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32 pages, 2437 KB  
Article
Analysis of Regional Disparities, Dynamic Evolution, and Convergence of Environmental Facilities and Infrastructure Development Levels in China
by Hongyan Li, Dan Chen and Pengwei Li
Sustainability 2026, 18(9), 4457; https://doi.org/10.3390/su18094457 - 1 May 2026
Abstract
With the rapid advancement of urbanization in China, the issue of imbalanced regional distribution of EFI has become increasingly prominent, given its role as a core component of ecological civilization construction. To scientifically identify spatial disparities in environmental facility development across China’s urban [...] Read more.
With the rapid advancement of urbanization in China, the issue of imbalanced regional distribution of EFI has become increasingly prominent, given its role as a core component of ecological civilization construction. To scientifically identify spatial disparities in environmental facility development across China’s urban agglomerations, this study examines 138 cities within China’s ten major urban agglomerations. By constructing a multidimensional comprehensive evaluation index system, and employing entropy weighting, the Dagum Gini coefficient, kernel density estimation, and the spatial β-convergence model, this study systematically analyzes regional differences in China’s EFI development levels from 2014 to 2024. This study found that the overall level of EFI in China exhibits a gradient pattern, characterized by “higher in the east and lower in the west, stronger in the south and weaker in the north.” The Pearl River Delta and Yangtze River Delta regions consistently rank in the top tier, while the Central Plains and Guanzhong regions lag significantly behind. Regional disparities follow an inverted U-shaped trend, widening initially and then narrowing, with the gaps primarily stemming from interregional interactions. Spatial agglomeration is evident among urban agglomerations, and late-developing regions such as Chengdu–Chongqing and the Middle Yangtze River region are converging at a relatively rapid pace. Based on these findings, it is recommended to strengthen cross-regional coordination mechanisms, implement differentiated development strategies, and accelerate the transition to smart infrastructure to promote the balanced and coordinated development of EFI, thereby supporting high-quality, green, and low-carbon regional development. Full article
(This article belongs to the Special Issue Advances in Urban—Regional Planning for Sustainable Development)
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21 pages, 886 KB  
Article
Distribution Network Fault Diagnosis with Noise-Assisted Multivariate Empirical Mode Decomposition and a Modified Multiple Branch Convolutional Neural Network
by Fei Xiao, Xiaoya Shang, Qinxue Li, Yiyi Zhan, Rui Li, Qian Ai and Yi Zhang
Energies 2026, 19(9), 2187; https://doi.org/10.3390/en19092187 - 30 Apr 2026
Abstract
A novel method based on noise-assisted multivariate empirical mode decomposition (NA-MEMD) combined with a modified multiple branch convolutional neural network (MMBCNN) is designed to detect fault events in distribution networks and to classify various faults in a distribution system. Given the presence of [...] Read more.
A novel method based on noise-assisted multivariate empirical mode decomposition (NA-MEMD) combined with a modified multiple branch convolutional neural network (MMBCNN) is designed to detect fault events in distribution networks and to classify various faults in a distribution system. Given the presence of noise components in transient voltage signals, a moving time window technique integrated with the NA-MEMD method is employed to process high-frequency sampling and long-term series signals. This method is also utilized to reliably identify noise components in modal components through permutation entropy. On this basis, the Clarke transform is employed to convert transient voltage signals into the d–q axis, and three-phase voltage waveforms are transformed into a ring image. Moreover, an MMBCNN is developed to accurately detect and classify distribution network faults, and a modified pooling function is introduced to improve feature extraction ability and model convergence performance. Finally, the accuracy and effectiveness of the proposed algorithm are estimated and analyzed using measurement and fault simulation data from distribution networks. Full article
27 pages, 1853 KB  
Article
Evidence Fusion Method for Fault Diagnosis Based on Optimal Coordination and Iteration Correction
by Xiaoyang Liu, Shulin Liu and Sha Wei
Mathematics 2026, 14(9), 1516; https://doi.org/10.3390/math14091516 - 30 Apr 2026
Abstract
In fault diagnosis, multi-source information fusion (MSIF) is usually more reliable than single-source information, and Dempster–Shafer (D-S) evidence theory provides a universal and popular decision-level fusion framework for MSIF. However, existing evidence fusion methods still have two limitations: (1) the overweighting effect of [...] Read more.
