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Keywords = multi-parameter inverse problem

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27 pages, 2027 KB  
Article
Multi-Scenario Decision-Making for Carbon Asset Management of Cement Industry Under China’s New Unified National Carbon Market
by Yiwen Zhang, Lu Yu, Yufan Dong, Boyan Zou and Yue Liu
Sustainability 2026, 18(12), 6054; https://doi.org/10.3390/su18126054 - 12 Jun 2026
Viewed by 160
Abstract
The inclusion of the cement industry into China’s national carbon emissions trading system in 2025 has fundamentally altered the compliance environment for high-emission enterprises, transforming carbon allowances from passive regulatory instruments into dynamic assets whose management directly affects financial performance. We develop a [...] Read more.
The inclusion of the cement industry into China’s national carbon emissions trading system in 2025 has fundamentally altered the compliance environment for high-emission enterprises, transforming carbon allowances from passive regulatory instruments into dynamic assets whose management directly affects financial performance. We develop a multi-scenario carbon asset management decision model tailored to the intensity-based benchmarking mechanism adopted by the national market. The model centres on the quota surplus-deficit variable EA4, which is computed from enterprise-level emission intensity relative to the industry benchmark, and decomposes the management problem into sequential selling and buying subproblems linked by coupled decision boundaries. A systematic parameter framework is constructed, and the model is applied to two cement enterprises—Enterprise A, a leading producer with a clear allowance surplus, and Enterprise B, a mid-tier producer operating near the benchmark boundary—through historical backtesting over the 2024–2025 period. Three principal findings emerge. First, the intensity benchmarking mechanism creates a dual-leverage effect whereby a 1.4% improvement in emission intensity (from 0.8112 to 0.8000 t/t) increases the quota surplus by 27%, a nonlinearity not captured by conventional compliance-cost models. Second, the model-driven strategy outperforms traditional experience-based approaches by 36.8% (baseline scenario, +95.20 vs. +69.58 MRMB) and 37.3% (risk scenario, −44.55 vs. −71.08 MRMB), with the improvement rate remaining consistent across both enterprises, suggesting that trading timing outweighs instrument selection in determining compliance cost outcomes. Third, dynamic CEA–CCER allocation captures an incremental 2.33 MRMB through the exploitation of a transient price inversion, a gain invisible to single-instrument strategies. Sensitivity analysis confirms that the relative advantage is robust to carbon price variations (±30%) and CCER offset caps (2–10%), while emission intensity and carry-over allowances represent the most consequential parameters for strategy direction, with EA4 crossing zero near the industry benchmark (I ≈ 0.85). The framework provides actionable decision support for cement and other high-emission enterprises navigating the unified carbon market, and contributes a quantitative methodology to the emerging field of environmental management accounting. This study contributes to Sustainable Development Goal 13 (Climate Action), Goal 7 (Affordable and Clean Energy), and Goal 9 (Industry, Innovation, and Infrastructure) by providing operational tools for decarbonisation in carbon-intensive industries. Full article
(This article belongs to the Special Issue Sustainable Development: Integrating Economy, Energy and Environment)
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23 pages, 2895 KB  
Article
A Hybrid Modelling and Simulation Framework for Energy-Efficient Operation of Heated Crude Oil Pipelines Under Small-Batch and Multi-Condition Operation
by Yi Guo, Chun Li, Yang Lv, Liuxiao Li, Yangfan Lu and Kai Wen
Modelling 2026, 7(3), 115; https://doi.org/10.3390/modelling7030115 - 12 Jun 2026
Viewed by 186
Abstract
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and [...] Read more.
