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Keywords = physics-guided neural networks

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32 pages, 1329 KB  
Review
Vertical Axis Wind Turbines: A Comprehensive Critical Review of Aerodynamic Theory, Design Configurations, Performance Analysis, and Future Perspectives
by Marouane Essahraoui, Mohamed-Amine Babay, Hamza Benzzine, Rachid El Bouayadi, Mustapha Mabrouki, Mohammed El Ganaoui and Aouatif Saad
Energies 2026, 19(11), 2544; https://doi.org/10.3390/en19112544 - 25 May 2026
Abstract
Vertical axis wind turbines (VAWTs) have regained attention for distributed, urban, and floating offshore applications, yet the literature remains fragmented across competing rotor concepts and modelling traditions. This review consolidates the principal archetypes—Savonius, H-Darrieus, troposkein Darrieus, helical Darrieus, and Savonius–Darrieus hybrids—through five governing [...] Read more.
Vertical axis wind turbines (VAWTs) have regained attention for distributed, urban, and floating offshore applications, yet the literature remains fragmented across competing rotor concepts and modelling traditions. This review consolidates the principal archetypes—Savonius, H-Darrieus, troposkein Darrieus, helical Darrieus, and Savonius–Darrieus hybrids—through five governing parameters: drag-versus-lift-driven operating principle, tip speed ratio λ = ωR/V (0.6–1.2 for Savonius; 2.5–5.0 for Darrieus), solidity σ = Nc/R (0.1–0.4), chord-based Reynolds number Re_c (105 − 106), and peak power coefficient Cp_max (0.15–0.25 for Savonius; 0.35–0.45 for optimized H-Darrieus). Off-design performance is dominated by unsteady mechanisms that quasi-steady streamtube models cannot resolve—leading edge vortex shedding, dynamic stall hysteresis, blade–wake interaction, and flow-curvature-induced virtual camber—each examined for its contribution to the instantaneous torque CT(θ) and the cycle-averaged Cp. Turbulence closures are benchmarked against phase-locked PIV and torque measurements: k – ω SST URANS captures peak-region Cp to within ±5–10% but over-predicts torque below λopt; the γ – Re_θ transition SST model reduces this error to ±3–5%; DES, DDES, and LES reach ±2 – 3% at one to two orders of magnitude higher cost. Best practice computational fluid dynamics (CFD) guidelines are consolidated: domain extents of 15 D upstream, 10 D downstream, and 20 D lateral; rotating sub-domain Drot » 1.5 D; y+ ≤ 1; Δθ ≤ 0.1°; and 20–30 revolutions before sampling. Performance enhancement strategies (variable pitch, guide vanes, helical twist, and hybridization) are reviewed quantitatively, with reported Cp gains of 5–30%. Four research priorities are identified: (i) transition-sensitive turbulence closures validated below Re_c = 5 × 105; (ii) coupled aero-hydro-servo-elastic models for floating offshore VAWTs; (iii) machine-learning-augmented turbulence modelling—including physics-informed neural networks (PINNs) and neural-network-corrected RANS closures—to improve unsteady flow prediction at sub-LES cost; and (iv) integrated aeroacoustic–aeroelastic frameworks for urban and building-integrated deployment. Full article
15 pages, 544 KB  
Article
Air Target ISAR Recognition Based on Data Augmentation and Transfer Learning
by Moqian Wang, Zuzhen Huang, Jinjian Cai, Tao Wu and Youquan Lin
Sensors 2026, 26(11), 3323; https://doi.org/10.3390/s26113323 - 23 May 2026
Abstract
Aiming at the problems of extremely scarce measured samples and significant domain shift between simulated and measured data in automatic target recognition (ATR) of air targets for spaceborne radar, this paper proposes an inverse synthetic aperture radar (ISAR) image recognition method for air [...] Read more.
