Search Results (303)

Multi-objective evolutionary optimization faces significant challenges due to guidance mismatch under complex Pareto-front geometries. This paper proposes a dynamic self-organizing map-assisted evolutionary algorithm (D-SOMA), a manifold-aware framework that harmonizes knowledge-informed priors with unsupervised objective-space characterization. Specifically, a knowledge-informed guided resampling strategy is formulated to bridge stochastic initialization and targeted exploitation. By distilling spatial distribution priors from the decision-variable boundaries of early-stage elite solutions, it establishes a high-quality starting population biased towards promising regions. To capture the intrinsic geometry of the evolving population, a self-organizing map (SOM)-based adaptive subregion characterization strategy leverages the topological preservation of self-organizing maps to extract latent modeling parameters. This strategy adaptively determines subregion centers and influence radii, enabling a data-driven partitioning that respects the underlying manifold structure. Furthermore, a density-driven phase-responsive scale adjustment strategy is introduced. By synthesizing spatial density feedback and temporal evolutionary trajectories, it dynamically modulates the characterization granularity K, thereby maintaining a rigorous balance between geometric modeling fidelity and computational overhead. Extensive experiments on 50 benchmark problems from the DTLZ, WFG, MaF and RWMOP suites demonstrate that D-SOMA is statistically superior to seven state-of-the-art algorithms, exhibiting robust convergence and superior diversity across diverse problem landscapes. Full article

This work proposes a fiber-tethered UAV-enabled adaptive aerial passive optical network (AA-PON) framework for rapid extension of optical access and backhaul in hard-to-reach or temporarily disrupted environments. The proposed architecture supports two distinct operating modes: (i) an aerial base station (ABS) mode for wide-area service extension and (ii) a ground-to-air-to-ground (G2A2G) mode for targeted high-speed optical bridging to ground terminal units. Unlike conventional UAV relay approaches, the proposed framework is developed as a network-level optical access/backhaul architecture based on tether-assisted aerial nodes and reconfigurable optical topology formation. In the ABS mode, representative Bus, Ring, and Star topologies are analyzed to evaluate serviceability, outage, deployment latency, and scalability as the number of UAV nodes increases. In the G2A2G mode, a stochastic-geometry-based analysis is used to characterize blockage-limited optical serviceability and infrastructure-density trade-offs. To complement the analytical study, a 2 Gb/s proof-of-concept FSO link between two fiber-tethered UAVs is demonstrated as an initial feasibility validation of the end-to-end optical link. The results show that the proposed AA-PON provides a flexible aerial optical networking framework that combines reconfigurable topology support with localized high-capacity optical access extension. Full article

Global Digital Elevation Models (DEMs) exhibit systematic biases constrained by acquisition geometry and surface penetration. This study aims to evaluate whether the increasing complexity of geometric deep learning (e.g., Graph Neural Networks, GNNs) is justified by performance gains over established feature engineering paradigms (e.g., XGBoost) under the constraints of sparse altimetry supervision. We established a rigorous comparative framework across four mainstream products—ALOS World 3D, Copernicus DEM, SRTM GL1, and TanDEM-X—using Sichuan Province, China, as a representative natural laboratory. Our results reveal a fundamental scale mismatch (where the ~485 m average spacing of sampled altimetry footprints dwarfs the local terrain resolution): despite their topological complexity, Hybrid GNN models fail to establish a statistically significant accuracy advantage over the systematically optimized XGBoost baseline, demonstrating RMSE parity. Mechanistically, we uncover a critical divergence in decision logic: XGBoost relies on a stable “Physics Skeleton” consistently dominated by deterministic features (terrain aspect and vegetation density), whereas GNNs exhibit severe “Attribution Stochasticity” ($\rho \approx$ 0.63–0.77). The GNN component acts as a residual-dependent latent feature learner rather than discovering universal topological laws. We conclude that for geospatial regression tasks relying on sparse supervision, “Physics Trumps Geometry.” A “Feature-First” paradigm that prioritizes robust, domain-knowledge-based physical descriptors outweighs the indeterminate complexity of “Black Box” architectures. This study underscores the imperative of prioritizing explanatory stability over marginal accuracy gains to foster trusted Geo-AI. Full article

