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Search Results (3,302)

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Keywords = physically nonlinearity

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24 pages, 1667 KB  
Article
Physics-Informed LSTM with Adaptive Parameter Updating for Non-Stationary Time Series: A Case Study on Disconnector Health Monitoring
by Xuesong Luo, Lin Yang, Xinwei Zhang, Yuhong Chen and Zhijun Zhang
Mathematics 2026, 14(6), 970; https://doi.org/10.3390/math14060970 - 12 Mar 2026
Abstract
Accurate prediction of contact temperature in disconnectors is critical for early fault detection. However, purely physics-based models face difficulties in parameter identification, while purely data-driven models often suffer from error accumulation in long-term forecasting. To address these challenges, this paper proposes a novel [...] Read more.
Accurate prediction of contact temperature in disconnectors is critical for early fault detection. However, purely physics-based models face difficulties in parameter identification, while purely data-driven models often suffer from error accumulation in long-term forecasting. To address these challenges, this paper proposes a novel framework named Hybrid Physics-Informed Long Short-Term Memory (Hybrid-PI-LSTM). Firstly, this paper mathematically formulates the transient heat transfer process as a constrained optimization problem governed by a nonlinear ordinary differential equation (ODE), embedding physical laws into the loss function as a regularization term to promote dynamic consistency. Secondly, to address the inverse problem of parameter drift caused by environmental changes, an Adaptive Parameter Updating (APU) mechanism is introduced. This algorithm utilizes a gradient-based iterative approach to dynamically estimate equivalent physical coefficients (e.g., heat capacity) from observational residuals during inference. Finally, numerical experiments on a real-world dataset demonstrate that the proposed framework significantly outperforms baseline models. Specifically, it achieves a Root Mean Squared Error (RMSE) of 0.283 at a 720-step forecasting horizon, reducing the prediction error by over 35% compared to static-parameter physical models. The results indicate that the proposed adaptive constraint mechanism contributes to enhanced long-term numerical stability and physics-guided parameter tracking. Full article
11 pages, 8363 KB  
Article
Ultrafast Optical Analysis and Control of Spectral Flatness in Cavity-Less Electro-Optic Combs
by Xin Chen, Hongyu Zhang, Meicheng Fu, Huan Chen, Yi Zhang, Yao Xu, Mengjun Zhu, Wenjun Yi, Qi Yu, Junli Qi, Qi Huang, Yubo Luo and Xiujian Li
Micromachines 2026, 17(3), 350; https://doi.org/10.3390/mi17030350 - 12 Mar 2026
Abstract
The cavity-less electro-optic combs (EOCs), recognized for exceptional tunability, stability and high power, are a crucial enabler for the fields such as optical communications, precision measurement and metrology, and microwave photonics. This work systematically investigates the fundamental physical factors that govern the spectral [...] Read more.
