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Keywords = forward and inverse models

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32 pages, 13948 KB  
Article
NeuroStat: An Open-Source EEG Connectivity Platform for Randomised Controlled Trials
by Usman Ghani, Iftikhar Ahmad, Shahbaz Pervez, Seyed Ebrahim Hosseini and Imran Khan Niazi
Sensors 2026, 26(13), 4019; https://doi.org/10.3390/s26134019 (registering DOI) - 24 Jun 2026
Abstract
Background: Electroencephalographic (EEG) functional connectivity analysis requires multiple signal-processing, source-modelling, and statistical steps that can limit its adoption in clinician-led randomised controlled trials (RCTs). NeuroStat was developed as a prototype research tool to integrate this workflow; formal usability validation with clinician end-users has [...] Read more.
Background: Electroencephalographic (EEG) functional connectivity analysis requires multiple signal-processing, source-modelling, and statistical steps that can limit its adoption in clinician-led randomised controlled trials (RCTs). NeuroStat was developed as a prototype research tool to integrate this workflow; formal usability validation with clinician end-users has not yet been conducted. Methods: NeuroStat is an open-source Python/PyQt6 desktop application that integrates automated artefact removal (a Generalised Eigenvalue Decomposition for Artefact Identification [GEDAI] pathway and a traditional Artefact Subspace Reconstruction (ASR)/Independent Component Analysis (ICA)/ICLabel pathway), boundary element model (BEM) source localisation using the Desikan–Killiany atlas (68 cortical regions), Phase Lag Index (PLI) connectivity estimation across five canonical frequency bands, and RCT-oriented statistical analysis. Evaluation separated sensor-space and source-space claims: a sensor-level simulation (repeated across five independent random seeds) tested preprocessing robustness, a repeated source-space simulation tested recovery of a known cortical parcel-pair contrast after forward projection and inverse reconstruction, a PhysioNet benchmark tested posterior Desikan–Killiany alpha PLI in 20 healthy adults, and an illustrative application to 20 sessions from a published chiropractic RCT demonstrated real-world workflow applicability. Results: In the sensor-level simulation benchmark, the Traditional pathway achieved a mean absolute error of 0.168±0.017 PLI units and root mean squared error of 0.219±0.045 (mean ± SD across five independent random seeds) across all artefact conditions. In the source-space simulation, reconstructed alpha PLI for the known bilateral lateral-occipital parcel pair exceeded anterior control edges across 60 repeated condition runs (mean known-control difference = 0.105 PLI units, 95% CI 0.096–0.114; t(59)=22.61, p<0.001). In the PhysioNet source-space benchmark, posterior Desikan–Killiany alpha PLI was higher during eyes-closed than eyes-open rest (Cohen’s d=0.85, p=0.001; 16/20 subjects showing the expected direction) after ICLabel-enabled preprocessing. In the pilot RCT application, all 20 sessions completed processing without manual intervention, with default-mode network alpha PLI showing a pre-to-post change of +0.071 in the intervention group versus +0.015 in the active control group. Conclusions: NeuroStat integrates preprocessing, source-space construction, connectivity estimation, and statistical reporting within a parameter-logged desktop workflow for EEG functional connectivity studies. Current evidence supports initial technical feasibility, sensor-level preprocessing robustness for one pathway in controlled simulations, source-space recovery of a known parcel-level contrast, source-space sensitivity to an expected posterior alpha resting-state contrast, and error-free processing across 20 real RCT sessions in a pilot workflow demonstration. Formal usability testing, test–retest reliability analysis, participant-specific source-model validation, and clinical-population validation remain necessary before clinician-facing or trial-deployment claims can be made. Full article
(This article belongs to the Special Issue Advances in Wearable Electroencephalography Sensor Technology)
15 pages, 5844 KB  
Article
A Stochastic Gauss–Newton Framework with Full-Data Line Search for Efficient 3D Magnetotelluric Inversion
by Gang Wen, Lian Liu, Dikun Yang, Yi Zhang and Jinghe Li
Minerals 2026, 16(7), 666; https://doi.org/10.3390/min16070666 (registering DOI) - 24 Jun 2026
Abstract
3D magnetotelluric (MT) inversion based on the Gauss–Newton (GN) framework plays an important role in deep mineral exploration by imaging subsurface electrical conductivity structures. However, large-scale 3D MT inversion remains computationally expensive due to the high cost of sensitivity-matrix construction. To address this [...] Read more.