Aiming at the problems of extremely scarce measured samples and significant domain shift between simulated and measured data in automatic target recognition (ATR) of air targets for spaceborne radar, this paper proposes an inverse synthetic aperture radar (ISAR) image recognition method for air targets combining physics-driven data augmentation guided by detection prior information with domain adversarial transfer learning. First, the mapping relationship between scattering point projection and ISAR images is established by using the target 3D point cloud and radar observation geometric priors, and a 2D sinc kernel function is introduced for energy distribution rendering. Then, under the unsupervised transfer learning paradigm, aiming at the distribution inconsistency between augmented data (source domain) and unlabeled simulated data (target domain), this paper designs a cross-domain recognition task experiment including six types of typical aircraft targets, and compares the cross-domain recognition performance of three transfer learning methods (model fine-tuning, deep domain confusion (DDC) and domain-adversarial neural networks (DANN)) on the target domain. Meanwhile, t-distributed stochastic neighbor embedding (t-SNE) visualization is used to analyze the feature distribution alignment ability of the models. Simulation experiments show that the DANN model with a dynamic inversion coefficient introduced in the gradient reversal layer (GRL) achieves a recognition accuracy of 99.5% on the unlabeled target domain, which is significantly superior to the model fine-tuning and DDC methods. Moreover, it makes the feature distributions of source and target domain samples highly overlapping, and maintains a strong inter-class discriminability while eliminating the domain shift. The proposed scheme provides a physically interpretable and robust technical path for few-shot radar target image recognition. Full article
(This article belongs to the Section Radar Sensors)
24 pages, 1304 KB  
Article
A Causally Constrained Framework Coupling Causal Discovery and SEIR Mechanisms for Interpretable Epidemic Modeling
by Rui Zhu, Yijiang Zhao, Zhixiong Fang and Yizhi Liu
Mathematics 2026, 14(10), 1776; https://doi.org/10.3390/math14101776 - 21 May 2026
Viewed by 146
Abstract
Infectious disease transmission is a complex dynamic process governed by intrinsic causal mechanisms rather than simple statistical correlations. Although deep learning paradigms have demonstrated powerful nonlinear representation capabilities, their “black-box” and purely data-driven nature often lead to a severe lack of causal consistency [...] Read more.
Infectious disease transmission is a complex dynamic process governed by intrinsic causal mechanisms rather than simple statistical correlations. Although deep learning paradigms have demonstrated powerful nonlinear representation capabilities, their “black-box” and purely data-driven nature often lead to a severe lack of causal consistency and logical transparency. To bridge this gap, this paper proposes CCSANet (Causally Constrained SEIR-Aware Network), an interpretable forecasting framework that seamlessly embeds epidemiological priors directly into the neural architecture. The model integrates SEIR dynamics into a temporal causal discovery framework, utilizing a mechanism-aware prior loss to guide a CausalFormer in learning a global temporal causal graph from multi-source heterogeneous data. This ensures that the identified relationships strictly adhere to the fundamental evolutionary logic of contagion. Subsequently, the extracted causal subgraphs are encoded as structural priors within a Causal-SCI-Block via a specialized masking mechanism, effectively forcing information to propagate exclusively along epidemiologically legitimate pathways. To ensure deep alignment between neural representations and physical reality, a causal strength alignment loss is introduced to synchronize the network’s attention weights with actual transmission intensities. Experimental evaluations on real-world multi-city datasets demonstrate that this integrated approach significantly outperforms baselines such as LSTM, Informer, and its predecessor, ESASNet. Under a 7-day sliding window configuration, the model maintains a Coefficient of Determination R2 stably above 0.97, achieving an accuracy improvement of 5.5% to 6.2% and an 8% to 10% reduction in SMAPE, thereby demonstrating that coupling causal discovery with SEIR constraints substantially enhances both predictive precision and physical interpretability. Full article
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27 pages, 10513 KB  
Article
A Physics-Informed Neural Network Model for Reservoir Seepage in Porous Media Based on Darcy’s Law
by Yun Zhang, Xiaofan Chen, Kuanguo Li and Yifan Zou
Processes 2026, 14(10), 1578; https://doi.org/10.3390/pr14101578 - 13 May 2026
Viewed by 188
Abstract
Purely data-driven machine-learning methods are currently limited by weak physical interpretability; meanwhile, the sparsity of well-site data in oil and gas fields further degrades the prediction performance of deep learning models for reservoir seepage simulation. To overcome this bottleneck, this study embeds Darcy’s [...] Read more.