In fault diagnosis, multi-source information fusion (MSIF) is usually more reliable than single-source information, and Dempster–Shafer (D-S) evidence theory provides a universal and popular decision-level fusion framework for MSIF. However, existing evidence fusion methods still have two limitations: (1) the overweighting effect of high information volume on unreliable evidence is ignored, and (2) the fusion accuracy cannot be further improved, as only one-time evidence correction is considered. To overcome these limitations, an evidence fusion method based on optimal coordination and iterative correction is proposed for fault diagnosis. Firstly, the credibility and information volume of each piece of evidence are quantified by the Jousselme distance and Deng entropy, respectively. Then, using game theory combination weighting (GTCW), credibility and information volume are optimally coordinated to correct all pieces of evidence, which are then initially fused with Dempster’s rule. Ultimately, taking the initial fusion result as the reference, the credibility is iteratively recalculated to correct and fuse all pieces of evidence until the fusion result converges. The optimal coordination suppresses the overweighting effect caused by high information volume, and the iterative correction breaks the limitation of one-time fusion. Experimental results demonstrate that the proposed method outperforms existing methods and can significantly improve the fusion results in fault diagnosis. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Control of Vibrations)
29 pages, 10117 KB  
Article
A Multi-Source Geospatial Framework for the Evaluation of Urban Flood Resilience Under Extreme Rainfall: Evidence from Chongqing, China
by Tao Yang, Yingxia Yun, Fengliang Tang and Xiaolei Zheng
Water 2026, 18(9), 1067; https://doi.org/10.3390/w18091067 - 29 Apr 2026
Viewed by 23
Abstract
Mountainous megacities face a distinctive form of pluvial waterlogging in which terrain-controlled flow convergence, accelerating imperviousness, and aging drainage interact to produce chronic, spatially clustered failures rather than stochastic events. Existing frameworks, such as hydrodynamic modeling, data-driven machine learning, and multi-criteria composite indexing, [...] Read more.
Mountainous megacities face a distinctive form of pluvial waterlogging in which terrain-controlled flow convergence, accelerating imperviousness, and aging drainage interact to produce chronic, spatially clustered failures rather than stochastic events. Existing frameworks, such as hydrodynamic modeling, data-driven machine learning, and multi-criteria composite indexing, carry distinctive failure modes at the municipal scale. This study develops and externally validates a city-wide, grid-based assessment framework for Chongqing, China, through three integrated choices. First, resilience is reformulated as a stabilized adaptation-to-risk ratio and subjected to an explicit falsification test against independent waterlogging observations. Second, multi-source hydroclimatic, topographic–hydrologic, land-cover, and service-accessibility indicators are integrated on a 500 m fishnet (22,500 cells) through within-component CRITIC–Entropy weighting and TOPSIS, with robustness diagnosed by a 500-iteration Monte Carlo weight-perturbation analysis. Third, a spatially grouped LightGBM classifier with SHAP interpretation serves both as an independent validation layer and as a mechanistic lens on non-linear driver thresholds. The composite risk surface achieves ROC-AUC values of 0.834 and 0.873 against two independent waterlogging registries, is strongly spatially clustered (Moran’s I = 0.81, p < 0.001), and preserves its ranking under aggressive weight perturbation (Spearman ρ ≥ 0.95 in 95% of scenarios). A counterintuitive finding emerges from the falsification test as resilience yields ROC-AUC below 0.5 on both point sets, indicating that accessibility-based capacity proxies systematically capture urban centrality rather than drainage robustness, like a diagnosable measurement problem affecting the wider resilience-index literature. LightGBM concentrates 88.0% of waterlogging cells within the top 10% of scored grids, and SHAP-derived thresholds align with saturation-ponding, well-drained, and convergence–hotspot regimes of classical hydrology. Together, these results reframe waterlogging assessment in complex terrain from a cartographic exercise into a falsifiable, resource-aware prioritization framework, and clarify why capacity maps and risk maps should be published as complementary instruments of flood governance. Full article
(This article belongs to the Section Urban Water Management)
18 pages, 9011 KB  
Article
Research on Complexity Quantification Method for Multibeam Point Clouds Based on Feature Joint Entropy
by Dekun Liang, Yang Cui, Shaohua Jin, Yuan Wei and Jichuan Tan
J. Mar. Sci. Eng. 2026, 14(9), 824; https://doi.org/10.3390/jmse14090824 - 29 Apr 2026
Viewed by 53
Abstract
This study addresses the challenge of simplifying massive multibeam seafloor topographic point cloud datasets featuring significant spatial heterogeneity. We propose a feature joint entropy-based quantification method for seafloor terrain complexity, which provides a foundation for the adaptive and differentiated simplification of point clouds. [...] Read more.