3D magnetotelluric (MT) inversion based on the Gauss–Newton (GN) framework plays an important role in deep mineral exploration by imaging subsurface electrical conductivity structures. However, large-scale 3D MT inversion remains computationally expensive due to the high cost of sensitivity-matrix construction. To address this challenge, we develop a stochastic Gauss–Newton (SGN) framework that reduces computational cost through random data subsampling while preserving the practical convergence behavior of GN inversion. In the proposed framework, only a randomly selected subset of data is used to approximate the GN search direction. By exploiting a key property of MT forward modelling, namely that responses at all receivers are obtained simultaneously for each frequency, the line search is performed using the full dataset, ensuring stable convergence of the inversion process. The SGN framework is validated using both a synthetic multiblock model and a field dataset from the Akebasitao area in Xinjiang, China. The recovered models remain highly consistent with those obtained using conventional full-data Gauss–Newton inversion across a wide range of sampling ratios. For the synthetic example, reducing the sampling ratio from 100% to 10% decreases peak memory consumption from approximately 433 GB to 242 GB and reduces runtime from 86.8 h to 23.9 h while maintaining comparable inversion quality. Similar computational savings are achieved for the field-data inversion. The field application successfully recovers the major conductive structures along the margins of the intrusion that are associated with hydrothermal alteration and fluid activity, highlighting the capability of SGN to delineate geologically meaningful targets relevant to deep mineral exploration. These results demonstrate that SGN provides an efficient and scalable approach for large-scale 3D MT inversion. Full article
15 pages, 31475 KB  
Article
Evaluation of Sequential Hybrid Inversion in the MASW Method: A Case Study in Santa Fe, Granada, Spain
by J. J. Hellín-Rodríguez, I. Valverde-Palacios, A. García-Jerez, P. Martínez-Pagán and M. Martínez-Segura
Appl. Sci. 2026, 16(13), 6343; https://doi.org/10.3390/app16136343 (registering DOI) - 24 Jun 2026
Abstract
The MASW (Multichannel Analysis of Surface Waves) method oriented toward seismic microzoning has been evolving consistently and steadily for several decades, providing increasingly reliable solutions that are consistent with field and laboratory data typical of classical geotechnics. This study evaluates the [...] Read more.
The MASW (Multichannel Analysis of Surface Waves) method oriented toward seismic microzoning has been evolving consistently and steadily for several decades, providing increasingly reliable solutions that are consistent with field and laboratory data typical of classical geotechnics. This study evaluates the improvement achieved when using a sequence of inversion algorithms on MASW test results: first with a global algorithm—specifically Differential Evolution (DE)—and subsequently, using the best model obtained from the global search, a second local algorithm—Trust Region Reflective (TRF). This second stage refines the previous model, further adjusting it to the borehole model used as the starting point of the sequence. The procedure has been automated using a Python script that incorporates two innovations compared to traditional inversion approaches. These consist of parameterising two variables: (i) an adaptive expansion factor for the Vs limits establisheda priori in the borehole model, and (ii) a subdivision into thinner layers for borehole models with excessively thick strata. This provides the algorithms with greater flexibility, particularly in scenarios with complex stratification. Additionally, to better define the deeper layers, the passive ESAC method in an “L-shape” configuration was also employed. The parameterised sequential hybrid inversion process was validated using synthetic data from two curves (Curve #1 and Curve #2), obtained by adding 5% Gaussian noise to the forward modelling results of the same initial synthetic model. The TRF refinement stage in the sequential hybrid inversion succeeded in reducing the error obtained by the global algorithm by percentages ranging from 59.7% to 5.8% across all conducted tests, confirming the stability of the methodology used. Full article
(This article belongs to the Collection Advances in Theoretical and Applied Geophysics)
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28 pages, 68840 KB  
Article
Joint Hyperspectral Image Deconvolution and Unmixing via Plug-and-Play Priors
by Sina Layazali and Chrysanthe Preza
Remote Sens. 2026, 18(13), 2066; https://doi.org/10.3390/rs18132066 (registering DOI) - 23 Jun 2026
Abstract
Hyperspectral imaging (HSI) provides rich spatial and spectral information for remote sensing, mineral exploration, and biomedical analysis, but its limited spatial resolution and sensor imperfections lead to blurred, noisy, and mixed-pixel observations. Addressing these degradations jointly—rather than sequentially—has been shown to improve physical [...] Read more.