Purely data-driven machine-learning methods are currently limited by weak physical interpretability; meanwhile, the sparsity of well-site data in oil and gas fields further degrades the prediction performance of deep learning models for reservoir seepage simulation. To overcome this bottleneck, this study embeds Darcy’s law-based seepage equations as physical constraints into the loss function of a deep learning framework, thereby constructing a physics-informed neural network (PINN) for seepage flow in porous media of oil and gas reservoirs. Numerical simulations are performed in heterogeneous porous media to compare the predictive performance of the proposed PINN against conventional purely data-driven approaches, via evaluation metrics including the coefficient of determination (R2) and root mean square error (RMSE). The results show that both models achieve comparable predictive accuracy with sufficient training samples. In contrast, the PINN retains high predictive accuracy even with a reduced number of samples, and it delivers prominent superiority under conditions of sparse well data and strong reservoir heterogeneity. This study clarifies the applicable scenarios of the two aforementioned methods (physics-informed neural networks and purely data-driven machine-learning models) for fluid flow simulation in porous media and provides a solid theoretical and technical foundation for the accurate prediction of reservoir seepage fields and the optimization of oil and gas reservoir development. This work also offers a validated physics-constrained deep learning framework to guide the deployment of intelligent algorithms in practical subsurface flow engineering. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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19 pages, 13510 KB  
Article
A Nonlinear Error Compensation Method for Heterodyne Interferometry Based on Self-Supervised Physics-Informed Neural Networks with Frequency-Domain Priors
by Yao Wang, Hongyu Sun, Jiakun Li, Chenlong Ma, Ying Zhang, Xiao Wang and Qibo Feng
Sensors 2026, 26(10), 3000; https://doi.org/10.3390/s26103000 - 10 May 2026
Viewed by 420
Abstract
Although laser heterodyne interferometric sensing systems offer exceptional theoretical resolution, practical precision is constrained by intractable nonlinear errors stemming from optical imperfections. Conventional compensation methods suffer from hardware dependency, complexity, and performance degradation under low signal-to-noise ratios (SNR). To address this, we propose [...] Read more.
Although laser heterodyne interferometric sensing systems offer exceptional theoretical resolution, practical precision is constrained by intractable nonlinear errors stemming from optical imperfections. Conventional compensation methods suffer from hardware dependency, complexity, and performance degradation under low signal-to-noise ratios (SNR). To address this, we propose a precision calibration method using a self-supervised Physics-Informed Neural Network (PINN) guided by frequency-domain priors with harmonic distribution characteristics. This approach establishes a robust compensation model by inverting equivalent parameter sets and error curves in a single step. Specifically, leveraging high-precision displacement references, the method extracts measurement residuals containing periodic physical features. Subsequently, it integrates frequency-domain priors into a physically constrained network architecture: theoretical frequency characteristics construct masks to generate high-confidence pseudo-labels, while the error equation is recast as a differentiable physical layer imposing explicit hard constraints during forward propagation. This mechanism enables precise identification of the system’s nonlinear physical properties against high background noise. Experimental results show that the root-mean-square (RMS) value of the nonlinear error was reduced from 1.90 nm to 0.23 nm, with a compensation rate reaching up to 88.13%. This method provides a reliable framework for the intelligent calibration and error self-characterization of heterodyne interferometric industrial sensors in the field of precision metrology sensors. Full article
(This article belongs to the Special Issue Intelligent Sensors and Signal Processing in Industry—2nd Edition)
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25 pages, 6321 KB  
Article
A Physics-Guided Two-Stage Learning Framework for Constitutive Modeling of TC4 Titanium Alloy: Validation Through Temperature and Strain-Rate Extrapolation
by Lu Cheng, Chenxi Shao and Peng Cheng
Metals 2026, 16(5), 510; https://doi.org/10.3390/met16050510 - 9 May 2026
Viewed by 270
Abstract
Accurate constitutive modeling of TC4 titanium alloy at elevated temperatures is critical for process design and numerical simulation in aerospace manufacturing. However, purely data-driven deep neural networks (DNNs) often suffer from severe overfitting and may yield physically unreasonable predictions in data-sparse or strictly [...] Read more.
