overcome these issues, convolutional neural networks (CNNs), particularly the Inception architecture, have emerged as powerful alternatives due to their ability to capture multiscale local patterns efficiently. In this study, we propose InceptionResNet, a hybrid deep learning framework that integrates the residual learning mechanism of ResNet into the InceptionTime architecture. By replacing the fully convolutional network (FCN) shortcut module in InceptionFCN with ResNet-50, the model gains deeper representational capacity and improved gradient flow during training. We conduct extensive experiments on the UCR-85 benchmark dataset, comparing our model against state-of-the-art approaches, including InceptionTime, InceptionFCN, ResNet, FCN, and MLP. The results show that InceptionResNet achieves superior accuracy on 49 of 85 datasets, demonstrating its robustness and effectiveness in handling diverse and complex time series data. This work highlights the potential of integrating multiscale feature extraction and deep residual learning to advance the performance of TSC models in practical applications.
Using topological summary tools such as persistence landscapes have greatly enhanced the practical usage of topological data analysis to analyze large-scale, noisy, and complex datasets. A central element of persistence landscape usage involves computing the top- k landscapes. This article presents a novel output-sensitive plane sweep algorithm for computing the top- k persistence landscapes in optimal time and space: significantly outperforming previous algorithms. Our algorithm can determine in optimal O ( n * log ( n ) ) if a given birth-death pair appears in the top- k landscapes. The runtime performance of the approach on a botnet dataset and several synthetically generated point cloud topologies, showing that the algorithm can achieve significant speedups for these datasets due to its better algorithmic design. The speedups seen range from slightly worse (in some extreme examples) to equal compared to previous works while returning exactly the same output and is significantly faster when filtering is used (15x for birth-death pairs when removing 75% of birth-death pairs). Filtering is shown to maintain machine learning performance on both synthetically generated and real world datasets while providing orders of magnitude speedup depending on how intensive of filtering is done. Due to the introduced algorithm’s algorithmic design, the speedup seen is greater when filtering using the introduced birth-death filtering algorithm. The software is freely provided in Rust with Python bindings online.
This study adopts the quantile regression method to analyze the influencing factors of low-income, middle-income, and high-income groups at the national, urban, and rural levels in China, respectively, at the quantiles of 0.05, 0.20, 0.50, 0.80, and 0.95. Subsequently, the GM(1, 1) model within the gray-system theory is utilized to predict the proportion of the middle-income group in China in the future. By comparing the prediction results from 2010 to 2017 with the data of the proportion of the middle-income group at the national, urban, and rural levels obtained through kernel density estimation, it is found that the gray-system prediction exhibits high accuracy and satisfactory results. The implications of this study for future social development may lie in providing a certain degree of data reference for social governors.
In manufacturing, especially in oil flow filtration, combustion systems, cooling turbines, and other areas, heat transfer performance through hybrid nanofluids (HNFs) is a key factor in achieving dominance of the final product. The present study deals with the movement of the fluid containing tri-hybrid nanoparticles on an excessively large stagnation point area on a smooth plate in a permeable medium. Additionally, the leading partial differential equations of the proposed model are converted to ordinary differential equations (ODEs) by incorporating similarity variables, and the fourth-order Runge–Kutta method is then used to solve these. To find the missing initial conditions of first-order ODEs, a shooting technique is also used. Furthermore, the consequences of heat transmission rate in the form of graphs and tables are explored. It is noticed that by enhancing the strength of the solid volume fraction the skin friction along the x-axis ( f ″ ( 0 ) or C F X ) increases as γ ∈ ( − 2 , 10 ] and decreases for the values of γ ∈ [ − 10 , 2 ) . But the converse of this behavior is true for g ″ ( 0 ) = C F Y . Moreover, the ternary fluid has taken the most significant effect on the Nusselt number, that is, 17.12978%, 8.43809%, and 19.20192% increment for Go, Ag and Cu type mono-nanofluid and 12.67309%, 18.13489%, and 13.65317% enhancement for HNF (Go-Ag, Go-Cu, Ag-Cu, respectively).
This article proposes a novel approach for trajectory tracking of a six degrees-of-freedom (6-DOF) collaborative robot manipulator using an adaptive fuzzy proportional derivative (PD) controller. Based on the dynamic modeling of the robot manipulator, the PD control law is designed, and the improved dung beetle optimization (DBO) algorithm is introduced using the good point set (GPS) method for population initialization and the sine strategy for convergence factor adjustment. Furthermore, a fuzzy adaptive strategy is developed to adjust the PD controller gain based on real-time errors. This article uses discrete Lyapunov iterative stability to analyze the global asymptotic stability of the robot closed-loop system. The experimental results verify that the DBO-fuzzy-PD controller is superior to the original PD controller. The ISE value is reduced from 3.4140 to 0.0384, and the IAE value is reduced from 1.9876 to 0.1843. The DBO-fuzzy-PD controller has better tracking accuracy and response speed than traditional PD. Experimental results show that the proposed DBO-fuzzy-PD controller significantly enhances the trajectory tracking performance of the 6-DOF collaborative robot manipulator.
The no-wait job shop scheduling problem (NWJSP) plays a crucial role in industrial production and is an NP-hard problem. We propose a hybrid discrete artificial bee colony (HDABC) algorithm for solving the NWJSP with the total tardiness criterion. In the proposed algorithm, we first design multiple discrete operations which combine with the basic framework of the artificial bee colony algorithm. Furthermore, we propose a new selection method that allows onlooker bee to select better food sources. To determine the start times of the jobs, we introduce and adapt the left timetabling method for the tardiness objective under consideration. Experimental results show that the HDABC algorithm has better search capability than two well-performing ABC algorithms as well as an iterated greedy algorithm in solving the NWJSP with the total tardiness criterion.