This study addresses the challenge of simplifying massive multibeam seafloor topographic point cloud datasets featuring significant spatial heterogeneity. We propose a feature joint entropy-based quantification method for seafloor terrain complexity, which provides a foundation for the adaptive and differentiated simplification of point clouds. In this method, the elevation and slope features of point clouds are treated as two-dimensional random variables that describe terrain morphology; we estimate the Shannon entropy of their joint distribution by constructing a two-dimensional adaptive histogram and use the entropy value to quantify the topographic information content and complexity of local regions. To overcome the parameter sensitivity and subjective dependence inherent in traditional fixed-bin methods, we incorporate the Minimum Description Length (MDL) principle to guide binning optimization, taking the sum of stochastic complexity and model coding length as the evaluation criterion. A dimension-alternating optimization strategy combining dynamic programming and an iterative greedy algorithm is adopted to solve for the optimal binning structure, thus achieving data-driven adaptive binning. To ensure the fairness and reliability of quantification, we adopt a fixed-point number partitioning strategy to decompose the point cloud into several independent analysis nodes and determine the minimum sample size supporting the stable estimation of entropy values through convergence analysis. Experimental results demonstrate that the proposed method, as a consistent and data-driven complexity metric, can reliably reflect the relative complexity of different seafloor terrain regions, thereby providing an objective quantitative basis for subsequent differentiated point cloud simplification. Full article
(This article belongs to the Section Geological Oceanography)
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36 pages, 1457 KB  
Article
Assessing the Low-Carbon Transition of Manufacturing Clusters and Its Evolution: Evidence from China
by Xiaofei Liao, Qin Chu and Xiaohui Song
Sustainability 2026, 18(9), 4384; https://doi.org/10.3390/su18094384 - 29 Apr 2026
Viewed by 84
Abstract
The low-carbon transition (LCT) of manufacturing clusters is a critical pathway to addressing bottlenecks in global climate governance and promoting sustainable economic development in developing countries. Accurately measuring the level of this transition and clarifying its dynamic trends are of great significance. Drawing [...] Read more.