Accurate constitutive modeling of TC4 titanium alloy at elevated temperatures is critical for process design and numerical simulation in aerospace manufacturing. However, purely data-driven deep neural networks (DNNs) often suffer from severe overfitting and may yield physically unreasonable predictions in data-sparse or strictly out-of-distribution (OOD) regions. To address this issue, this study proposes a physics-guided two-stage neural network framework, termed NN-PhysicsInit, for the constitutive modeling of TC4 alloy. In Stage I, a large synthetic dataset generated from a strain-compensated Arrhenius-type constitutive equation is used to pre-train the network, thereby introducing analytical prior knowledge into the initial topological space. In Stage II, the pre-trained model is fine-tuned using rigorously corrected experimental data obtained from isothermal compression tests conducted over 800–980 °C and 0.001–1 s−1 to improve material-specific predictive accuracy. To evaluate generalization capability, a rigorous dual-perspective extrapolation validation scheme is designed separately in the temperature (1010 °C) and strain-rate (10 s−1) dimensions. The results demonstrate that, compared with direct black-box training, the proposed framework successfully prevents non-physical divergence and better preserves macroscopic thermodynamic smoothness in unseen domains. Specifically, the extrapolation average absolute relative error (AARE) is significantly reduced from 34.21% to 14.34% in the temperature extrapolation task, and from 27.91% to 8.92% in the strain-rate extrapolation task. These findings confirm that physics-based initialization acts as a powerful implicit regularizer, effectively mitigating the extrapolation catastrophe while maintaining high fitting accuracy. The proposed framework provides a robust and practical strategy for the constitutive modeling of complex alloys under limited-data conditions. Full article
(This article belongs to the Section Computation and Simulation on Metals)
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21 pages, 4372 KB  
Article
Physics-Informed Domain Adaptation for Stator Inter-Turn Short Circuit Diagnosis in Synchronous Machines Using Excitation Current Signatures
by Jarosław Kozik
Energies 2026, 19(9), 2231; https://doi.org/10.3390/en19092231 - 5 May 2026
Viewed by 290
Abstract
Inter-turn short-circuit faults (ITSC) in the stator winding of large synchronous machines are among the most critical failures in power systems and may lead to severe insulation damage and unplanned outages. At the same time, such faults, due to their nature in critical [...] Read more.
Inter-turn short-circuit faults (ITSC) in the stator winding of large synchronous machines are among the most critical failures in power systems and may lead to severe insulation damage and unplanned outages. At the same time, such faults, due to their nature in critical industrial scenarios, make it difficult to collect sufficiently rich labeled datasets for data-driven and deep-learning-based diagnostic methods. Training diagnostic models purely on simulated signals often results in a severe domain shift between the digital twin and the physical machine due to nonlinearities, mechanical noise, and measurement imperfections, causing a significant degradation of performance when the model is deployed in practice. This paper proposes a hybrid diagnostic framework that combines a nonlinear physics-based digital twin of a synchronous machine, formulated using an extended Park’s transformation model with a dedicated fault loop, with a Domain-Adversarial Neural Network (DANN) driven by a minimal physics-guided feature vector composed of the 100 Hz and 200 Hz harmonic amplitudes of the excitation current. Simulated data from the digital twin are used as a labeled source domain, whereas test-bench measurements of the excitation current form an unlabeled target domain, enabling unsupervised sim-to-real transfer of the stator fault resistance. The proposed architecture achieves accurate regression of the stator fault-loop resistance on a laboratory machine without any labeled measurements of real faults. Experimental results demonstrate Mean Absolute Error (MAE) below 3% across the investigated fault severity range, significantly outperforming baseline approaches that lack domain adaptation. The industrial significance of this approach lies in its potential to facilitate a transition from reactive to predictive maintenance. By enabling early-stage detection, the framework allows power plant operators to avoid catastrophic failures and significantly reduce exceptionally high costs associated with unplanned outages and cascading grid disturbances. Full article
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22 pages, 5557 KB  
Article
Exhaust Gas Temperature Prediction of a Marine Gas Turbine Engine Using a Thermodynamic Knowledge-Driven Graph Attention Network Model
by Jinwei Chen, Jinxian Wei, Weiqiang Gao, Yifan Chen and Huisheng Zhang
J. Mar. Sci. Eng. 2026, 14(9), 857; https://doi.org/10.3390/jmse14090857 - 3 May 2026
Viewed by 251
Abstract
The exhaust gas temperature (EGT) of the gas generator is a critical indicator for the health management system of a marine gas turbine engine. Therefore, EGT prediction can not only support predictive maintenance decision-making but also serves as a reliable virtual sensor for [...] Read more.