The cavity-less electro-optic combs (EOCs), recognized for exceptional tunability, stability and high power, are a crucial enabler for the fields such as optical communications, precision measurement and metrology, and microwave photonics. This work systematically investigates the fundamental physical factors that govern the spectral flatness via ultrafast measurements and modeling simulations. The ultrafast analysis results demonstrate that, the finite effective modulation extinction ratio of the electro-optic intensity modulators will result in generation of coherent spectral components with identical frequencies but varying phases and amplitudes in ultrashort temporal scale, finally lead to remarkable spectral interference and further intensity fluctuations across the combs spectrum. Furthermore, the established mathematical relationship between the spectral flatness and the modulation extinction ratio of the intensity modulators exhibits a nonlinear dependence up to the third order. Cascading intensity modulators has been exploited to mitigate the spectral interference and improve the modulation extinction ratio, which has been verified by using home-made high sensitive autocorrelator and frequency-resolved optical gating (FROG), and finely spectral flatness of 0.54 dB among 11 lines has been achieved, which recognized for the first time that modulation extinction ratio related spectral interference phenomenon play a subtle role in EOCs generation. Furthermore, photonic analog-to-digital converters (PADCs) have been investigated and an obvious enhancement in signal-to-noise-and-distortion (SINAD) is achieved, These findings will provide crucial theoretical and experimental support for optimizing EOCs performance, and advance the development and application. Full article
(This article belongs to the Special Issue Advanced Optoelectronic Materials/Devices and Their Applications)
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21 pages, 8746 KB  
Article
A Hybrid STPA-BN Framework for Quantitative Risk Assessment of Runway Incursions: A Case Study of the Austin–Bergstrom Incident
by Yujiang Feng, Weijun Pan, Rundong Wang, Yanqiang Jiang, Dajiang Song and Xiqiao Dai
Appl. Sci. 2026, 16(6), 2711; https://doi.org/10.3390/app16062711 - 12 Mar 2026
Abstract
The escalating complexity of airport surface operations challenges traditional risk quantification methods. Conventional linear models often fail to capture the non-linear interactions within sociotechnical systems. While hybrid System-Theoretic Process Analysis (STPA) and Bayesian Network (BN) models provide an alternative, existing integrations are frequently [...] Read more.
The escalating complexity of airport surface operations challenges traditional risk quantification methods. Conventional linear models often fail to capture the non-linear interactions within sociotechnical systems. While hybrid System-Theoretic Process Analysis (STPA) and Bayesian Network (BN) models provide an alternative, existing integrations are frequently constrained by ad hoc structural translations and rare-event data sparsity. To address these methodological limitations, this study proposes an enhanced STPA-BN framework. A formalized mapping mechanism (M1–M4) translates qualitative STPA scenarios into a BN topology to quantify non-linear causal dependencies across environmental precursors, operator cognitive states, unsafe control actions, and systemic hazards. Parameterization is achieved via a logic-guided strategy, fusing historical incident data mining with deterministic physical constraints to correct rare-event probabilities. The framework is validated through a reconstruction of the 2023 Austin–Bergstrom runway incursion incident. Results indicate that under low visibility and degraded surveillance, incursion probability escalates to 86%. Sensitivity analysis reveals that while restoring surveillance infrastructure reduces collision risk by ~13%, communication compliance improvements prove insufficient in sensory-deprived environments. These findings quantitatively demonstrate that administrative controls cannot substitute for robust engineering safeguards in complex operations. Full article
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28 pages, 22437 KB  
Article
LightGBM–SHAP-Based Study of the Threshold and Synergistic Effects of Physical and Perceptual Scene Elements on Spatial Vitality in Historic Cultural Districts
by Gaojie Zhang and Zhongshan Huang
Sustainability 2026, 18(6), 2778; https://doi.org/10.3390/su18062778 - 12 Mar 2026
Abstract
The revitalization of vitality in historic cultural districts can enhance a city’s cultural attractiveness and promote the upgrading of the urban cultural industry and sustainable development. Revealing the threshold and synergistic effects of different districts’ scene elements on district vitality helps to identify [...] Read more.