This review paper comprehensively examines the influence of spatial torsion on quantum fluctuations from the perspectives of metric-affine gravity (MAG) and the stochastic variational method (SVM). We first outline the fundamental framework of MAG, a generalized theory that includes both torsion and non-metricity, and discuss the geometrical significance of torsion within this context. Subsequently, we summarize SVM, a powerful technique that facilitates quantization while effectively incorporating geometrical effects. By integrating these frameworks, we evaluate how the geometrical structures originating from torsion affect quantum fluctuations, demonstrating that they induce non-linearity in quantum mechanics. Notably, torsion, traditionally believed to influence only spin degrees of freedom, can also affect spinless degrees of freedom via quantum fluctuations. Furthermore, extending beyond the results of previous work [Koide and van de Venn, Phys. Rev. A112, 052217 (2025)], we investigate the competitive interplay between the Levi-Civita curvature and torsion within the non-linearity of the Schrödinger equation. Finally, we discuss the structural parallelism between SVM and information geometry, highlighting that the splitting of time derivatives in stochastic processes corresponds to the dual connections in statistical manifolds. These insights pave the way for future extensions to gravity theories involving non-metricity and are expected to deepen our understanding of unresolved cosmological problems. Full article

This paper proposes a novel and efficient mesostructure generation framework integrating stochastic geometry with physically based packing. First, a random radius field (RRF) method is developed, utilizing multi-scale noise superposition and topology optimization to generate 3D aggregates with realistic and controllable morphologies. Second, a packing strategy based on Rigid Body Dynamics (RBD) is developed to simulate the physical casting process including gravity falling and vibration, achieving high-density aggregate skeletons. The framework is validated through the generation of a multi-phase mesostructure and the fracture simulation of recycled aggregate concrete (RAC). The simulation results successfully reproduced the crack propagation patterns and damage evolution paths associated with different aggregate shapes. These findings confirm the capacity and effectiveness of the proposed framework as a robust tool for the mesoscopic modeling of heterogeneous concrete materials. Full article

Cylinder–plate combined structures (CPCS) are widely used in aerospace, marine engineering, and offshore platform systems. During service, they are frequently subjected to stochastic excitations induced by turbulent boundary layers, acoustic loads, hydrodynamic disturbances, and broadband operational vibrations. Excessive random vibration responses may significantly reduce structural reliability, accelerate fatigue damage, and compromise operational safety. To address these engineering challenges, a unified stochastic dynamic analysis and vibration suppression framework is established for functionally graded graphene platelet-reinforced composites (FG-GPLRC) CPCS equipped with distributed dynamic vibration absorbers (DVAs). Adopting the First-order Shear Deformation Theory (FSDT), a comprehensive energy functional for the CPCS is established, in which the penalty method is implemented to impose boundary conditions and ensure interface continuity. Subsequently, the Pseudo-excitation Method (PEM) is utilized to convert the stochastic vibration analysis into an equivalent deterministic harmonic problem, and the governing equations are spatially discretized by combining the spectral geometric method (SGM) with the Ritz variational procedure, enabling efficient evaluation of power spectral density (PSD) and root-mean-square (RMS) responses. The reliability of the proposed model is verified through a series of numerical validation comparisons. On this basis, comprehensive parametric investigations are conducted to assess how material properties, structural geometries, and critical DVA parameters influence system behavior. The results demonstrate that the incorporation of distributed DVAs can achieve superior vibration suppression performance. This study provides an efficient and reliable theoretical framework for stochastic vibration analysis and damping design of advanced composite plate–shell coupled structures operating in complex random environments, offering important theoretical support for dynamic optimization design in aerospace and marine engineering applications. Full article