Hyperspectral imaging (HSI) provides rich spatial and spectral information for remote sensing, mineral exploration, and biomedical analysis, but its limited spatial resolution and sensor imperfections lead to blurred, noisy, and mixed-pixel observations. Addressing these degradations jointly—rather than sequentially—has been shown to improve physical interpretability, yet existing joint deblurring–unmixing methods rely primarily on hand-crafted regularizers that do not fully exploit spatial–spectral structure. Meanwhile, recent plug-and-play (PnP) approaches applied to HSI leverage deep priors but focus solely on either deconvolution or unmixing in isolation. To bridge this gap, we formulate the joint inverse problem of hyperspectral deblurring and spectral unmixing and propose, to our knowledge, the first plug-and-play framework tailored for this coupled task using the Alternating Direction Method of Multipliers (ADMM) and a pretrained deep denoiser (DnCNN) as an implicit PnP prior. Our method uses the natural splitting properties of ADMM to separate a physics-driven subproblem that enforces fidelity to the hyperspectral forward model, which includes linear mixing and blur under a linear, space-invariant convolution approximation, from the data-driven prior step. This synergy of model-based fidelity and learned spatial prior enables more accurate abundance estimates than those obtained with approaches relying solely on analytical regularizers. Experimental results on real hyperspectral datasets demonstrate that the proposed Plug-and-Play Joint Deconvolution and Unmixing (PnP-JDU) method outperforms conventional unmixing baselines, stand-alone PnP unmixing methods, and the Deblurring and Sparse Unmixing via the Alternating Direction Method with Total Variation (DSUnADM-TV) baseline in reconstruction and abundance accuracy metrics. Across the tested datasets and imaging conditions, PnP-JDU achieves lower RMSE, higher PSNR, lower reconstruction and abundance errors, and lower SAD values, while preserving fine spatial details and producing physically meaningful abundance maps. Full article
22 pages, 1833 KB  
Article
Kinematic Modeling of a Novel (31)-Degree-of-Freedom Planar Parallel Manipulator Using Screw Theory+
by Jaime Gallardo-Alvarado, Alvaro Sanchez-Rodriguez, Horacio Orozco-Mendoza, Ramon Rodriguez-Castro and Luis A. Alcaraz-Caracheo
Algorithms 2026, 19(7), 502; https://doi.org/10.3390/a19070502 (registering DOI) - 23 Jun 2026
Abstract
This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. [...] Read more.
This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. The proposed architecture is motivated by the search for structurally simple mechanisms with favorable analytical properties for screw-theoretic formulation and potential applications in robotic systems requiring compact and efficient planar motion. For completeness, the displacement analysis is included. Thanks to the simple topology of the otherwise complex mechanism, the inverse–forward displacement problem is resolved through straightforward quadratic equations. The velocity input–output relationship is derived without reliance on passive joint rate velocities, and the acceleration input–output equation is obtained independently of passive joint rate accelerations. These simplifications are achieved by exploiting reciprocal line properties. Numerical examples are provided to illustrate the robustness and effectiveness of the proposed kinematic analysis method across the main topics addressed in this contribution. Full article
54 pages, 2019 KB  
Review
Physics-Informed Neural Networks in Aerospace Engineering: A Systematic Review of Architectures, Training Strategies, and Open Challenges
by Przemysław Gryt and Piotr Przystałka
Appl. Sci. 2026, 16(13), 6282; https://doi.org/10.3390/app16136282 (registering DOI) - 23 Jun 2026
Viewed by 86
Abstract
This paper provides a systematic synthesis of recent developments in physics-informed neural networks (PINNs) applied to aerospace engineering, with an emphasis on their role in physically consistent surrogate modeling, forward simulation, and inverse parameter estimation. Using a PRISMA-based methodology, the study surveys peer-reviewed [...] Read more.
This paper provides a systematic synthesis of recent developments in physics-informed neural networks (PINNs) applied to aerospace engineering, with an emphasis on their role in physically consistent surrogate modeling, forward simulation, and inverse parameter estimation. Using a PRISMA-based methodology, the study surveys peer-reviewed works published between 2017 and 2025 across aviation- and space-related domains, including aerodynamics, structural mechanics, aeroelasticity, propulsion, control, structural health monitoring, satellite-orbit prediction, space-debris collision avoidance, and spacecraft radiation-impact modeling. The analysis shows that embedding governing equations, boundary conditions, and observational data into composite loss functions enables PINNs to improve predictive consistency, reduce dependence on dense simulation or experimental datasets, and support parameter identification under sparse or noisy measurements. Attention is given to architectural variants such as XPINNs, cPINNs, gPINNs, operator-learning approaches, and hybrid PINN-CFD/FEM formulations, as well as to training strategies based on adaptive sampling, domain decomposition, transfer learning, and dynamic loss weighting. Reported benefits include reduced approximation error, improved convergence in selected high-gradient or multiphysics problems, and enhanced interpretability compared with purely data-driven models. At the same time, the review identifies persistent open challenges, including scalability to large aerospace domains, sensitivity to loss-weighting and collocation strategies, limited robustness under noise and uncertainty, high computational cost, and the lack of standardized aerospace benchmarks. Overall, the review highlights PINNs as a promising but still developing framework for fast, interpretable, and physically consistent modeling of aircraft and spacecraft systems. Full article
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27 pages, 4069 KB  
Article
A Two-Scale Dynamic Friction Model Incorporating Measured Roll Roughness for Mixed-Lubricated Cold Rolling Interfaces
by Huajie Wu, Qiaoyi Wang, Laihua Tao, Xin Jiang and Longwei Geng
Lubricants 2026, 14(6), 246; https://doi.org/10.3390/lubricants14060246 (registering DOI) - 20 Jun 2026
Viewed by 152
Abstract
Friction at the cold rolling interface is affected jointly by the surface roughness, lubrication state, local pressure, and relative sliding. A constant friction coefficient is therefore insufficient to describe its non-uniform distribution along the contact arc. Accordingly, this study proposes a macro–micro two-scale [...] Read more.