The revitalization of vitality in historic cultural districts can enhance a city’s cultural attractiveness and promote the upgrading of the urban cultural industry and sustainable development. Revealing the threshold and synergistic effects of different districts’ scene elements on district vitality helps to identify the distribution patterns of district vitality and provides a basis for managerial decision-making. This study first uses a geographic information system (ArcGIS) to overlay Baidu heatmaps with the street-network distribution in order to depict the spatiotemporal heterogeneity of district vitality and to compute vitality values by partitions at the district scale. Subsequently, based on an explanatory framework that integrates the physical space and subjective cognition, multi-source data such as street-view panoramas and points of interest (POIs) are quantified to obtain scene-element values for each unit area. Then, the scene-element values and vitality values are integrated into a consolidated database. Additionally, the LightGBM model and the SHAP method are employed to evaluate each element’s marginal contribution and relative importance to district vitality, thereby screening out the key scene elements. Finally, by means of SHAP dependence plots and interaction-effect analysis, the threshold intervals of the key elements and their synergistic relationships are identified, revealing the nonlinear threshold effects and synergies by which scene elements influence spatial vitality. The results show that during rest days, district vitality exhibits stronger diffusion, and the synergistic effect between Leisure-Facility Attractiveness and Street-Network Accessibility is the most prominent in enhancing vitality. High Exhibition-Facility Attractiveness is difficult to sustain crowds on its own; only when Leisure-Facility Attractiveness is likewise high does its effectiveness increase significantly. When Transport Accessibility is within the 0.20–0.40 interval, the positive effect of Leisure-Facility Attractiveness is significantly amplified. An excessive Traditional–Modern Facility Mix readily leads to homogenization of districts; therefore, when introducing modern business formats, local cultural characteristics must be retained. Overall, the generation of district vitality relies more on the synergy between material factors and subjective cognition than on improvements to any single element. The findings of this study provide suggestions for the planning of scene elements and the enhancement of vitality in historic cultural districts. Full article
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36 pages, 417 KB  
Article
A Dynamical Approach to General Relativity Based on Proper Time
by Jaume de Haro
Universe 2026, 12(3), 79; https://doi.org/10.3390/universe12030079 - 12 Mar 2026
Abstract
This work places the invariant ds2 at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension of Fermat’s principle to [...] Read more.
This work places the invariant ds2 at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension of Fermat’s principle to massive particles—namely, the requirement that freely falling bodies follow trajectories that extremize proper time, which for timelike motion corresponds to a local maximum—and invoking the universality of Galilean free fall, we derive the form of ds2 in a static gravitational field. Lorentz invariance then provides the natural framework to extend this result to systems involving moving matter. The invariant derived through this procedure matches the weak-field limit of General Relativity formulated in the harmonic gauge. Within this linearized regime, we show that the structure of the theory already contains the seeds of its nonlinear completion: any dynamically consistent extension to strong gravitational fields necessarily involves the Ricci tensor. From this viewpoint, Einstein’s field equations appear not as a postulated geometric law but as the unique covariant closure required to ensure energy–momentum conservation and the self-consistency of the gravitational interaction. Full article
23 pages, 1246 KB  
Article
Accuracy of Fiber Propagation Evaluation Using Phenomenological Attenuation and Raman Scattering Models in Multiband Optical Networks
by Giuseppina Maria Rizzi and Vittorio Curri
Network 2026, 6(1), 16; https://doi.org/10.3390/network6010016 - 12 Mar 2026
Abstract
The constant growth of IP data traffic, driven by sustained annual increases surpassing 26%, is pushing current optical transport infrastructures towards their capacity limits. Since the deployment of new fiber cables is economically demanding, ultra-wideband transmission is emerging as a promising cost-effective solution, [...] Read more.