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and conservative energy use. To address this problem, this study develops a hybrid modelling and simulation framework for the energy-efficient operation of heated crude oil pipelines. The framework integrates operating-state perception, online parameter inversion, transient thermo-hydraulic simulation, data assimilation, and rolling optimization. First, an online parameter inversion method based on inverse problem solving is established to dynamically identify the overall heat-transfer coefficient and friction correction factor from Supervisory Control and Data Acquisition (SCADA) measurements. Second, a transient thermo-hydraulic simulation and data-assimilation model is constructed to predict pressure, temperature, and safety margins under changing boundary conditions. Third, a constraint-aware rolling optimization strategy is introduced to coordinate heating and pumping operations while satisfying temperature and pressure constraints. The proposed framework is validated using a practical crude oil pipeline. Under a representative low-flow-rate condition, online parameter inversion corrects the overestimation of the thermo-hydraulic state by the fixed-parameter model: the total temperature drop along the pipeline is revised from 33.12 °C to 35.65 °C, and the minimum station-inlet oil temperature is revised from 24.77 °C to 21.61 °C. After optimization is introduced, the total operating energy consumption decreases from 11,715.65 kW to 11,287.43 kW, corresponding to a reduction of 3.66%, while all temperature and pressure constraints remain satisfied. Under time-varying boundary conditions, the rolling optimization strategy further adjusts heating-furnace operation according to variations in inlet flow rate, inlet oil temperature, and ambient temperature, thereby reducing cumulative heating energy consumption while maintaining safe operation. The results demonstrate that the proposed framework provides an implementable modelling and simulation approach for online state assessment, transient prediction, and energy-efficient operation of heated crude oil pipelines under variable operating conditions. Full article
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25 pages, 6027 KB  
Article
Data-Driven Inverse Design of Turbine Blade Passages
by Francesco Porta, Antonio Pucciarelli and Sergio Lavagnoli
Energies 2026, 19(12), 2796; https://doi.org/10.3390/en19122796 - 10 Jun 2026
Viewed by 268
Abstract
To overcome the computational bottlenecks of iterative Computational Fluid Dynamics (CFD) in turbomachinery design, this study introduces a real-time, data-driven inverse design framework for 2D uncooled, high-Reynolds turbine blades. The novelty of this work lies in the application of Kolmogorov–Arnold Networks (KAN), a [...] Read more.
To overcome the computational bottlenecks of iterative Computational Fluid Dynamics (CFD) in turbomachinery design, this study introduces a real-time, data-driven inverse design framework for 2D uncooled, high-Reynolds turbine blades. The novelty of this work lies in the application of Kolmogorov–Arnold Networks (KAN), a distinct deep-learning architecture, to predict blade geometry and performance metrics from aerodynamic loading inputs. The foundation of the model is a comprehensive database of approximately 30,000 blade profiles, generated through an automated optimization pipeline coupled with the MISES solver. This dataset explores an extensive design space, covering inlet flow angles from 50 to 0 and outlet angles from 50 to 75, with flow turning up to 125. A rigorous benchmarking campaign compares KAN against Multi-Layer Perceptrons (MLPs) and Gaussian Process Regression (GPR), highlighting KAN’s capability to overcome the scalability bottlenecks of Gaussian Process Regression to enable real-time performance while achieving MLP-level accuracy with significantly fewer parameters. A further analysis regarding the trade-off between database size and filtration of unfeasible designs indicates that an optimal data filtration threshold exists, balancing noise reduction with model robustness. The final KAN tool achieves real-time inference speeds (∼0.1 s), reducing the design cycle by four orders of magnitude compared to traditional solvers, while maintaining high accuracy (mean outlet angle error of 0.086 and Mach profile RMS error of 0.004). Furthermore, the model’s predicted RMS error is exploited as a quantitative proxy for aerodynamic feasibility, identifying ill-posed inverse problems where the target loading cannot be physically realized. This metric enables the generation of comprehensive maps that rigorously delineate the boundaries of the viable design space across arbitrary aerodynamic loading styles, providing physics-aware guidelines for preliminary design. Full article
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36 pages, 3275 KB  
Article
A Symmetry-Driven Inverse Design Framework for Multi-Agent Cooperative Deployment Under Line-of-Sight Constraints
by Fenghua Chen, Mindong Liu, Fuchao Dai and Weipeng Zhou
Symmetry 2026, 18(6), 980; https://doi.org/10.3390/sym18060980 - 5 Jun 2026
Viewed by 148
Abstract
Cooperative deployment of mobile agents under geometric and line-of-sight constraints gives rise to high-dimensional constrained optimization problems whose underlying physical configuration often exhibits exploitable structure. This paper develops a symmetry-driven inverse design framework that leverages two structural features of the engagement geometry—the [...] Read more.