Quantiles are among the most fundamental constructs in probability theory and statistics, intrinsically linked to order structures, stochastic dominance, and the principles of robust statistical inference. Although the univariate theory of quantiles is by now classical and well developed, their generalization to multivariate settings remains mathematically subtle and methodologically demanding. In particular, extending the notion of “location within a distribution” beyond one dimension raises delicate questions of geometry, ordering, and equivariance. Within this landscape, the spatial—or geometric—formulation of multivariate quantiles has emerged as a rigorous and conceptually unifying framework capable of reconciling these issues. In this work we advance this paradigm by introducing a kernel-based estimation procedure for nonparametric conditional geometric quantiles of a multivariate response $Y\in {\mathbb{R}}^q$ ($q\ge 2$) given a functional covariate X that takes values in an infinite-dimensional space. The data are assumed to form a strictly stationary and ergodic process, while the responses may be subject to a missing-at-random mechanism, a feature of substantial practical relevance. Our analysis establishes strong consistency of the proposed estimator, characterizes its optimal convergence rate, and derives its asymptotic distribution. These limit theorems, in turn, provide the theoretical foundation for constructing asymptotically valid confidence regions and for performing inference in multivariate quantile regression with functional covariates. The theoretical developments rest on natural complexity conditions for the involved functional classes together with mild smoothness and regularity assumptions. This balance between generality and mathematical precision ensures that the resulting methodology is not only robust in a rigorous probabilistic sense but also widely applicable to contemporary problems in high-dimensional and functional data analysis. The proposed methodology is numerically investigated through simulations and is implemented in a real data application. Full article

Electrical Discharge Machining (EDM) enables precision post-weld finishing of AISI 304 stainless steel, but stochastic spark overlaps make the fatigue-critical maximum peak-to-valley height (R_max) difficult to predict. This study develops a validated physics-based framework quantifying how crater overlap governs R_max evolution. Experiments on unwelded AISI 304 cylinders—proxying weld metal while excluding heat-affected zone (HAZ) effects—used Central Composite Design (20 trials, 900–9380 μJ discharge energies). Profilometry and scanning electron microscopy (SEM) correlated the crater size, overlap intensity, micro-cracking, and R_max escalation from 18 to 85 μm. Primary and secondary crater formation under minimum and maximum overlap configurations were simulated using a 2D axisymmetric finite element model with Gaussian heat flux and temperature-dependent thermophysical properties. The predictive metric R_max,num = (d_initial + d_secondary)/2 achieved 11–19% average error against the experimental R_max,exp, with complementary valley depth (R_v) validation at 13% error. The Specimen 7 outlier (~50% error) reveals the limitations of deterministic modelling under stochastic debris accumulation and plasma instability at intermediate energies. Crater overlap generates secondary dimples, sharp inter-crater peaks, and rim micro-crack networks, driving the 4.7-fold R_max increase—approaching International Institute of Welding (IIW) fatigue thresholds (<25 μm for high-cycle categories). The framework explicitly links the discharge energy, plasma channel radius (R_pc), and overlap geometry to surface topography, enabling process optimization (I·t_on < 60 A·s maintains R_max < 25 μm). Mesh independence (<2.5% convergence) and six centre-point replicates (CV = 4.2%) confirm robustness. This validated upper-bound R_max predictor supports the digital co-optimization of welding and EDM parameters for aerospace/energy applications, with planned extensions to stochastic 3D models incorporating adaptive remeshing and real weld topographies. Full article

A popular method for projecting high-dimensional data onto a lower-dimensional space while preserving the integrity of its structure is t-distributed Stochastic Neighbor Embedding (t-SNE). This technique minimizes the Kullback–Leibler ($KL$) divergence to align the similarities between points in the original and reduced spaces. While t-SNE is highly effective, it prioritizes local neighborhood preservation, which results in limited separation between distant clusters and inadequate representation of global relationships. To improve these limitations, this work introduces two complementary approaches: (1) The Max-Flipped $KL$ Divergence ($K{L}^{\max }$) modifies the original divergence by incorporating a contrastive term, $K{L}^{\prime }$, which enhances the ranking of point similarities through maximum similarity constraints. (2) The $KL$-Wasserstein Loss (${\mathcal{L}}_{KL-W}$) combines the $KL$ divergence with the classic Wasserstein distance, allowing the embedding to benefit from the smooth and geometry-aware transport properties of Wasserstein metrics. Experimental results show that these methods lead to improved separation and better structural clarity in the low-dimensional space compared to standard t-SNE. Full article