The constant growth of IP data traffic, driven by sustained annual increases surpassing 26%, is pushing current optical transport infrastructures towards their capacity limits. Since the deployment of new fiber cables is economically demanding, ultra-wideband transmission is emerging as a promising cost-effective solution, enabled by multi-band amplifiers and transceivers spanning the entire low-loss window of standard single-mode fibers. In this scenario, an accurate modeling of the frequency-dependent fiber parameters is essential to reliably model optical signal propagation. In particular, the combined impact of attenuation variations with frequency and inter-channel stimulated Raman scattering (SRS) fundamentally shapes the power evolution of wide wavelength division multiplexing (WDM) combs and directly affects nonlinear interference (NLI) generation, as well as the amount of ASE noise. In this work, we review a set of analytical approximations, based on phenomenological approaches, for frequency-dependent attenuation and Raman scattering gain, and analyze their impact on achieving an effective balance between computational efficiency and physical fidelity. Through extensive analyses performed with the open-source software GNPy (version 2.12, Telecom Infra Project) on an optical line system exploring multi-band scenarios spanning C+L+S, C+L+E, and U-to-E transmission, we demonstrate that the proposed approximations reproduce the reference SRS power evolution and NLI profiles with root mean square errors (RMSEs) consistently below 0.03 dB, and down to the 10−3–10−2 dB range for the most accurate configurations. Although the current implementation does not yet provide a direct reduction in computational time, the proposed framework lays the groundwork for future developments toward closed-form or semi-analytical solutions, enabling more efficient modeling and optimization of ultra-wideband optical transmission. Full article
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29 pages, 3044 KB  
Article
Shadow of a Nonlinear Electromagnetic Generalized Kerr–Newman–AdS Black Hole
by Mohsen Fathi
Galaxies 2026, 14(2), 21; https://doi.org/10.3390/galaxies14020021 - 11 Mar 2026
Abstract
In this work, we investigate the shadow properties of the Kerr–Newman–Anti-de Sitter black hole coupled to nonlinear electrodynamics. The shadow is constructed by employing the celestial coordinate approach for an observer located at a finite distance, which is required due to the non-asymptotically [...] Read more.
In this work, we investigate the shadow properties of the Kerr–Newman–Anti-de Sitter black hole coupled to nonlinear electrodynamics. The shadow is constructed by employing the celestial coordinate approach for an observer located at a finite distance, which is required due to the non-asymptotically flat structure of the spacetime. The size, distortion, area, and oblateness of the shadow are analyzed in terms of the black hole parameters, namely, the spin, the effective charge, and the nonlinearity parameter. We show that the nonlinear electrodynamics significantly modifies the photon region and therefore changes the shadow observables, while the rotation mainly controls the deformation of the silhouette. We further confront the theoretical results with the Event Horizon Telescope observations of M87* and Sgr A* in order to constrain the parameter space of the model. The allowed ranges of the effective charge depend sensitively on the nonlinearity parameter, and the combination of both sources leads to tighter and physically more consistent bounds. In addition, we study the energy emission rate derived from the shadow radius and the Hawking temperature and discuss how it is affected by the rotation and the nonlinear electromagnetic field. Our analysis shows that the considered black hole solution provides a consistent extension of the Kerr geometry in a non-asymptotically flat background and that the shadow observables can be used as an efficient tool to test the effects of nonlinear electrodynamics in strong gravity. Full article
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13 pages, 2290 KB  
Article
Research on Kinematic Error of Pendulum Interferometer Based on Optomechanical Coupled Simulation
by Zhijie Wu, Dacheng Li, Wei Xiong, Wenpeng Liu, Zhicheng Cao and Yangyu Li
Photonics 2026, 13(3), 270; https://doi.org/10.3390/photonics13030270 - 11 Mar 2026
Abstract
To address the issue of normal displacement deviation induced by the geometric nonlinearity of cross-spring flexural pivots in pendulum-type interferometers, which leads to modulation attenuation, this study proposes a co-simulation method combining Finite Element Analysis (FEA) and Physical Optics. First, an optomechanical model [...] Read more.