Cooperative deployment of mobile agents under geometric and line-of-sight constraints gives rise to high-dimensional constrained optimization problems whose underlying physical configuration often exhibits exploitable structure. This paper develops a symmetry-driven inverse design framework that leverages two structural features of the engagement geometry—the Z2×Z2 mirror symmetries of the extended target silhouette and a closed-form forward–inverse correspondence between line-of-sight-aligned burst locations and physical agent parameters—to construct low-dimensional seeds for subsequent physical parameter optimization. The framework is developed and validated on a representative naval defense instance in which a fleet of unmanned aerial vehicles (UAVs) releases spherical obscuration payloads to interrupt the line of sight between incoming mobile threats and a cylindrical extended target. Instead of searching only over the four-dimensional UAV parameter space (heading angle, speed, drop time, fuse delay), the method first specifies a desired burst location in a two-dimensional inverse space and analytically back-calculates feasible agent parameters, which are then refined by multi-start Nelder–Mead optimization in the physical parameter space. A conservative three-dimensional cylindrical line-of-sight obscuration model is developed by constructing four extreme tangent sightlines from the missile to the cylindrical target and verifying whether the spherical smoke cloud simultaneously blocks all of them. A hierarchical multi-agent task allocation framework combines a performance matrix, assignment enumeration, and joint multi-start refinement. Numerical experiments on five progressively complex sub-problems demonstrate obscuration durations of 1.362 s (single fixed shot), 4.580 s (optimized shot), 7.324 s (three-shot relay), 11.140 s (three-UAV cooperation), and 20.652 s (full five-UAV three-missile assignment). Additional high-dimensional benchmarks, sensitivity tests, and error analyses clarify the reproducibility and limitations of the approach. Full article
(This article belongs to the Section Engineering and Materials)
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25 pages, 3018 KB  
Review
Inversion of Sound Speed Profile Controlled by Sparse Observations: Research Background, Current Status and Technical Analysis
by Haopeng Fan, Shuling Xie and Shuqiang Xue
Oceans 2026, 7(3), 45; https://doi.org/10.3390/oceans7030045 - 29 May 2026
Viewed by 327
Abstract
The sound speed profile (SSP) is a core environmental parameter for underwater acoustic detection, navigation, communication, and other applications. However, its accurate acquisition is constrained by the sparsity of observational data and the ill-posed nature of inversion problems. This paper systematically reviews the [...] Read more.
The sound speed profile (SSP) is a core environmental parameter for underwater acoustic detection, navigation, communication, and other applications. However, its accurate acquisition is constrained by the sparsity of observational data and the ill-posed nature of inversion problems. This paper systematically reviews the research progress of SSP inversion under sparse observation constraints. The review traces the technical evolution from early physical models to current intelligent paradigms, classifies and compares mainstream inversion methods, presents typical application scenarios with quantitative case studies, provides a comparison of all kinds of SSP acquisition routes, and discusses critical challenges and future trends. The review reveals that current AI-driven methods achieve a practical accuracy of approximately 1–2 m/s but face bottlenecks in interpretability, cross-regional generalization, and extreme-condition robustness. Fusing physical constraints with multi-source sparse data (remote sensing, in-situ discrete measurements) emerges as the core direction for balancing inversion accuracy, efficiency, and cost. This paper provides a comprehensive reference for technical selection in marine acoustics, ocean observation, and underwater operations. Full article
(This article belongs to the Special Issue Ocean Observing Systems: Latest Developments and Challenges)
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22 pages, 19644 KB  
Article
Joint Inversion of Core Porosity and Permeability Based on GeoFE-PPNet
by Tong Wu, Junjie Huang, Qihao Qian and Quanhou Li
Processes 2026, 14(11), 1745; https://doi.org/10.3390/pr14111745 - 27 May 2026
Viewed by 183
Abstract
To address the problems of strong vertical heterogeneity in thin interbedded reservoirs of the N block in Daqing Oilfield, the complex coupling between porosity and permeability, and the difficulty of conventional single-parameter inversion methods in balancing local details with global geological background, a [...] Read more.