Friction at the cold rolling interface is affected jointly by the surface roughness, lubrication state, local pressure, and relative sliding. A constant friction coefficient is therefore insufficient to describe its non-uniform distribution along the contact arc. Accordingly, this study proposes a macro–micro two-scale mixed-lubrication and dynamic friction model based on the measured roll roughness. First, the measured roll roughness profile was represented within a finite effective scale interval by a scaled and truncated Weierstrass–Mandelbrot (W–M) function. The parameters D and G were obtained as finite-scale W–M roughness parameters and were introduced into a mixed-lubrication load-sharing model to calculate the local mixed-lubrication friction coefficient. The pressure distribution along the contact arc was calculated using the Karman equation, and the local macroscopic pressure was mapped to a representative microscopic contact load. Finally, the mixed-lubrication friction coefficient was used to calibrate the dynamic friction factor separately in the forward-slip and backward-slip zones, and the friction stress distribution along the contact arc was calculated. For the selected effective scale interval and preprocessing procedure, the fitted W–M roughness parameters were D = 1.528 and G = 9.15 × 10−8 m. The W–M parameter D had a more significant influence on the mixed-lubrication friction coefficient and load-sharing behavior than the scale parameter G. Increasing the rolling speed strengthened the oil-film load-carrying effect and reduced the equivalent interfacial friction coefficient. The friction stress was positive in the backward-slip zone and negative in the forward-slip zone, with a direction reversal near the neutral point. Field forward-slip inversion showed that both the simulated and measured equivalent friction coefficients decreased with increasing rolling speed, with a difference of approximately 0.009~0.017. The proposed model can capture the main trend of cold rolling interfacial friction with variations in the rolling speed and contact state. Full article
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26 pages, 17107 KB  
Article
Full-Spectrum Inverse Design of Compact Ring-Curve Fractal-Maze Acoustic Metamaterials via an LSTM–PPS-Net Tandem Framework
by Guangyao Zhu, Tao Chen, Yao Xiao, Caixia Yang, Jingyue Liang and Fei Lin
Crystals 2026, 16(6), 400; https://doi.org/10.3390/cryst16060400 - 18 Jun 2026
Viewed by 191
Abstract
Low-frequency sound insulation remains a major challenge for conventional passive materials, as improved attenuation is usually achieved at the expense of increased thickness and mass. In this work, a smooth fixed third-order ring-curve fractal-maze acoustic metamaterial is proposed for compact low-frequency sound insulation, [...] Read more.