To address the issue of normal displacement deviation induced by the geometric nonlinearity of cross-spring flexural pivots in pendulum-type interferometers, which leads to modulation attenuation, this study proposes a co-simulation method combining Finite Element Analysis (FEA) and Physical Optics. First, an optomechanical model was established based on the retroreflective property of cube-corner prisms and a double-pendulum differential scanning architecture (where the optical path difference is four times the mechanical displacement). Using the ANSYS Workbench 2022 R1 transient dynamics module with the “Large Deflection” algorithm enabled, the nonlinear motion trajectories of single-pivot and dual-pivot flexural hinges were quantitatively compared. Subsequently, a multi-physics data mapping interface was established to map mechanical motion errors into a physical optics simulation model, where the interference modulation was accurately calculated via electromagnetic field tracing. Results demonstrate that under ambient temperature (25 °C) and a spectral resolution of 1 cm−1, the normal displacement deviation of the single-pivot hinge is only 0.00165 mm, representing a 95.6% reduction compared to the dual-pivot structure (0.03765 mm). Furthermore, the modulation of the single-pivot structure remains above 0.98 throughout the scanning range, significantly outperforming the nonlinear decay characteristic of the dual-pivot structure. These findings provide a theoretical basis for the structural optimization and selection of high-precision portable FTIR spectrometers. Full article
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31 pages, 6044 KB  
Review
From Physical Replacement to Biological Symbiosis: Evolutionary Paradigms and Future Prospects of Auditory Reconstruction Brain–Computer Interfaces
by Li Shang, Juntao Liu, Shiya Lv, Longhui Jiang, Yu Liu, Sihan Hua, Jinping Luo and Xinxia Cai
Micromachines 2026, 17(3), 343; https://doi.org/10.3390/mi17030343 - 11 Mar 2026
Abstract
Auditory Brain–Computer Interfaces (BCIs) constitute the vital intervention for profound sensorineural hearing loss where the auditory nerve is compromised, yet their clinical efficacy remains restricted by substantial biological bottlenecks and limited spectral resolution. This review critically examines the evolutionary paradigm of auditory restoration, [...] Read more.
Auditory Brain–Computer Interfaces (BCIs) constitute the vital intervention for profound sensorineural hearing loss where the auditory nerve is compromised, yet their clinical efficacy remains restricted by substantial biological bottlenecks and limited spectral resolution. This review critically examines the evolutionary paradigm of auditory restoration, tracing the transition from static physical replacement to dynamic biological symbiosis. We systematically analyze physiological barriers across cochlear, brainstem, and cortical levels, elucidating how rigid interfaces provoke chronic tissue responses and why linear encoding protocols fail in distorted central tonotopy. The article synthesizes emerging methodologies in material science, demonstrating how soft, bio-integrated electronics and biomimetic topologies effectively address mechanical impedance mismatches. Furthermore, the trajectory of neural encoding is evaluated, highlighting the paradigm shift from traditional envelope extraction to deep learning-driven non-linear mapping and adaptive closed-loop neuromodulation. Finally, the potential of high-resolution modulation techniques, including optogenetics and sonogenetics, alongside AI-facilitated intent perception for active listening, is assessed. It is concluded that future neuroprostheses must evolve into symbiotic systems capable of seamlessly integrating with neural plasticity to enable high-fidelity cognitive reconstruction. Full article
(This article belongs to the Section B:Biology and Biomedicine)
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34 pages, 1111 KB  
Review
A Structured Review of Artificial Intelligence Techniques for Ferroresonance Detection and Mitigation in Power Systems
by Salem G. Alshahrani, Mohammed R. Qader and Fatema A. Albalooshi
Encyclopedia 2026, 6(3), 58; https://doi.org/10.3390/encyclopedia6030058 - 10 Mar 2026
Viewed by 41
Abstract
Ferroresonance is a nonlinear phenomenon in power systems capable of producing irregular oscillations and severe overvoltages that threaten transformers, voltage transformers, cables, and associated equipment. This paper presents a structured comprehensive review of ferroresonance detection and mitigation techniques reported up to 2025, with [...] Read more.