To address the problems of strong vertical heterogeneity in thin interbedded reservoirs of the N block in Daqing Oilfield, the complex coupling between porosity and permeability, and the difficulty of conventional single-parameter inversion methods in balancing local details with global geological background, a joint inversion method for porosity and permeability based on GeoFE-PPNet and logging imaging tensors is proposed. Using conventional logging curves, including GR, RT, RHOB, NPHI, DT, and PE, the method constructs a logging imaging tensor by integrating multi-channel responses with shale constraints and extracts intra-layer textural features through local encoding. Meanwhile, sequence decomposition and frequency enhancement are introduced to capture vertical trend variations and high-frequency non-stationary responses of the reservoir. On this basis, geological constraint fusion and dual-task collaborative prediction are employed to achieve joint inversion of porosity and permeability. Experimental results show that the proposed method achieves favorable inversion accuracy and cross-well generalization under complex reservoir conditions, with a porosity R2 of 0.931, a permeability R2 of 0.887, and an overall accuracy of 90.74%. Ablation and noise robustness experiments further demonstrate the effectiveness of the logging imaging tensor, frequency enhancement, geological constraints, and dual-task collaboration in improving model performance. The study indicates that the proposed method can more accurately characterize the vertical variation in reservoir physical properties and provides a new technical approach for fine reservoir evaluation and intelligent log interpretation. Full article
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48 pages, 8425 KB  
Article
Fractional Epidemic Modeling: Theoretical Constructions and Estimation Strategies
by Mieczysław Cichoń and Kinga Cichoń
Appl. Sci. 2026, 16(11), 5347; https://doi.org/10.3390/app16115347 - 26 May 2026
Viewed by 262
Abstract
This paper presents a generalized epidemic modeling framework based on g-tempered Caputo fractional derivatives with discrete time delays. The proposed approach incorporates nonlocal memory effects, nonlinear temporal scaling, and delayed epidemiological responses within a unified mathematical structure. The introduction of the nonlinear [...] Read more.
This paper presents a generalized epidemic modeling framework based on g-tempered Caputo fractional derivatives with discrete time delays. The proposed approach incorporates nonlocal memory effects, nonlinear temporal scaling, and delayed epidemiological responses within a unified mathematical structure. The introduction of the nonlinear time transformation g(t) and the tempering parameter λ eliminates the unrealistic infinite-memory behavior associated with classical power-law kernels while simultaneously introducing new challenges related to parameter identifiability and inverse problems. We investigate the structural properties of the resulting dynamical systems and show that the associated inverse problem is inherently ill-posed. To illustrate the practical implications of these results, the framework is applied to a delayed SIQR epidemiological model. Numerical simulations are performed using a generalized L1-type scheme adapted to delayed fractional histories, and a multi-phase parameter estimation procedure is proposed to address the ill-posedness of the reconstruction problem. The results demonstrate the ability of the model to capture both short- and long-term memory effects in epidemic evolution while highlighting the challenges of statistical identifiability in generalized fractional systems. Full article
(This article belongs to the Special Issue Data Statistics for Epidemiological Research—2nd Edition)
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45 pages, 20057 KB  
Article
Multi-Objective Robotics Optimization Using Improved MO-BxR Algorithms
by Ravipudi Venkata Rao, Harishankar Morazha Variam and Joao Paulo Davim
Appl. Sci. 2026, 16(10), 5162; https://doi.org/10.3390/app16105162 - 21 May 2026
Viewed by 321
Abstract
Robotics optimization is essential for improving the performance, efficiency, and reliability of robotic systems, especially when dealing with complex engineering problems involving multiple conflicting objectives. Algorithm-specific parameter-free metaheuristic algorithms have gained attention in such applications because they eliminate the need for problem-specific parameter [...] Read more.