Low-frequency sound insulation remains a major challenge for conventional passive materials, as improved attenuation is usually achieved at the expense of increased thickness and mass. In this work, a smooth fixed third-order ring-curve fractal-maze acoustic metamaterial is proposed for compact low-frequency sound insulation, and a physics-guided long short-term memory–physics prediction surrogate network (LSTM–PPS-Net) tandem framework is developed for its full-spectrum inverse design. Different from conventional Hilbert-type, right-angled, or sharply folded labyrinthine structures, the proposed topology uses recursively arranged curved channels to extend the effective acoustic propagation path and enhance phase accumulation within a limited space. Based on this mechanism, four physically meaningful parameters, namely slit width d, characteristic radius R3, wall thickness tw, and inter-column spacing lE, are selected to construct a low-dimensional design space. A COMSOL–MATLAB automated finite-element method (FEM) workflow is established to generate 1000 valid transmission-loss (TL) spectra over 100–1700 Hz with a 5 Hz interval. For forward prediction, PPS-Net is developed by integrating geometry encoding, frequency-conditioned spectral decoding, and peak-weighted learning. The proposed PPS-Net achieves the best prediction accuracy among the tested models, with a mean absolute error (MAE) of 0.75 dB, a root mean square error (RMSE) of 1.88 dB, and a coefficient of determination (R2) of 0.96, outperforming multi-layer perceptron (MLP), convolutional neural network (CNN) and Transformer models under the same dataset and training protocol. For inverse design, the LSTM encoder extracts frequency-ordered spectral features from the target TL curve, while the frozen PPS-Net decoder provides differentiable acoustic-response feedback, thereby addressing the non-unique mapping from acoustic response to structural parameters. Furthermore, a compactness-oriented optimization strategy is introduced to balance spectral consistency, peak alignment, bandwidth preservation, and occupied-area reduction. In two representative cases, the optimized designs reduce the occupied area by approximately 21% in both representative cases, while maintaining the target attenuation characteristics after FEM verification. These results demonstrate that the proposed framework provides an efficient and physically interpretable route for the full-spectrum inverse design and compact optimization of low-frequency acoustic metamaterials. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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29 pages, 13320 KB  
Article
Modeling One-Dimensional Consolidation Problems Using Physics-Informed Neural Networks with Domain Decomposition
by Yang Chen, De’an Sun and Jie Zhou
Appl. Sci. 2026, 16(12), 6065; https://doi.org/10.3390/app16126065 - 15 Jun 2026
Viewed by 178
Abstract
Soil consolidation modeling is essential for estimating settlement and pore-water pressure dissipation, but analytical solutions are limited for layered soils with complex drainage and interface conditions. This study evaluates physics-informed neural networks (PINNs) for one-dimensional consolidation of saturated soils and extends them to [...] Read more.
Soil consolidation modeling is essential for estimating settlement and pore-water pressure dissipation, but analytical solutions are limited for layered soils with complex drainage and interface conditions. This study evaluates physics-informed neural networks (PINNs) for one-dimensional consolidation of saturated soils and extends them to a domain-decomposed XPINN framework for two-layered soils. Governing equations, boundary conditions, interface-continuity constraints, and synthetic measurement data are embedded in the loss function. Layer-wise locally adaptive activation functions (L-LAAF) and residual-based adaptive resampling (RAR) are used to improve training stability. For homogeneous soil, the PINN accurately reproduces the analytical solution, although conventional finite difference methods remain more efficient for simple single-query forward analysis. For heterogeneous soil, the full XPINN model achieves a relative L2 error of 0.0173 ± 0.0058, whereas removing RAR, L-LAAF, or domain decomposition increases the error to 0.0578 ± 0.0555, 0.1488 ± 0.0378, and 0.1673 ± 0.0104, respectively. In inverse tests using synthetic noisy measurements, denser and lower-noise observations improve the identification of unknown drainage coefficients. The framework provides a meshless and continuous representation for forward and inverse layered consolidation problems, but validation with laboratory or field data remains necessary. Full article
(This article belongs to the Section Civil Engineering)
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23 pages, 2144 KB  
Article
Wind-Robust Methane Source-Rate Inversion from Remote-Sensing Plume Imagery: Soft Physics Guidance Versus Hard IME Coupling
by Quanyi Dong, Sining Duan, Zhigang Chen, Yue Li, Shuhe Zhao and Fanghong Ye
Remote Sens. 2026, 18(12), 1992; https://doi.org/10.3390/rs18121992 - 15 Jun 2026
Viewed by 130
Abstract
Methane source-rate inversion from remote-sensing plume imagery is essential for emissions monitoring, but its accuracy is often limited by uncertainty in ancillary wind information. This study examines how physical knowledge can be integrated into a deep-learning inversion model when the available wind input [...] Read more.