Ferroresonance is a nonlinear phenomenon in power systems capable of producing irregular oscillations and severe overvoltages that threaten transformers, voltage transformers, cables, and associated equipment. This paper presents a structured comprehensive review of ferroresonance detection and mitigation techniques reported up to 2025, with particular emphasis on artificial intelligence (AI)-based approaches published during the last five years. A systematic literature search was conducted across IEEE Xplore, Scopus, Web of Science, and Google Scholar using predefined ferroresonance- and AI-related keywords. Eligible studies were screened using explicit inclusion criteria requiring demonstrated ferroresonance relevance. Numerical modeling approaches, electromagnetic transient tools, ferroresonance modes, and mitigation strategies are synthesized, followed by a critical evaluation of machine learning, deep learning, fuzzy logic, evolutionary algorithms, and hybrid intelligent frameworks. Particular emphasis is placed on signal preprocessing, data representation, real-time protection constraints, and cross-topology robustness. The review identifies key research gaps, including the scarcity of benchmark datasets, limited validation under realistic network variability, and the absence of standardized evaluation methodologies. While this work is presented as a structured comprehensive review, PRISMA-inspired screening principles were applied to enhance transparency and reproducibility. Current evidence indicates that hybrid approaches combining physics-informed preprocessing—particularly wavelet-based feature extraction—with lightweight neural classifiers offer the most practical pathway for relay-grade ferroresonance protection in modern smart grids. Full article
(This article belongs to the Section Engineering)
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30 pages, 7652 KB  
Article
Adaptive Force Planning-Integrated Coupled Dynamical Systems for Underwater Soft Hands Grasping Stability Under Marine Disturbances
by Qingjun Zeng, Weiwei Yang, Xiaoqiang Dai, Ning Zhang and Jinxing Liu
J. Mar. Sci. Eng. 2026, 14(6), 520; https://doi.org/10.3390/jmse14060520 - 10 Mar 2026
Viewed by 106
Abstract
As critical end-effectors enabling the practical deployment of marine robotic systems, soft hands face persistent challenges including multi-finger asynchronization, unbalanced force distribution, and insufficient anti-disturbance robustness, compounded by constraints from soft material nonlinearity and harsh marine environmental disturbances. To address these limitations, this [...] Read more.
As critical end-effectors enabling the practical deployment of marine robotic systems, soft hands face persistent challenges including multi-finger asynchronization, unbalanced force distribution, and insufficient anti-disturbance robustness, compounded by constraints from soft material nonlinearity and harsh marine environmental disturbances. To address these limitations, this paper proposes a dexterous grasping method integrating coupled dynamical systems and adaptive force planning control, designed to enhance operational reliability in complex marine environments. An intermediate dynamic layer is embedded to ensure precise multi-finger synchronization, a hybrid force planning algorithm balances force uniformity and constraint satisfaction, and an adaptive controller synergizes with a Neo-Hookean model to compensate for nonlinear deviations. Simulations and physical experiments demonstrate that the method delivers excellent grasping stability and accuracy for uneven mass distribution targets such as cylinders and spheres, while balancing synchronization precision, constraint compliance, and anti-disturbance capability. Compared with the traditional coupled dynamical systems (DSs), the constraint violation is reduced by up to 18.2%, the friction force is increased by 4.0%, and the force distribution uniformity is improved by approximately 5.1%.Compared with the particle swarm optimization (PSO) strategy, the constraint violation is reduced by up to 50.5%, the friction force is increased by 40.9%, and the force distribution uniformity is also improved by about 5.1%. This work fills a key gap in balancing multiple performance metrics for marine soft hands, providing a reliable technical solution to accelerate the real-world deployment of marine robotic systems. Full article
(This article belongs to the Special Issue Wide Application of Marine Robotic Systems)
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33 pages, 2341 KB  
Article
Digital Twin-Based Hybrid Simulation–Prediction Framework for KPI Optimization in Sustainable Digital Printing
by Diana Bratić, Suzana Pasanec Preprotić, Hrvoje Cajner and Branimir Preprotić
Technologies 2026, 14(3), 170; https://doi.org/10.3390/technologies14030170 - 10 Mar 2026
Viewed by 139
Abstract
The increasing emphasis on sustainability in digital printing requires quantitative methods for optimizing key performance indicators (KPIs) under technical and operational constraints. The term digital twin is used here in a methodological and analytical sense, as a simulation framework for analyzing interdependence, prediction, [...] Read more.