The exhaust gas temperature (EGT) of the gas generator is a critical indicator for the health management system of a marine gas turbine engine. Therefore, EGT prediction can not only support predictive maintenance decision-making but also serves as a reliable virtual sensor for EGT measurement. However, the engine EGT exhibits strongly nonlinear coupling relationships with other gas path variables, which causes challenges for data-driven prediction. Graph neural networks (GNNs) are particularly effective in capturing the coupling relationships among gas path sensor variables. However, conventional static graph structures fail to characterize the varying coupling strengths under different operating conditions. In this study, a thermodynamic knowledge-driven graph attention network (TKD-GAT) method is proposed for accurate and robust EGT prediction. First, a physics-guided graph topology is constructed based on the gas turbine thermodynamic equations. Subsequently, a multi-head attention mechanism is introduced to generate edge weights that capture the varying thermodynamic coupling strengths under different operation conditions. The proposed model is evaluated on a real-world LM2500 gas turbine, which is widely used in modern propulsion systems of commercial and military ships. The ablation study confirms that the thermodynamic knowledge-driven graph topology and the attention mechanism-based edge weights are both necessary to enhance the EGT prediction performance. The TKD-GAT model shows the best performance with an RMSE of 0.446% and an R2 of 0.971 compared with state-of-the-art models. The paired t-test and effect size measurement (Cohen’s d) statistically confirm the significance of performance improvements. The statistical results from multiple independent experiments prove the stability of the TKD-GAT model. Additionally, the model achieves a competitive computational cost despite the integration of a physics-guided graph topology and attention mechanisms. Crucially, an interpretability analysis confirms that the learned attention weights adhere to thermodynamic principles under different operation conditions. The proposed TKD-GAT model provides an effective solution for EGT prediction in health management systems. Full article
(This article belongs to the Section Ocean Engineering)
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28 pages, 6191 KB  
Article
Prediction of Groove Depth in Femtosecond Laser Ablation via Attention Mechanism and Monotonic Constraint
by Guangxian Li, Luyang Ding, Meng Liu, Hui Xie and Songlin Ding
Machines 2026, 14(5), 509; https://doi.org/10.3390/machines14050509 - 3 May 2026
Viewed by 221
Abstract
Femtosecond laser ablation (FLA) is efficient for the machining of micro-groove arrays on the surface of ultrahard cutting tools. The depth of the groove determines the precision and efficiency of ablation. In this study, an “Attention-based Monotonic Physics-Guided Neural Network” (AM-PGNN) algorithm is [...] Read more.
Femtosecond laser ablation (FLA) is efficient for the machining of micro-groove arrays on the surface of ultrahard cutting tools. The depth of the groove determines the precision and efficiency of ablation. In this study, an “Attention-based Monotonic Physics-Guided Neural Network” (AM-PGNN) algorithm is proposed to accurately predict groove depth in the FLA of tungsten carbide (WC). The new algorithm incorporates machining parameters directly governing the energy deposition and thermal accumulation, thereby determining the prediction of the micro-groove depth generation. By embedding the physics-guided monotonic relationships of parameter depth into the learning process, a dedicated physical loss coupled with an attention mechanism to enable adaptive feature weighting is constructed, which strengthens the representation of causal dependencies. Experimental data for training and testing are obtained from the FLA of WC with different machining parameters. Comparison between AM-PGNN and typical algorithms, including a Support Vector Machine (SVM), Deep Neural Network (DNN), Convolutional Neural Network (CNN), Gradient Boosting Decision Tree (GBDT), and a conventional PGNN, demonstrates that the proposed AM-PGNN achieves superior prediction accuracy. Moreover, AM-PGNN attains a physical consistency degree (PCD) of 100%, indicating strict adherence to monotonicity consistent with the actual situation. AM-PGNN also exhibits enhanced robustness to input perturbations, as reflected by reduced standard deviation (Std) and normalized absolute deviation (NAD). Finally, AM-PGNN is shown to be applicable in the FLA of different materials through additional experiments on Cu and SiC, achieving R2 values above 0.93 while maintaining a PCD of 100%. Full article
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25 pages, 9166 KB  
Article
Deep Surrogate Modeling for Conducted EMI Prediction and Filter Optimization in a Three-Level NPC Inverter: From Experimental Data to Compliance-Aware Design
by Fatih Tulumbaci, Rabia Korkmaz Tan and Suayb Cagri Yener
Electronics 2026, 15(9), 1938; https://doi.org/10.3390/electronics15091938 - 3 May 2026
Viewed by 364
Abstract
Conducted electromagnetic interference (EMI) in multilevel power converters is governed by nonlinear interactions among passive filter components, operating conditions, and resonance-sensitive spectral behavior, making analytical prediction and trial-and-error tuning insufficient for systematic compliance-oriented design. This study presents an experimentally grounded, data-driven framework for [...] Read more.