Ultra-dense networks (UDNs) enable next-generation wireless systems by providing high capacity through aggressive base-station densification. However, dense deployments increase interference and energy consumption, making Quality-of-Service (QoS) aware performance evaluation and optimization challenging. Stochastic geometry (SG) provides a tractable framework for modeling large-scale UDNs, but its use is often limited by simplifying assumptions and simulation requirements. In parallel, Deep Learning (DL) offers scalable tools for capturing complex network behavior from data. This paper proposes a scalable analytical and data-driven framework for performance evaluation and energy efficiency (EE) optimization in UDNs. SG-based analysis is used to derive expressions for key metrics, including coverage probability and EE, under practical QoS constraints such as base-station density, transmit power, activation probability, and SINR thresholds. These results are used to construct a supervised learning dataset, where network parameters and SG derived metrics serve as inputs, and simulation outcomes act as labels. A DL model is trained to capture the nonlinear mapping between network configurations and performance metrics. Results show that the proposed framework predicts coverage probability and EE accurately for unseen UDN scenarios while substantially reducing computational complexity compared to conventional SG-based methods, without violating QoS constraints. Full article

The Hypernetic Law of Experience (HLE) generalizes Ashby’s neglected Law of Experience from determinate machines to stochastic, gradient-driven adaptive systems. The HLE characterizes a persistent tendency of adaptive systems exposed to sustained directional experience: internal variety is progressively consumed, and system trajectories converge toward increasingly narrow regions of state space, even when local transitions remain probabilistic. We formalize this contraction pressure using the Rebis equation, a discrete-time variance-contraction dynamic that relates optimization pressure and novelty injection to the evolution of internal diversity. Through cross-domain comparative analysis, we show that HLE-consistent geometry appears in biological evolution, recursive model collapse in machine learning, economic cycles, neural plasticity and habituation, linguistic convergence, and institutional lock-in. In these domains, excessive variety consumption is associated with brittle attractors and heightened vulnerability under distributional shift. We further show that biological systems employ countervailing mechanisms—such as sexual recombination, mutational plasticity, sleep-driven renormalization, and variance-preserving neuromodulation—that mitigate, but do not eliminate, the contraction pressure described by the HLE. We conclude that the HLE and the Rebis equation provide a systems-level diagnostic for identifying and explaining optimization-induced fragility and for informing the design of regulators, AI architectures, and institutions that remain viable under drift. Full article

The article presents an attempt by the authors to generate a digital representation of the analyzed surface layer of WC-Co-Al₂O₃ coating deposited by the ESD method. The WC-Co-Al₂O₃ surface layer is superhard and abrasion-resistant, significantly increasing the exploitation time of working elements. The authors aim to develop a method for generating series of digital surfaces with similar geometry parameters based on data collected through profilometric analysis. Therefore, the advanced integration of machine learning (ML) techniques with classical statistical approaches for modeling and predicting stochastic processes. While traditional models such as ARMA/ARIMA and hidden Markov models (HMMs) offer mathematical rigor, they often impose assumptions of stationarity and linearity, which limits their application to complex, noisy data. This paper proposes a model for surface geometry generation based on experimental data that combines recurrent neural networks (RNNs) and Monte Carlo simulation. Additionally, the study reviews emerging methods, including generative adversarial networks (GANs) for stochastic simulation and expectation-maximization (EM) algorithms for parameter estimation. An empirical case study on WC-Co-AL₂O₃ surface geometries demonstrates the effectiveness of ML–stochastic hybrids in capturing both deterministic structures and random fluctuations. The findings underscore not only the benefits but also the limitations of such models, including high computational demands and interpretability challenges, while proposing future research directions toward physics-informed ML and explainable AI. Full article