The increasing emphasis on sustainability in digital printing requires quantitative methods for optimizing key performance indicators (KPIs) under technical and operational constraints. The term digital twin is used here in a methodological and analytical sense, as a simulation framework for analyzing interdependence, prediction, and multi-criteria optimization of KPIs, rather than as a direct virtual replica of a specific physical production system. This paper proposes a hybrid simulation–prediction model based on a digital twin framework for optimization of KPIs in sustainable digital printing, with particular emphasis on overall equipment effectiveness (OEE). Due to the limited availability of structured industrial data, the model is developed using a synthetically generated dataset constructed in accordance with industry-reported operating ranges and technically realistic digital printing process variables. Random Forest and XGBoost algorithms are applied to model nonlinear relationships between process parameters and KPIs, including material waste, energy consumption, machine downtime, and OEE. Based on these predictive models, a constrained multi-objective optimization procedure is performed to identify Pareto-efficient configurations that reduce material waste and energy consumption while maintaining acceptable downtime and OEE levels. The results characterize structural trade-offs among environmental and operational KPIs within a formally defined decision space. Full article
(This article belongs to the Special Issue Agentic AI-Driven Optimization in Advanced Manufacturing Systems)
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27 pages, 5395 KB  
Article
ML-Driven Decision Support for Dynamic Modeling of Calcareous Sands
by Abdalla Y. Almarzooqi, Mohamed G. Arab, Maher Omar and Emran Alotaibi
Mach. Learn. Knowl. Extr. 2026, 8(3), 68; https://doi.org/10.3390/make8030068 - 9 Mar 2026
Viewed by 96
Abstract
Dynamic characterization of calcareous (carbonate) sands is essential for performance-based design of offshore foundations, coastal reclamation, and marine infrastructure in tropical and subtropical regions. In contrast to silica sands, carbonate sediments are biogenic and typically comprise angular, irregular grains with intra-particle voids and [...] Read more.
Dynamic characterization of calcareous (carbonate) sands is essential for performance-based design of offshore foundations, coastal reclamation, and marine infrastructure in tropical and subtropical regions. In contrast to silica sands, carbonate sediments are biogenic and typically comprise angular, irregular grains with intra-particle voids and fragile skeletal microstructure. These traits promote grain crushing and fabric evolution at relatively low-to-moderate confinement, leading to pronounced stress dependency, strong nonlinearity with strain amplitude, and substantial scatter in laboratory stiffness and damping measurements. Consequently, empirical correlations calibrated primarily on quartz sands may yield biased estimates when transferred to carbonate environments. This study presents an ML-driven, leakage-aware benchmarking framework for predicting two key dynamic parameters of biogenic calcareous sands, damping ratio D and shear modulus G, using standard tabular descriptors commonly available in geotechnical practice. Two consolidated experimental databases were curated from resonant column and cyclic triaxial measurements (D: n=890; G: n=966), spanning mean effective confining stress 25  σm1600 kPa and a wide range of density and gradation conditions. To emphasize transferability, explicit deposit/site labels were excluded, and missingness arising from heterogeneous reporting was handled through a consistent preprocessing pipeline (training-only imputation, categorical encoding, and scaling). Eleven regression algorithms were evaluated, covering linear baselines, regularized regression, neighborhood learning, single trees, bagging and boosting ensembles, kernel regression, and a feedforward neural network. Performance was assessed using R2, RMSE, and MAE on training/validation/test splits, and engineering credibility was supported through explainability-based diagnostics to verify mechanically plausible sensitivities. Results show that ensemble-tree models (Extra Trees and Random Forest) provide the most reliable accuracy–robustness balance across both targets, consistently outperforming linear models and the tested SVR configuration and exhibiting stable validation-to-test behavior. The explainability audit confirms physically meaningful separation of governing controls: stiffness is primarily stress-controlled (σm dominant for G), whereas damping is primarily strain-controlled (γ dominant for D). The proposed framework supports practical deployment as a fast surrogate for generating Gγ and Dγ curves within the training domain and for guiding targeted laboratory test planning in carbonate settings. Full article
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34 pages, 605 KB  
Article
A Physically Constrained KPP–Rate-and-State Reaction–Diffusion Framework for Stable Large-Scale Modeling of Stress Evolution
by Boi-Yee Liao
Electronics 2026, 15(5), 1131; https://doi.org/10.3390/electronics15051131 - 9 Mar 2026
Viewed by 160
Abstract
The emergence of large-scale models and machine learning has transformed the modeling of complex nonlinear systems, such as postseismic stress evolution. However, purely data-driven approaches often lack interpretability and numerical stability, leading to physically inconsistent long-term predictions. This study addresses these limitations by [...] Read more.