Robotics optimization is essential for improving the performance, efficiency, and reliability of robotic systems, especially when dealing with complex engineering problems involving multiple conflicting objectives. Algorithm-specific parameter-free metaheuristic algorithms have gained attention in such applications because they eliminate the need for problem-specific parameter tuning. However, their performance can be further enhanced by improving convergence and maintaining solution diversity in multi-objective optimization. This paper proposes three multi-objective variants—archive, opposition, and self-adaptive multi-population (SAMP)—for the algorithm-specific parameter-free BxR algorithms such as Best–Mean–Random (BMR), Best–Worst–Random (BWR), and Best–Mean–Worst–Random (BMWR). The proposed variants are evaluated on five robotic optimization problems spanning two to six objectives, including Autonomous Underwater Vehicle shape optimization, power line inspection robot design, inverse kinematics of a 4-DOF manipulator, wall-building robot trajectory planning, and optimization of a reconfigurable parallel cutting and grinding mechanism. Their performance is compared with several established multi-objective algorithms using metrics such as GD, IGD, SPC, and HV, supported by rigorous statistical testing involving Friedman tests, Conover post hoc analysis with Holm correction, and Vargha–Delaney A12 effect sizes over 30 independent runs. The results show that archive variants achieve the best IGD rank in four of the five case studies and the best HV rank in three of them, with the five-objective trajectory planning problem being the sole exception where SAMP and base BxR variants show improved IGD performance. The base BxR algorithms prove to be strong competitors, consistently outperforming established parameter-dependent methods on IGD across all five problems. The opposition variants do not provide consistent improvement; however, they also do not cause catastrophic degradation, suggesting that refined opposition strategies warrant further investigation. The study demonstrates the effectiveness of the proposed algorithms as practical optimization tools for complex robotic optimization problems. Full article
(This article belongs to the Section Mechanical Engineering)
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9 pages, 1490 KB  
Communication
A Study on Thin-Film Dispersion Interference Spectral Measurement by Integrating Deep Learning and Physical Model Fitting
by Tong Wu, Haopeng Li, Chenxu Liu, Chuan Zhang, Jiahao Wu, Jingwei Yu, Jianjun Liu, Zepei Zheng, Bosong Duan, Anyu Sun and Bingfeng Ju
Metrology 2026, 6(2), 33; https://doi.org/10.3390/metrology6020033 - 15 May 2026
Viewed by 259
Abstract
In the context of the increasing demands of precision manufacturing and nanotechnology, especially for emerging fields such as Oxide oxide films in Nuclear nuclear fuel assemblies, the measurement of multi-layer inhomogeneous thin films faces significant challenges. Traditional spectroscopic interference thickness measurement techniques have [...] Read more.
In the context of the increasing demands of precision manufacturing and nanotechnology, especially for emerging fields such as Oxide oxide films in Nuclear nuclear fuel assemblies, the measurement of multi-layer inhomogeneous thin films faces significant challenges. Traditional spectroscopic interference thickness measurement techniques have limitations in handling dispersion interference, parameter coupling, and the efficient solution of nonlinear inverse problems. This study proposes a new model that integrates deep learning and physical model fitting. It constructs a theoretical model of multi-layer thin-film interference spectroscopy based on the Lorentz–Drude formula, uses a generative adversarial network (GAN) for initial structure analysis, and builds a two-layer optimization framework of “deep learning rough positioning—physical model fine fitting”. The research aims to break through the limitations of traditional methods, improve measurement accuracy and anti-noise ability, and provide a key technical support for emerging fields. Full article
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29 pages, 20397 KB  
Article
Mayfly–Deep Learning Fusion for High-Dimensional Parameter Identification and Reinforcement of Historical Buildings
by Zhong Peng, Bin Cheng, Shanjun Zhang, Zhiyong Li and Wei Li
Buildings 2026, 16(10), 1908; https://doi.org/10.3390/buildings16101908 - 11 May 2026
Viewed by 500
Abstract
Structural health assessment of historic buildings frequently relies on finite element (FE) model updating, yet high-dimensional parameter identification under sparse, noise-contaminated modal data can reduce robustness and lead to prohibitive computational cost. This paper proposes an application-oriented integrated workflow that improves identification stability [...] Read more.