Conducted electromagnetic interference (EMI) in multilevel power converters is governed by nonlinear interactions among passive filter components, operating conditions, and resonance-sensitive spectral behavior, making analytical prediction and trial-and-error tuning insufficient for systematic compliance-oriented design. This study presents an experimentally grounded, data-driven framework for predicting and optimizing conducted EMI in an IGBT-based, SVPWM-controlled three-level neutral-point-clamped (NPC) inverter equipped with an active harmonic filter. A dataset of 1000 conducted-emission measurements was constructed from 250 filter parameter combinations evaluated under four operating scenarios: constant-current average, constant-current peak, standby average, and standby peak, over the 10 kHz–30 MHz range. Four surrogate architectures were trained and evaluated: a multilayer perceptron (ANN), a convolutional neural network (CNN), a deep neural network (DNN), and a physics-informed neural network (PINN). Model reliability was assessed through nested cross-validation, standard 5-fold cross-validation, Monte Carlo resampling, and SHAP-based interpretability analysis. Among the tested architectures, the CNN achieved the most consistent predictive performance and stability, whereas the PINN provided smoother and more physically disciplined spectral reconstructions in several load-related conditions. The trained surrogates were embedded in a Python 3.11-based graphical user interface and further employed within a compliance-oriented optimization framework to identify filter parameter sets capable of satisfying legal conducted-emission limits. Experimental verification confirmed that surrogate-guided optimized designs achieved positive worst-case legal margins between 7.26 and 11.50 dBµV. Relative to the best measured pre-optimization combination, which still exhibited a worst-case margin of −3.7 dBµV, the best experimentally validated optimized design improved the worst-case legal margin by 15.20 dBµV. These results demonstrate that experimentally trained surrogate models can support not only high-resolution EMI prediction but also regulation-aware filter design and practical engineering decision making. Full article
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25 pages, 17499 KB  
Article
Optimization of Exoskeleton Assistance Function Based on Physics-Guided Dynamic Fusion Model
by Haochen Tian, Jiaxin Wang, Shijie Guo, Feng Cao and Lei Liu
Bioengineering 2026, 13(5), 531; https://doi.org/10.3390/bioengineering13050531 - 1 May 2026
Viewed by 1789
Abstract
Wearable lower-limb exoskeletons can enhance mobility, reduce metabolic cost, and aid rehabilitation. Effective human-exo cooperation requires personalized assistance profiles that match biomechanical principles. Existing methods often rely on fixed curves, involve complex tuning, and lack biomechanical interpretability. To address this, we propose a [...] Read more.
Wearable lower-limb exoskeletons can enhance mobility, reduce metabolic cost, and aid rehabilitation. Effective human-exo cooperation requires personalized assistance profiles that match biomechanical principles. Existing methods often rely on fixed curves, involve complex tuning, and lack biomechanical interpretability. To address this, we propose a “Physics-guided perception and physiology-driven optimization” approach. First, a Physics-guided Dynamic Fusion Model (PDFM) is proposed, which integrates Newton–Euler dynamics, LSTM, and NTM to estimate multi-plane hip joint moments without ground reaction forces, employing biomechanical models as complementary fusion factors rather than the embedded hard constraints used in conventional physics-informed neural networks (PINNs). The model achieved correlation coefficients of 0.938, 0.924, and 0.929, and relative root mean square error (rRMSE) values of 5.29%, 9.79%, and 5.61%, in the sagittal, coronal, and transverse planes, respectively. These results outperformed all single-network baselines across all three anatomical planes. Second, an assistance profile derived from estimated moments is individually optimized using Bayesian optimization based on multi-muscle sEMG. Compared to no-exo walking, the optimized system reduced target muscle loading by 49.31% and metabolic cost by 14.75%; relative to the pre-optimized profile, the reductions were 23.64% and 5.74%, respectively. This work provides a laboratory-validated framework for personalized hip exoskeleton assistance in healthy adults, establishing a foundation for future clinical translation. Full article
(This article belongs to the Section Biomedical Engineering and Biomaterials)
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23 pages, 4083 KB  
Article
RD-DETR: A Robust Vehicle Detector via Reaction–Diffusion Mechanisms
by Yi Huang, Yishi Chen, Kaiming Pan, Xiangning Wu, Haoxiang Huang and Yanmei Meng
Appl. Sci. 2026, 16(9), 4378; https://doi.org/10.3390/app16094378 - 30 Apr 2026
Viewed by 207
Abstract
Vehicle detection is a fundamental perception task in intelligent transportation systems and autonomous driving. Although state-of-the-art detectors achieve competitive performance under normal conditions, their robustness degrades substantially under adverse conditions such as rain, fog, low illumination, and sensor noise. To address this challenge, [...] Read more.