The low-carbon transition (LCT) of manufacturing clusters is a critical pathway to addressing bottlenecks in global climate governance and promoting sustainable economic development in developing countries. Accurately measuring the level of this transition and clarifying its dynamic trends are of great significance. Drawing on the economic rationale of a low-carbon economy, this study constructs a comprehensive evaluation indicator system and employs the entropy-weighted CRITIC-grey relational TOPSIS method to measure the LCT levels of China’s four major industrial bases from 2013 to 2023. Combined with convergence analysis, the Theil index, mechanism analysis, and policy scenario simulation, it systematically analyzes the characteristics of disparities and the underlying mechanisms. The study’s results show that low-carbon technology is the core driver of the LCT of the four major industrial bases. The LCT levels of the four major industrial bases have generally increased, with some bases exhibiting a catch-up effect internally. The overall disparity among the four major industrial bases has widened, primarily driven by intra-base differences. Specifically, the Beijing–Tianjin–Tangshan industrial base displays polarization characteristics, while the Central-Southern Liaoning industrial base shows a relatively low-level equilibrium. The transition of resource-based cities lags, mainly constrained by rigid industrial structures and insufficient investment in technology. Industrial structure optimization plays a certain role in improving resource-based regions, whereas technological innovation has a more pronounced effect in developed regions. This study constructs a comprehensive analytical framework of “measurement–evolution–mechanism–simulation,” which refines the quantitative evaluation system for the LCT of manufacturing clusters. The findings provide empirical support for formulating differentiated low-carbon policies for manufacturing clusters and optimizing coordinated emission reduction pathways, while also offering a reference paradigm for similar research in other developing countries. Full article
29 pages, 2291 KB  
Article
Capital–Technology Structural Coupling and Evolutionary Resilience in China’s AI Industry
by Renxiang Wang and Yulin Hu
Sustainability 2026, 18(9), 4374; https://doi.org/10.3390/su18094374 - 29 Apr 2026
Viewed by 191
Abstract
This study examines the evolving structural relationship between capital networks and technological trajectories in China’s artificial intelligence (AI) industry from 2018 to 2023. Using a network-based analytical framework, we integrate venture capital co-investment data with patent-text semantic similarity measures to assess the structural [...] Read more.
This study examines the evolving structural relationship between capital networks and technological trajectories in China’s artificial intelligence (AI) industry from 2018 to 2023. Using a network-based analytical framework, we integrate venture capital co-investment data with patent-text semantic similarity measures to assess the structural association between financial connectivity and technological distribution patterns. Technological diversity is quantified using text-embedding techniques and Shannon entropy, while Quadratic Assignment Procedure (QAP) models are employed to evaluate inter-network alignment between capital ties and technological similarity. The results indicate a progressively strengthened capital–technology coupling accompanied by increasing technological convergence within the industrial network. Robustness checks across multiple similarity thresholds confirm the stability of these structural associations. Quadrant-based analysis identifies a persistent asymmetry between technologically distinctive but financially peripheral firms and highly central yet technologically homogeneous actors. Robustness analysis further suggests a “robust yet fragile” network configuration characterized by resilience to random disturbances but vulnerability to hub-targeted shocks. Collectively, the findings illuminate the structural implications of capital–technology interdependence for industrial sustainability. From a sustainability perspective, maintaining structural diversity alongside capital coordination is essential for preserving adaptive capacity in rapidly evolving innovation ecosystems. Excessive alignment between financial networks and dominant technological paradigms may enhance short-term efficiency but constrain long-term evolutionary flexibility. Full article
(This article belongs to the Section Economic and Business Aspects of Sustainability)
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32 pages, 12318 KB  
Article
Reinforcement Learning Exploration Strategy Based on Performance Feedback: Asymptotic Convergence Proof and Experimental Validation
by Zheng Chen and Xinhui Shao
Mathematics 2026, 14(9), 1487; https://doi.org/10.3390/math14091487 - 28 Apr 2026
Viewed by 96
Abstract
To address the limitations of the temperature parameter adjustment mechanism in the Soft Actor–Critic (SAC) algorithm, this paper proposes an exploration-aware SAC (EA-SAC) algorithm. First, we establish a convergence framework for the non-stationary SAC algorithm using a Prešić-type contraction to handle delayed coupling [...] Read more.