The emergence of large-scale models and machine learning has transformed the modeling of complex nonlinear systems, such as postseismic stress evolution. However, purely data-driven approaches often lack interpretability and numerical stability, leading to physically inconsistent long-term predictions. This study addresses these limitations by introducing a coupled Kolmogorov–Petrovsky–Piskunov–Rate-and-State (KPP–RS) reaction–diffusion system as a rigorous physical prior for large-scale modeling of stress-driven dynamics. Using analytic semigroup theory and Banach’s fixed-point theorem, we establish the global existence and uniqueness of solutions, ensuring that the governing dynamics are mathematically well posed—a necessary prerequisite for stable learning-based frameworks. We further prove the global dissipativity of the system and identify a bounded absorbing set in the H1 phase space, which imposes intrinsic physical constraints and limits unphysical parameter exploration in large-scale optimization or black-box modeling. In addition, a Courant–Friedrichs–Lewy (CFL) stability condition is derived, providing a theoretical benchmark for time-step selection in numerical implementations, including physics-informed or hybrid neural architectures. This analytical framework supplies a mathematically controlled foundation for developing robust, interpretable, and stable pattern-recognition or time-series representations in complex geophysical systems. Full article
27 pages, 8552 KB  
Article
A Data-Constrained and Physics-Guided Conditional Diffusion Model for Electrical Impedance Tomography Image Reconstruction
by Xiaolei Zhang and Zhou Rong
Sensors 2026, 26(5), 1728; https://doi.org/10.3390/s26051728 - 9 Mar 2026
Viewed by 141
Abstract
Electrical impedance tomography (EIT) provides noninvasive, high-temporal-resolution imaging for medical and industrial applications. However, accurate image reconstruction remains challenging due to the severe ill-posedness and nonlinearity of the inverse problem, as well as the limited robustness of existing single-source learning-based methods in real [...] Read more.
Electrical impedance tomography (EIT) provides noninvasive, high-temporal-resolution imaging for medical and industrial applications. However, accurate image reconstruction remains challenging due to the severe ill-posedness and nonlinearity of the inverse problem, as well as the limited robustness of existing single-source learning-based methods in real measurement scenarios. To address these limitations, a data-constrained and physics-guided Multi-Source Conditional Diffusion Model (MS-CDM) is proposed for EIT image reconstruction. Unlike conventional conditional diffusion methods that rely on a single measurement or an image prior, MS-CDM utilizes boundary voltage measurements as data-driven constraints and incorporates coarse reconstructions as physics-guided structural priors. This multi-source conditioning strategy provides complementary guidance during the reverse diffusion process, enabling balanced recovery of fine boundary details and global topological consistency. To support this framework, a Hybrid Swin–Mamba Denoising U-Net is developed, combining hierarchical window-based self-attention for local spatial modeling with bidirectional state-space modeling for efficient global dependency capture. Extensive experiments on simulated datasets and three real EIT experimental platforms demonstrate that MS-CDM consistently outperforms state-of-the-art numerical, supervised, and diffusion-based methods in terms of reconstruction accuracy, structural consistency, and noise robustness. Moreover, the proposed model exhibits robust cross-system applicability without system-specific retraining under multi-protocol training, highlighting its practical applicability in diverse real-world EIT scenarios. Full article
(This article belongs to the Section Sensing and Imaging)
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