Structural health assessment of historic buildings frequently relies on finite element (FE) model updating, yet high-dimensional parameter identification under sparse, noise-contaminated modal data can reduce robustness and lead to prohibitive computational cost. This paper proposes an application-oriented integrated workflow that improves identification stability while accelerating the updating process. A multi-indicator objective function is formulated by combining residuals of natural frequencies and mode shapes with sensitivity-based consistency relations. The inverse problem is solved using the Mayfly Algorithm (MA), and a deep neural network (DNN) surrogate is introduced to replace repeated FE modal analyses during the optimization, thereby reducing the overall computational burden. The proposed workflow is demonstrated on the Christian Lutheran Church in Wuhan, China, constructed from 1923 to 1924, using operational modal testing data collected at 25 measurement points. A refined FE model is updated by identifying 24 grouped stiffness reduction coefficients that represent columns, beams, walls, and slabs across different floors. The updated model shows substantially improved agreement with the measured first four natural frequencies and corresponding mode shapes, enabling a quantitative diagnosis of stiffness degradation and supporting stiffness-oriented reinforcement planning. A stiffness enhancement target of 20% is adopted to guide intervention measures, and an analytical modal enhancement check is provided to relate the stiffness target to the expected frequency gain. The workflow offers a reproducible route for data-informed decision support in heritage building assessment and rehabilitation, while uncertainty quantification and post-intervention validation are identified as key priorities for future work. Under the available sparse modal information, the inverse problem is underdetermined; therefore, the reported stiffness-reduction coefficients should be interpreted as non-unique grouped solutions affected by modelling and measurement uncertainty, and the reinforcement measures are presented only as planning-level design proposals requiring post-intervention verification. Full article
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57 pages, 13008 KB  
Article
Corrosion Diagnosis of Hydroelectric Grounding Grids Based on Voltage Distribution Symmetry Deviation via a Quantum-Inspired Candidate Pool Guided Sine Cosine Algorithm
by Xinyue Zhang, Keying Wang and Liangliang Li
Symmetry 2026, 18(5), 753; https://doi.org/10.3390/sym18050753 - 27 Apr 2026
Viewed by 343
Abstract
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution [...] Read more.
Hydropower stations, as critical infrastructure for basic energy supply, play a pivotal role in ensuring the reliability of power systems through their safe and stable operation. Grounding grids operating long-term in complex soil environments are prone to corrosion and degradation, disrupting current distribution balance and causing spatial asymmetry in the voltage field, thereby compromising system safety. Corrosion branch resistance increment identification based on the electrical network method is typically modeled as a parameter inversion optimization problem. However, this problem exhibits underdetermination and other characteristics, making it difficult for traditional analytical methods to obtain stable solutions. To address this, this paper proposes a quantum perturbation scheduling candidate pool-guided sine–cosine algorithm (QSPSCA). Building upon the classical sine–cosine algorithm framework, it incorporates a dynamic candidate pool with multi-source attractor points and a quantum-inspired long-tail scheduling local refinement operator. This achieves an enhanced and smooth transition between global exploration and local refinement. Comparative experiments based on the CEC2017 benchmark and a hydropower station grounding grid corrosion diagnosis case demonstrate that QSPSCA outperforms multiple comparison algorithms in terms of average optimality and result stability. Furthermore, QSPSCA is applied to three typical engineering-constrained optimization problems. Results demonstrate that, whilst satisfying engineering constraints, this method consistently yields higher-quality feasible solutions with superior convergence accuracy and stability compared to alternative algorithms. Therefore, QSPSCA is not only applicable to underdetermined inversion diagnostics but also provides a solution framework with broad applicability for complex engineering optimization problems under structural symmetry perturbations. Full article
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27 pages, 5409 KB  
Article
Frequency-Domain Physics-Informed Neural Networks for Modeling and Parameter Inversion of Wave-Induced Seabed Response
by Weiyun Chen, Hairong Tao, Lei Wang and Shaofen Fan
J. Mar. Sci. Eng. 2026, 14(8), 690; https://doi.org/10.3390/jmse14080690 - 8 Apr 2026
Viewed by 627
Abstract
Modeling the dynamic response of saturated marine soils is crucial yet computationally challenging for traditional methods. Meanwhile, purely data-driven models suffer from sparse data and lack of physical interpretability. To overcome these limitations, this study proposes an intelligent engineering framework based on a [...] Read more.