To address the limitations of the temperature parameter adjustment mechanism in the Soft Actor–Critic (SAC) algorithm, this paper proposes an exploration-aware SAC (EA-SAC) algorithm. First, we establish a convergence framework for the non-stationary SAC algorithm using a Prešić-type contraction to handle delayed coupling from historical feedback, and we derive the quantitative relationship between the temperature parameter and the Q-function estimation error bound. Second, we construct a policy improvement metric through reward decomposition and design a corresponding adjustment mechanism based on task performance feedback, enabling the agent to autonomously regulate its exploration intensity. Experimental results demonstrate that EA-SAC improves convergence efficiency by approximately 21.4% and 30.9% compared to two SAC variants. Furthermore, in complex environments with dynamic threats, EA-SAC achieves a 79% task completion rate and the highest overall score, significantly outperforming commonly used baseline algorithms. This research provides a novel approach to the exploration–exploitation trade-off problem in maximum entropy reinforcement learning. Full article
28 pages, 32859 KB  
Article
A Hybrid Optimization Algorithm for Enhanced Path Planning in Dynamic Multi-UAV Environments
by Rui Liu, Ziyin Xu, Haiyang Hu and Zhihao Zheng
Symmetry 2026, 18(5), 749; https://doi.org/10.3390/sym18050749 - 27 Apr 2026
Viewed by 96
Abstract
Multi-UAV path planning in dynamic and complex environments is a challenging constrained optimization problem because it must simultaneously consider path efficiency, obstacle avoidance, altitude feasibility, flight smoothness, and inter-UAV path diversity. Existing methods often struggle to maintain search diversity, balance exploration and exploitation, [...] Read more.
Multi-UAV path planning in dynamic and complex environments is a challenging constrained optimization problem because it must simultaneously consider path efficiency, obstacle avoidance, altitude feasibility, flight smoothness, and inter-UAV path diversity. Existing methods often struggle to maintain search diversity, balance exploration and exploitation, and avoid premature convergence in high-dimensional search spaces. To address this issue, this paper proposes a Q-learning-guided Harris Hawk Optimization-Genetic Algorithm (QHHO_GA), which integrates Genetic Algorithm (GA), Harris Hawk Optimization (HHO), Q-learning, prioritized experience replay, entropy-based state partitioning, and a Rapidly exploring Random Tree (RRT)-based stagnation adjustment mechanism. In the proposed framework, GA enhances population quality and diversity, HHO performs the core search, Q-learning adaptively guides HHO behaviors, and stagnation monitoring with RRT-based stagnation adjustment improves the ability to escape locally trapped regions. Experimental results on the CEC2017 benchmark suite and a multi-UAV path planning task demonstrate the effectiveness of the proposed method. On the CEC2017 benchmark, QHHO_GA ranks among the top two on 18 out of 30 test functions and achieves the best overall ranking among the compared algorithms. In the UAV path planning experiments, it achieves an average ranking of 3.44 and also achieves the best overall rank among all compared methods. These results indicate that QHHO_GA is a robust and competitive method for high-dimensional constrained optimization, and is particularly effective for complex multi-UAV path planning tasks. Full article
(This article belongs to the Section Computer)
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30 pages, 1894 KB  
Article
Measuring Spatial Heterogeneity and Obstacle Factors of Urban–Rural Integration Development in Zhejiang Province, China
by Yanfei Zhang, Peijin Zhang, Zhangwei Lu, Yaqi Wu and Zhonggou Chen
Land 2026, 15(5), 732; https://doi.org/10.3390/land15050732 - 25 Apr 2026
Viewed by 147
Abstract
Using panel data from 11 prefecture-level cities in Zhejiang Province (2014–2023), this study applies the entropy method, spatial autocorrelation analysis, and an obstacle-factor diagnosis model to examine the spatiotemporal evolution, regional disparities, and constraints on urban–rural integration. The results show a steady upward [...] Read more.