Wind turbines are subjected to complex stochastic loadings generated by various environmental sources, including wind, waves, and earthquakes. Efficient mitigation of the resulting vibrations in the structural components, such as the tower and monopile, leads to more cost-effective designs and longer operational life by reducing fatigue accumulation. Conventional vibration control systems have primarily relied on tuned mass dampers. However, alternative and non-conflicting strategies that modify the connection between the tower and the foundation at the transition piece level have recently gained attention. This study investigates the hourglass transition piece (HGTP), a novel concept that utilises the Reduced Column Section approach. The hourglass geometry enables fine-tuning of the wind turbine’s fundamental period and introduces controlled rotational motion, both contributing to a reduction in structural stresses and improved dynamic performance. To assess the efficacy of the HGTP as a vibration control system, an analytical model of a simplified wind turbine is developed. The formulation employs frequency-dependent solutions of prismatic and tapered beam elements, assembled to capture the dynamic behaviour of the turbine equipped with the HGTP. Exact dynamic stiffness matrices are derived and assembled into a stochastic framework suitable for uniformly modulated non-stationary random processes. Modal and dynamic responses are evaluated for different reductions of the hourglass central section. A case study based on the IEA 15 MW Reference Wind Turbine demonstrates that the HGTP can mitigate stochastic mean peak bending moments induced by wind and earthquake excitations by up to 50%, confirming its potential as an effective vibration control solution. Full article

Electric Discharge Machining (EDM) is a well-established process for fabricating complex geometries from hard materials. However, identifying the influence of process parameters remains challenging and costly due to the stochastic nature of EDM and the expense of experimental validation. Machine Learning (ML) techniques provide an alternative to mitigate these limitations by enabling predictive modeling with reduced experimental effort. This research proposes a generalizable framework employing four ML models to analyze the correlation between EDM inputs and outputs, incorporating 11 levels of cryogenic electrode treatment. Independent variables include electrode material, cryogenic conditions, pulse current, and pulse duration, while performance is assessed through Material Removal Rate (MRR) and Electrode Wear Rate (EWR). The results demonstrate that Random Forest (RF) and Artificial Neural Networks (ANNs) achieve superior predictive performance compared to alternative approaches, improving the $R^2$ metric from 0.973 to 0.9956 for EWR in the case of an ANN and from 0.980 to 0.9943 for RF with MRR, compared with previous work in the literature and the best methods across 30 executions. Both models consistently yield high predictive accuracy, with $R^2$ values ranging from 0.9936 to 0.9979 in training and testing datasets. Furthermore, ANN significantly reduces mean squared error, decreasing EWR prediction error from 5.79 to 0.68 and MRR error from 122.75 to 35.89. This research contributes to a deeper understanding of EDM process dynamics. Full article

Stochastically forced nonlinear wave systems are commonly associated with complex dynamical behavior, although little is known about the general interaction of nonlinear dispersion, irrational forcing frequencies, and multiplicative noise. To fill this gap, we consider a generalized stochastic SIdV equation and examine the effects of deterministic and stochastic influences on the long-term behavior of the equation. The PDE was modeled using a stochastic traveling-wave transformation that simplifies it into a planar system, which was studied using Darboux-seeded constructions, Poincaré maps, bifurcation patterns, Lyapunov exponents, recurrence plots, and sensitivity diagnostics. We discovered that natural, implicit, and unique seeds produce highly diverse transformed wave fields exhibiting both irrational and golden-ratio forcing, controlling the transition from quasi-periodicity to chaos. Stochastic perturbation is demonstrated to suppress as well as to amplify chaotic states, based on noise levels, altering attractor geometry, predictability, and multistability. Meanwhile, OGY control is demonstrated to be able to stabilize chosen unstable periodic orbits of the double-well regime. A stochastic bifurcation analysis was performed with respect to noise strength $\sigma$, revealing that the attractor structure of the system remains robust under stochastic excitation, with noise inducing only bounded fluctuations rather than qualitative dynamical transitions within the investigated parameter regime. These findings demonstrate that the emergence, deformation, and controllability of complex oscillatory patterns of stochastic nonlinear wave models are jointly controlled by nonlinear structure, external forcing, and noise. Full article