Modeling the dynamic response of saturated marine soils is crucial yet computationally challenging for traditional methods. Meanwhile, purely data-driven models suffer from sparse data and lack of physical interpretability. To overcome these limitations, this study proposes an intelligent engineering framework based on a frequency-domain physics-informed neural network (FD-PINN) for the forward simulation and inverse parameter identification of saturated seabed soils. Constrained directly by physical laws during the learning process, FD-PINN remains highly reliable even when training data is sparse. By formulating the governing equations in the frequency domain, it directly predicts complex-valued displacement and pore-pressure phasors. Multiscale Fourier feature mappings mitigate spectral bias and capture boundary layers and high-frequency effects. For inverse problems, a phase-sensitive lock-in extraction strategy transforms time-domain measurements into robust frequency-domain targets, enabling the accurate and noise-tolerant identification of poroelastic parameters with clear physical meaning (nondimensional storage parameter S and permeability parameter Γ). Numerical experiments show that FD-PINN substantially outperforms conventional time-domain PINN, achieving relative L2 errors of 102103 for single- and multi-frequency excitations typical of wave-induced loadings. In particular, Γ is consistently recovered with sub-percent relative error, while S can be reliably identified with multi-frequency data. The framework offers a data-efficient, noise-robust approach for high-fidelity modeling and robust parameter inversion, which is particularly valuable in offshore environments where high-quality data is scarce. Full article
(This article belongs to the Special Issue Advances in Marine Geomechanics and Geotechnics)
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13 pages, 3260 KB  
Article
Efficient Deep Image Prior with Spatial-Channel Attention Transformer
by Weiwei Lin, Zeqing Zhang, Jin Lin and Ying You
Mathematics 2026, 14(7), 1185; https://doi.org/10.3390/math14071185 - 1 Apr 2026
Viewed by 599
Abstract
The deep image prior (DIP) suggests that it is possible to train a randomly initialized network with a suitable architecture to solve inverse imaging problems by simply optimizing its parameters to reconstruct a single degraded image. However, the prior knowledge exploited by vanilla [...] Read more.
The deep image prior (DIP) suggests that it is possible to train a randomly initialized network with a suitable architecture to solve inverse imaging problems by simply optimizing its parameters to reconstruct a single degraded image. However, the prior knowledge exploited by vanilla DIP relies on basic local convolutions, which inevitably limits the performance of inverse imaging tasks to the generative capacity of the model. Furthermore, image information is often not only related to neighboring pixels but also dependent on global color features and spatial distribution. Simple local convolutions used in inverse imaging cannot capture precise fine-grained details. Moreover, DIP is an unsupervised process but requires iterations to learn inverse imaging, consuming computational power and limiting the adaptation of global attention. To solve these problems, this article explores an efficient global prior module—a tri-directional multi-head self-attention mechanism—aiming to learn pixel-wise correlations along three directions: horizontal, vertical, and channel-wise. Our observations found that global learning can effectively enhance the detail information of edge pixels, making images more vivid and textures clearer. In addition, tri-directional multi-head self-attention can efficiently replace the global perception ability of pixel-level self-attention. Finally, we demonstrate that global learning can effectively improve the imaging effect of inverse imaging problems and enhance the information of texture edge pixels. Moreover, tri-directional multi-head self-attention can effectively alleviate the computation redundancy of pixel-level self-attention, thus achieving efficient and high-quality inverse imaging tasks. The principle of this method lies in global feature capture and efficient attention modeling, striking a balance between detail fidelity and computational practicality. Full article
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48 pages, 14824 KB  
Review
Convergence of Multidimensional Sensing: A Review of AI-Enhanced Space-Division Multiplexing in Optical Fiber Sensors
by Rabiu Imam Sabitu and Amin Malekmohammadi
Sensors 2026, 26(7), 2044; https://doi.org/10.3390/s26072044 - 25 Mar 2026
Viewed by 1470
Abstract
The growing demand for high-fidelity, multi-parameter, distributed sensing in critical domains such as structural health monitoring, oil and gas exploration, and secure perimeter surveillance is pushing traditional optical fiber sensors (OFS) to their performance limits. Although conventional multiplexing techniques such as time-division and [...] Read more.