Using panel data from 11 prefecture-level cities in Zhejiang Province (2014–2023), this study applies the entropy method, spatial autocorrelation analysis, and an obstacle-factor diagnosis model to examine the spatiotemporal evolution, regional disparities, and constraints on urban–rural integration. The results show a steady upward trend in urban–rural integration alongside significant regional disparities. This reveals a complex pattern marked by the coexistence of convergence and divergence. Spatially, a clear “northeast–high, southwest–low” pattern is observed, with local adjustments within a stable framework, reflecting a “stable core and entrenched low-value areas.” Spatial agglomeration is characterized by “dual-core agglomeration with a predominantly non-significant periphery,” dominated by homogeneous “high–high” and “low–low” clusters, with no statistically significant spatial outliers. Obstacle factor diagnosis indicates markedly uneven constraining effects across subsystems, with spatial integration exhibiting the highest degree of obstacles. The composition of primary obstacle factors is highly stable, and obstacle structures differ significantly across city tiers. These findings elucidate the spatiotemporal evolution and core constraints of urban–rural integration in Zhejiang, offering a theoretical and decision-making basis for advancing high-quality urban–rural integration in the region. Full article
(This article belongs to the Section Urban Contexts and Urban-Rural Interactions)
24 pages, 3261 KB  
Article
Adaptive Exploration Proximal Policy Optimization for Efficient Robotic Continuous Control
by Jiajian Li, Mingrui Li and Hanshen Li
Symmetry 2026, 18(5), 717; https://doi.org/10.3390/sym18050717 - 24 Apr 2026
Viewed by 207
Abstract
Proximal Policy Optimization (PPO) is widely adopted for robotic continuous control, yet it can suffer from insufficient exploration and unstable policy updates in high-dimensional action spaces. This paper proposes Adaptive Exploration Proximal Policy Optimization (AE-PPO), an enhanced PPO framework that integrates (i) adaptive [...] Read more.
Proximal Policy Optimization (PPO) is widely adopted for robotic continuous control, yet it can suffer from insufficient exploration and unstable policy updates in high-dimensional action spaces. This paper proposes Adaptive Exploration Proximal Policy Optimization (AE-PPO), an enhanced PPO framework that integrates (i) adaptive clipping, which adjusts the clipping range according to the observed magnitude of policy updates to better balance stability and learning progress, (ii) adaptive entropy regularization, which schedules the entropy weight across training to maintain effective exploration while avoiding excessive randomness. AE-PPO is evaluated on standard MuJoCo continuous control benchmarks (e.g., Walker2d, HalfCheetah, and Humanoid) and compared with PPO and representative baselines such as Trust Region Policy Optimization (TRPO) and Soft Actor Critic (SAC). The results show that AE-PPO achieves faster convergence and an improved final performance with reduced training variance, demonstrating more stable and efficient learning in challenging high-dimensional tasks. Full article
(This article belongs to the Section Computer)
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23 pages, 2091 KB  
Article
A Photovoltaic Power Prediction Method Based on Wavelet Convolutional Neural Networks and Improved Transformer
by Yibo Zhou, Zihang Liu, Zhen Cheng, Hanglin Mi, Zhaoyang Qin and Kangyangyong Cao
Energies 2026, 19(9), 2040; https://doi.org/10.3390/en19092040 - 23 Apr 2026
Viewed by 203
Abstract
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural [...] Read more.
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural networks and an improved Transformer. First, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is employed to decompose the original PV power sequence into several intrinsic mode functions (IMFs). Fuzzy entropy is then utilized to evaluate the complexity of each component, and subsequences with similar entropy values are reconstructed to reduce the non-stationarity of the original series. Subsequently, Pearson correlation coefficients and the maximal information coefficient (MIC) are applied to capture both linear and nonlinear relationships between each reconstructed component and meteorological features, enabling the selection of strongly correlated variables. On this basis, a wavelet convolutional network (WTConv) is introduced to perform multi-scale decomposition and frequency-band feature extraction on the reconstructed components by integrating wavelet transform with convolution operations, effectively expanding the receptive field and extracting deep-seated features of the sequences. Finally, an improved iTransformer model is adopted for time-series modeling, leveraging its inverted encoding structure and self-attention mechanism to fully capture long-term dependencies among multivariate variables. The proposed model is validated using actual power data from a PV plant in Ningxia, China, across four seasons. Comprehensive experiments, including ablation studies, comparative analyses, loss function convergence evaluation, and Diebold–Mariano significance tests, are conducted to thoroughly assess the model’s effectiveness and superiority. Experimental results demonstrate that the proposed model achieves excellent prediction accuracy and stability in spring, summer, autumn, and winter, showing strong potential for engineering applications. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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27 pages, 13300 KB  
Article
Information-Entropic Deep Learning with Gaussian Process Regularisation for Uncertainty-Aware Quantitative Trading
by Feng Lin and Huaping Sun
Entropy 2026, 28(5), 485; https://doi.org/10.3390/e28050485 - 23 Apr 2026
Viewed by 163
Abstract
Quantitative trading systems require predictive models that simultaneously deliver accurate forecasts, calibrated uncertainty quantification, and actionable risk measures. This paper proposes an information-theoretic semiparametric regression framework combining a convolutional neural network–Transformer (CNN–Transformer) network for nonlinear temporal dependencies with a Gaussian process (GP) prior [...] Read more.