Methane source-rate inversion from remote-sensing plume imagery is essential for emissions monitoring, but its accuracy is often limited by uncertainty in ancillary wind information. This study examines how physical knowledge can be integrated into a deep-learning inversion model when the available wind input is imperfect. Using a controlled large-eddy-simulation (LES) benchmark designed for EnMAP/PRISMA-style imaging-spectrometer methane quantification, we compare six models that span image-only regression, flexible wind conditioning, simplified hard integrated-mass-enhancement (IME) coupling, and soft physics-guided learning under clean inputs, deterministic wind bias, stochastic Gaussian wind noise, and source-rate-stratified tests. Under clean benchmark conditions, flexible wind conditioning provides the best scalar accuracy, with FiLM reaching a mean absolute percentage error (MAPE) of 6.19% and a root mean squared error (RMSE) of 1323.36, followed closely by Concat (MAPE 6.37%, RMSE 1325.69). The simplified hard-coupling model is sensitive to wind perturbations: DIN-hard rises from MAPE 8.44% under clean inputs to 31.39% and 26.89% under deterministic wind-bias multipliers α = 0.7 and α = 1.3, respectively, and becomes unstable under stronger Gaussian wind noise in the tested protocol. By contrast, DIN-soft-v2 remains competitive under clean conditions (MAPE 6.39%, RMSE 1360.94), follows smoother degradation under biased or noisy wind, and improves plume spatial diagnostics relative to DIN-soft (center-of-mass shift 3.92 versus 4.07 pixels; plume alignment degree 2.60 versus 2.72 degrees). The calibrated IME-style physical baseline reaches a clean MAPE 24.45%, indicating that the learning-based models substantially outperform this benchmark physical proxy. Within this LES-based benchmark and the tested wind-perturbation protocols, the results suggest that IME-inspired physical knowledge is more robustly incorporated as a calibratable soft prior than as the simplified hard log-additive forward coupling considered here; however, transfer to real satellite scenes still requires validation. Full article
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38 pages, 714 KB  
Article
Reduced Integer–Fractional Dynamics of Hydrothermal Memory in Volcanic Gas and Isotope Signals
by Sebastiano Ettore Spoto
Mathematics 2026, 14(12), 2139; https://doi.org/10.3390/math14122139 - 15 Jun 2026
Viewed by 119
Abstract
Volcanic gas and isotope time series are indirect observables of coupled magmatic and hydrothermal dynamics. We formulate a reduced integer–fractional model in which ordinary differential equations describe deep recharge, pressure, gas-phase volatile inventory, and source mixing, whereas Caputo equations describe shallow hydrothermal pressure, [...] Read more.
Volcanic gas and isotope time series are indirect observables of coupled magmatic and hydrothermal dynamics. We formulate a reduced integer–fractional model in which ordinary differential equations describe deep recharge, pressure, gas-phase volatile inventory, and source mixing, whereas Caputo equations describe shallow hydrothermal pressure, thermal excess, gas pathway effectiveness, permeability, and scrubbing. Under explicit local regularity and admissibility assumptions, the mixed-order Volterra problem is locally well-posed and the physically admissible state set is positively invariant. We derive componentwise dissipative estimates and state conditions for global continuation under bounded trajectories and analyze finite-interval consistency with the integer-order limit and local stability of a frozen commensurate hydrothermal linearization. Conservative observation equations link hidden states to gas ratios, fluxes, and isotope ratios. The inverse problem is treated diagnostically; global identifiability is not claimed. Local sensitivity screening, Fisher information concepts, and scalar recovery tests are used only as preliminary local diagnostics of information content under known or misspecified forcing. Synthetic demonstrations and a reference forward solver illustrate how hydrothermal memory and sulfur scrubbing can reshape carbon dioxide/sulfur dioxide (CO2/SO2) anomalies before site-specific calibration. Full article
(This article belongs to the Special Issue Differential Equations Applied in Fluid Dynamics)
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36 pages, 14641 KB  
Article
Physics-Informed Inference of Historical Stair Usage from Geometric Wear Profiles in Heritage Structures
by Jianchao Yu, Yating Zhong, Ziheng Luo, Yuqi Guo and Jufang Hu
Appl. Sci. 2026, 16(12), 6025; https://doi.org/10.3390/app16126025 - 14 Jun 2026
Viewed by 133
Abstract
Wear on historic staircases is often used as evidence for conservation assessment and historical interpretation, yet existing studies are largely descriptive and rarely provide a quantitative explanation of how observed wear relates to long-term pedestrian use. To address this limitation, this paper proposes [...] Read more.