The growing demand for high-fidelity, multi-parameter, distributed sensing in critical domains such as structural health monitoring, oil and gas exploration, and secure perimeter surveillance is pushing traditional optical fiber sensors (OFS) to their performance limits. Although conventional multiplexing techniques such as time-division and wavelength-division multiplexing (TDM, WDM) have been commercially successful, they are rapidly approaching fundamental bottlenecks in sensor density, spatial resolution, and data capacity. This review argues that the synergistic convergence of space-division multiplexing (SDM) and artificial intelligence (AI) represents a paradigm shift, enabling a new generation of intelligent, high-dimensional sensing networks. We comprehensively survey the state of the art in SDM-based OFS, detailing the operating principles and applications of multi-core fibers (MCFs) for ultra-dense sensor arrays and 3D shape sensing, as well as few-mode fibers (FMFs) for mode-division multiplexing and enhanced multi-parameter discrimination. However, the unprecedented spatial parallelism provided by SDM introduces significant challenges, including inter-channel crosstalk, complex signal demultiplexing, and massive data volumes. This paper systematically explores how AI, particularly machine learning (ML) and deep learning (DL), is being leveraged not merely as a tool but as an indispensable core technology to mitigate these impairments. We critically analyze AI’s role in digital crosstalk suppression, intelligent mode demultiplexing, signal denoising, and solving complex inverse problems for parameter estimation. Furthermore, we highlight how this AI–SDM synergy enables capabilities beyond the reach of either technology alone, such as super-resolution sensing and predictive analytics. The discussion is extended to include the critical supporting pillars of this ecosystem, such as advanced interrogation techniques and the associated data management challenges. Finally, we provide a forward-looking perspective on the trajectory of the field, outlining a path toward cognitive sensing networks that are self-calibrating, adaptive, and capable of autonomous decision-making. This review is intended to serve as a foundational reference for researchers and engineers at the intersection of photonics and intelligent systems, illuminating the pathway toward tomorrow’s intelligent sensing infrastructure. Full article
(This article belongs to the Collection Artificial Intelligence in Sensors Technology)
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24 pages, 50347 KB  
Article
Analysis Model of Load Transfer Method Based on Domain Decomposition Physics-Informed Neural Networks
by Xiaoru Jia, Keshen Zhang, Junwei Liu, Wenchang Shang, Yahui Zhang, Yuxing Ding and Guangyu Qi
Buildings 2026, 16(6), 1114; https://doi.org/10.3390/buildings16061114 - 11 Mar 2026
Viewed by 416
Abstract
The load transfer method is important for the settlement prediction of axially loaded piles, but in multi-layered complex soils, it lacks analytical solutions. Traditional numerical methods such as the finite element method suffer from strong dependence on mesh generation, time-consuming iterative calculations, and [...] Read more.
The load transfer method is important for the settlement prediction of axially loaded piles, but in multi-layered complex soils, it lacks analytical solutions. Traditional numerical methods such as the finite element method suffer from strong dependence on mesh generation, time-consuming iterative calculations, and high computational costs for back-analysis. This paper proposes a load transfer analysis model based on a Domain Decomposition Physics-Informed Neural Network. A multi-subnet parallel architecture is adopted to simulate multi-layered soils, solving the problem of inter-layer stress–strain discontinuity through interface coupling and gradient continuity constraints; a non-dimensionalization system and a hard constraint mechanism are introduced to enhance training efficiency and physical consistency; and a two-stage analysis framework comprising surrogate model forward analysis and field data inversion is established. Numerical experimental results indicate that the forward analysis of this model is in high agreement with FEM simulation results, and computational efficiency is improved by six orders of magnitude; based on a small amount of field static load test data, multi-layer soil parameters are accurately inverted, achieving more precise pile settlement prediction than FEM. Comparative analysis validates the effectiveness of the domain decomposition multi-subnet over a single network, demonstrating extensibility to hyperbolic and exponential multi-soil constitutive models. Full article
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