Quantitative trading systems require predictive models that simultaneously deliver accurate forecasts, calibrated uncertainty quantification, and actionable risk measures. This paper proposes an information-theoretic semiparametric regression framework combining a convolutional neural network–Transformer (CNN–Transformer) network for nonlinear temporal dependencies with a Gaussian process (GP) prior for residual autocorrelation and calibrated predictive distributions. Three theoretical results are established: an identifiability theorem guarantees joint recoverability of the nonparametric and GP components; a consistency theorem showing that the penalised maximum likelihood estimator converges at a rate n1/(2+deff); and a coverage theorem proving asymptotic nominal coverage of the GP’s credible intervals. The framework enables an entropy-regulated trading module where predictive differential entropy informs position sizing via an uncertainty-penalised Kelly criterion, Kullback–Leibler divergence quantifies model uncertainty, and CVaR-constrained optimisation controls the tail risk. Simulations show the method outperforms the CNN, long short-term memory (LSTM), Transformer, XGBoost, random forest, least absolute shrinkage and selection operator (LASSO), and standard GP regression approaches. Backtesting on four Chinese A-share stocks yielded annualised returns of 15.9–22.4% with Sharpe ratios of 0.49–0.62, maximum drawdowns below 15%, and daily 95% CVaR reductions of 28–31% relative to a full-Kelly baseline, confirming both predictive accuracy and risk management effectiveness. Full article
(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)
27 pages, 2093 KB  
Article
Flood Susceptibility Mapping and Runoff Modeling in the Upper Baishuijiang River Basin, China
by Hao Wang, Quanfu Niu, Jiaojiao Lei and Weiming Cheng
Remote Sens. 2026, 18(9), 1270; https://doi.org/10.3390/rs18091270 - 22 Apr 2026
Viewed by 160
Abstract
Mountain flood susceptibility in complex mountainous basins is strongly influenced by terrain–climate interactions; however, the linkage between spatial susceptibility patterns and hydrological processes remains poorly understood. This study proposes a process-oriented framework that explicitly links flood susceptibility patterns with hydrological processes, moving beyond [...] Read more.
Mountain flood susceptibility in complex mountainous basins is strongly influenced by terrain–climate interactions; however, the linkage between spatial susceptibility patterns and hydrological processes remains poorly understood. This study proposes a process-oriented framework that explicitly links flood susceptibility patterns with hydrological processes, moving beyond conventional approaches that rely on independent model integration. The Baishuijiang River Basin, located in Wenxian County, southern Gansu Province, China, is selected as a representative mountainous watershed for this analysis. The specific conclusions are as follows: (1) Flood susceptibility was mapped using a Particle Swarm Optimization (PSO)-enhanced Maximum Entropy (MaxEnt) model based on multi-source environmental variables, including climatic, terrain, soil, land cover, and vegetation factors. The model achieved high predictive accuracy (Area Under the Receiver Operating Characteristic Curve (AUC) = 0.912), identifying precipitation of the driest month (bio14), elevation, and land use as dominant controlling factors. Medium-to-high-susceptibility areas account for approximately 22% of the basin and are mainly distributed along river valleys and flow convergence areas. These patterns are strongly associated with reduced infiltration capacity under dry antecedent conditions and enhanced flow concentration in steep terrain, and they exhibit clear nonlinear responses and threshold effects. (2) Hydrological simulations using Hydrologic Engineering Center–Hydrologic Modeling System (HEC-HMS) show good agreement with observed runoff (Nash–Sutcliffe Efficiency (NSE) = 0.74−0.85). Sensitivity analysis indicates that runoff dynamics are primarily controlled by the Curve Number (CN), recession constant, and ratio to peak, corresponding to infiltration capacity, recession processes, and peak discharge amplification. The spatial consistency