Wear on historic staircases is often used as evidence for conservation assessment and historical interpretation, yet existing studies are largely descriptive and rarely provide a quantitative explanation of how observed wear relates to long-term pedestrian use. To address this limitation, this paper proposes a physics-constrained inversion framework for analyzing directional preference and wear-related usage regimes from geometric wear profiles of heritage staircases. An Archard-type wear model is extended to account for spatial footfall distribution, cumulative abrasion, material deterioration, and environmental loss, and the reconstruction problem is formulated as an inverse parameter estimation task. Bayesian uncertainty quantification is introduced to estimate posterior distributions, credible intervals, and parameter coupling. A unified workflow is developed for staircase geometry representation, reference surface reconstruction, profile extraction, regularized height field construction, forward simulation, and inverse solution. Nine synthetic scenarios with different usage levels and directional preferences are tested under 1%, 3%, and 5% noise, and the method is further applied to a publicly available three-dimensional heritage staircase model. Under 3% noise, profile correlation coefficients for three representative scenarios reach 0.9646, 0.9807, and 0.9868, indicating strong recoverability of geometric wear morphology under model-consistent conditions. The results indicate that directional preference, material hardness, and some degradation-related parameters are identifiable, whereas pedestrian volume and the wear coefficient show strong compensation. Overall, the proposed framework provides a quantitative basis for identifying directional asymmetry, analyzing parameter identifiability, and supporting geometry-based interpretation in heritage staircase studies. Full article
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22 pages, 5336 KB  
Article
Characterization and Optimization of Intelligent Dampers Based on Bionic Principles
by Niancheng Guo, Yujing Zhang, Hao Cheng, Wei Zhao, Yang Gao, Wei Li and Yanle Li
Biomimetics 2026, 11(6), 411; https://doi.org/10.3390/biomimetics11060411 - 11 Jun 2026
Viewed by 275
Abstract
From the perspective of human vibration perception, reducing vibration stimuli transmitted to occupants is essential for improving ride comfort and reducing fatigue. Intelligent dampers, as key actuators in semi-active suspension systems, provide adjustable damping capabilities for vibration control. This article combines them with [...] Read more.
From the perspective of human vibration perception, reducing vibration stimuli transmitted to occupants is essential for improving ride comfort and reducing fatigue. Intelligent dampers, as key actuators in semi-active suspension systems, provide adjustable damping capabilities for vibration control. This article combines them with biomimetic control principles to study the vibration control of semi-active suspension. The effects of damper forward and inverse models, damping force ranges, and time delays on suspension performance were analyzed. The results show that a function prediction-based damper model, a damping force range below 0.2 times and above 1.4 times the passive curve, and a 10 ms delay could balance vibration reduction and economy. Particle swarm optimization is used to optimize LQR control parameters for different road grades and typical speeds. Inspired by the adaptive behavior of chameleons, graded weights are assigned according to road characteristics, with greater emphasis on comfort on Grade A and B roads and driving stability on Grade C and D roads. The results show that proper matching of damper models and parameter constraints can fully exploit the adjustable damping capability of smart dampers. These findings provide a theoretical basis for designing and optimizing semi-active suspension control strategies. Full article
(This article belongs to the Special Issue Computer-Aided Biomimetics: 3rd Edition)
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34 pages, 5849 KB  
Article
WaveDroughtNet: A Multi-Modal Wavelet-Enhanced Temporal Convolutional Network for Multi-Horizon Drought Forecasting and Onset Analysis
by K. Venkatachalam, Claudia Cherubini and Alphonse Anushya
Water 2026, 18(12), 1415; https://doi.org/10.3390/w18121415 - 10 Jun 2026
Viewed by 305
Abstract
Drought is a slowly evolving, multi-driver hydro-meteorological hazard whose accurate early prediction is a cornerstone of climate-smart agriculture and water-resource planning. Existing data-driven drought forecasting frameworks suffer from three persistent limitations: (i) most models concatenate heterogeneous climate variables into a single flat feature [...] Read more.
Drought is a slowly evolving, multi-driver hydro-meteorological hazard whose accurate early prediction is a cornerstone of climate-smart agriculture and water-resource planning. Existing data-driven drought forecasting frameworks suffer from three persistent limitations: (i) most models concatenate heterogeneous climate variables into a single flat feature vector, implicitly assuming a single dominant driver such as precipitation, even though atmospheric moisture demand, radiation and wind-mediated evapotranspiration co-determine drought onset; (ii) wavelet preprocessing is typically applied to the full series, introducing future-information leakage that violates the operational causality requirement of forecasting; and (iii) most architectures predict a single horizon and provide no causal attribution explaining when, where and which climatic variables initiated the event. This study proposes WaveDroughtNet, a multi-modal, multi-horizon deep-learning framework that addresses these limitations through five integrated components: (a) a strictly causal Daubechies-4 wavelet decomposition computed in a rolling fashion; (b) six modality-specific encoders with stochastic