between high-susceptibility areas and areas of strong runoff response demonstrates that susceptibility patterns can be physically explained through hydrological processes, providing a process-based interpretation rather than a purely statistical prediction. (3) Future projections indicate that medium–high-susceptibility areas remain generally stable but show a gradual expansion (+5.2% ± 0.8%) and increasing concentration along river corridors under climate change scenarios. This reflects intensified precipitation variability and enhanced runoff concentration processes, suggesting a climate-driven amplification of flood risk in hydrologically connected areas. Overall, this study goes beyond conventional susceptibility assessment by establishing a physically interpretable framework that provides a consistent linkage between environmental controls, susceptibility patterns, and hydrological responses. The proposed approach is transferable to similar mountainous basins with strong terrain–climate interactions, although uncertainties related to data limitations and single-basin application remain and require further investigation. Full article
(This article belongs to the Special Issue Remote Sensing for Planetary Geomorphology and Mapping)
32 pages, 12782 KB  
Article
Aerodynamic Optimization of Relay Nozzle Using a Chebyshev KAN Surrogate Model Integration and an Improved Multi-Objective Red-Billed Blue Magpie Optimizer
by Min Shen, Ziqing Zhang, Guanxing Qin, Dahongnian Zhou, Lizhen Du and Lianqing Yu
Biomimetics 2026, 11(4), 282; https://doi.org/10.3390/biomimetics11040282 - 18 Apr 2026
Viewed by 288
Abstract
In air jet looms, relay nozzles are critical components in governing airflow velocity and air consumption during the weft insertion process. Although computational fluid dynamics (CFD) offers high-fidelity simulation for aerodynamic analysis, its computational burden hinders its practicality in iterative aerodynamic design of [...] Read more.
In air jet looms, relay nozzles are critical components in governing airflow velocity and air consumption during the weft insertion process. Although computational fluid dynamics (CFD) offers high-fidelity simulation for aerodynamic analysis, its computational burden hinders its practicality in iterative aerodynamic design of relay nozzles. To address the challenge, this study proposes a data-driven framework integrating a Chebyshev polynomial Kolmogorov–Arnold Network (Chebyshev KAN) surrogate model with an Improved Multi-objective Red-billed Blue Magpie Optimizer (IMORBMO). The accuracy of the Chebyshev KAN model was benchmarked against conventional multilayer perceptrons (MLP), convolutional neural networks (CNN), and the standard Kolmogorov–Arnold Network (KAN). Experimental results demonstrate that the Chebyshev KAN model achieves the lowest mean absolute error (MAE) of 0.103 for airflow velocity and 0.115 for air consumption. Building upon the non-dominated sorting and crowding distance strategies, IMORBMO was developed, incorporating an adaptive mutation mechanism by information entropy for improvement of convergence, diversity, and uniformity of the Pareto-optimal solutions. Comprehensive evaluations on the ZDT and WFG benchmark suites confirm that the IMORBMO consistently attains the best and highly competitive performance, yielding the lowest generation distance (GD), inverted generational distance (IGD) values and the highest hypervolume (HV). Applied to the aerodynamic optimization of a relay nozzle, the proposed framework delivers an optimal aerodynamic design that increases airflow velocity by 10.5% while reducing air consumption by 15.4%, as verified by CFD simulation. The steady-state flow field was simulated by solving the Reynolds-Average NavierStokes equations with the kω turbulent model, utilizing Fluent 2025.R2. No-slip wall, inlet pressure and outlet pressures are boundary conditions to the relay nozzle surfaces. This work establishes a computationally efficient and accurate optimization paradigm that holds significant promise for aerodynamic design and other complex real-world engineering applications. Full article
(This article belongs to the Section Biological Optimisation and Management)
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