modality dropout (p = 0.15); (c) cross-modal multi-head attention with four heads; (d) a four-layer temporal convolutional network (TCN) backbone with dilation factors yielding a 240-step receptive field; and (e) a post hoc DroughtOriginTracer that combines temporal attention, modal-attribution and inter-district propagation scans. The Standardised Precipitation Evapotranspiration Index (SPEI), used as the supervisory target, is computed following the canonical Vicente-Serrano formulation. water balance D=PPET (Hargreaves PET) at a 4-week (≈1-month) timescale, fitted with a three-parameter log-logistic distribution via L-moments, validated by Kolmogorov–Smirnov goodness-of-fit testing (α=0.05) per district, and standardised through the inverse-normal cumulative distribution function. Trained on 18,304 weekly district records from NASA POWER reanalysis (2014–2025) covering all 32 districts of Tamil Nadu, India, WaveDroughtNet uses only 256,869 parameters and produces, in a single forward pass, four forecasts (1 week, 1 month, 3 months, 1 year). On the held-out 2024 test partition (N=1728), the model attains weighted F1=0.9221 and R2=0.8512 at the 1-week horizon, and weighted F1=0.8498 and R2=0.6812 at the 1-year horizon. Diebold–Mariano tests confirm that WaveDroughtNet significantly outperforms naive persistence, seasonal naive, LSTM, ConvLSTM and a vanilla Transformer at the 3-month and 1-year horizons (p < 0.001). The DroughtOriginTracer successfully back-projects 15 Coimbatore events to causal origins 29–41 weeks prior to onset. We explicitly acknowledge three limitations that constrain operational deployment in its current form—zero severe events in the 2024 test partition (F1severe = 0.000), static inter-district modelling, and absence of vegetation-index supervision—and propose concrete mitigation pathways in the Discussion. Full article
(This article belongs to the Special Issue Sea Level Rise Vulnerability and Coastal Management)
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Article
A Physics-Regularized Neural Inversion Framework for Well-Test Parameter Identification in Long Horizontal Wells Intersecting Multiple Faults
by Changyong Li, Peng Xiao, Tao Cao, Zhaoxu Wang, Yiyao Li, Wenrui Lv, Zhenye Xu and Ren-Shi Nie
Processes 2026, 14(12), 1846; https://doi.org/10.3390/pr14121846 - 7 Jun 2026
Viewed by 176
Abstract
Long horizontal wells in high-permeability fault-block reservoirs may intersect multiple faults, leading to complex pressure-transient responses, strong parameter coupling in conventional well-test interpretation, inefficient manual history matching, and pronounced non-uniqueness in fault-property identification. To address these challenges, this study proposes a physics-regularized neural [...] Read more.
Long horizontal wells in high-permeability fault-block reservoirs may intersect multiple faults, leading to complex pressure-transient responses, strong parameter coupling in conventional well-test interpretation, inefficient manual history matching, and pronounced non-uniqueness in fault-property identification. To address these challenges, this study proposes a physics-regularized neural inversion framework based on a PINN parameterization and low-weight physics regularization for well-test parameter inversion in long horizontal wells intersecting multiple faults. The proposed method takes the multiple-fault pressure response of a long horizontal well as the target problem. Both the pressure–drawdown curve and the pressure–drawdown derivative curve are used as data constraints. At the same time, parameter scaling and stage-wise training are introduced to jointly invert the reservoir permeability, fault transmissibility coefficient, skin factor, and effective producing length of the horizontal well. Considering that the simplified line-source forward model is not fully consistent with the two-dimensional pressure-diffusion equation and the fault-interface residuals, a physics-loss consistency test is performed to determine safe weighting ranges for the PDE residual and the fault-interface residual. These residuals are then incorporated into the training process as low-weight physics regularization terms to improve the physical plausibility of the inversion results. Results from the base case, different fault types, multiple-fault combinations, noise-robustness tests, ablation experiments, and method comparisons show that the proposed method can stably fit pressure–drawdown and pressure–drawdown derivative curves and effectively identify key well-test parameters in single-fault cases and some multiple-fault cases. In single-fault cases, the order of magnitude of the fault transmissibility coefficient can be identified stably. Reliable inversion performance is obtained for medium- to high-transmissibility faults and some multiple-fault combinations. In contrast, ambiguity remains between sealing faults and strong-baffle faults in multiple low-transmissibility fault combinations. The results further indicate that, under multiple random initializations, the physics-regularized neural inversion framework provides improved inversion stability in the tested synthetic low-transmissibility multiple-fault cases compared with the traditional least-squares method. Therefore, the proposed framework can serve as an intelligent auxiliary tool for well-test parameter inversion and fault-connectivity evaluation in complex fault-block reservoirs. Nevertheless, fine discrimination of low-transmissibility faults and interpretation of highly noisy field data still require joint constraints from geological, seismic, and production-dynamic information. A preliminary reduced field PINN fitting test using the well X falloff event further provides an engineering-scale applicability check for real pressure-transient data, with a pressure NRMSE of 2.457% for the extracted shut-in response. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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