Vehicle detection is a fundamental perception task in intelligent transportation systems and autonomous driving. Although state-of-the-art detectors achieve competitive performance under normal conditions, their robustness degrades substantially under adverse conditions such as rain, fog, low illumination, and sensor noise. To address this challenge, we propose RD-DETR, a vehicle detector that incorporates reaction–diffusion mechanisms into deep feature learning. The RDNet backbone adopts a pyramid-based enhancement strategy in which shallow layers preserve fine-grained texture details while deep layers employ reaction–diffusion-inspired dynamics to suppress noise and enhance target representations. The Phase-Guided Spatial Attention (PGSA) module leverages phase-related structural cues that are relatively less sensitive to global illumination and contrast variations, helping recover vehicle boundaries when appearance cues become unreliable under adverse imaging conditions. The Content-Aware Adaptive Fusion Module (CA-AFM) dynamically aggregates multi-scale features according to scene complexity, improving detection across diverse traffic scenarios. Experiments on BDD100K and DAWN show that RD-DETR yields mAP@0.5 improvements of 3.2 and 4.0 percentage points over RT-DETR, respectively, while reducing model parameters by 27.6%, indicating a favorable balance between accuracy and efficiency under the evaluated settings. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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15 pages, 1174 KB  
Article
Research on Data-Driven Modeling of Solid Rocket Motor Plume Temperature Distribution with Physics Guidance
by Bo Cheng, Chengyuan Qian, Xinxin Chen and Chengfei Zhang
Appl. Sci. 2026, 16(9), 4373; https://doi.org/10.3390/app16094373 - 29 Apr 2026
Viewed by 283
Abstract
Aiming at the problems of the large prediction error of model-driven algorithms and poor interpretability (even potential violation of physical laws) of pure data-driven algorithms in the prediction of aerospace vehicle plume characteristics, a physics mechanism-guided prediction algorithm for aerospace vehicle plume characteristics [...] Read more.
Aiming at the problems of the large prediction error of model-driven algorithms and poor interpretability (even potential violation of physical laws) of pure data-driven algorithms in the prediction of aerospace vehicle plume characteristics, a physics mechanism-guided prediction algorithm for aerospace vehicle plume characteristics was proposed. Taking the long short-term memory (LSTM) network as the backbone, this algorithm constructed a hybrid physics–data model by embedding the prior knowledge of physical laws and empirical rules into the neural network, and designed a loss function combined with physical mechanisms to guide network training. The aerospace vehicle plume dataset was preprocessed through characteristic parameter extraction, extended physical parameter calculation, data splicing and sliding window operation, and the LSTM network structure was optimized by adjusting hyperparameters such as the number of hidden layers and neurons. Experimental results show that the proposed algorithm achieves a Mean Absolute Error (MAE) of 31.89 and a Physical Inconsistency of 0.1723 on the test set, with MAE reduced by 14% and Physical Inconsistency reduced by 7.5% compared with traditional machine learning models such as Random Forest. Ablation experiments verify that the introduction of physical mechanisms can improve the prediction accuracy of the model by about 25%. This algorithm makes up for the defects of traditional prediction algorithms, has good generalization ability and physical consistency, and provides an effective method for the prediction of engine exhaust plume temperature distribution. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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24 pages, 4822 KB  
Article
Heuristic-Guided Safe Multi-Agent Reinforcement Learning for Resilient Spatio-Temporal Dispatch of Energy-Mobility Nexus Under Grid Faults
by Runtian Tang, Yang Wang, Wenan Li, Zhenghui Zhao and Xiaonan Shen
Electronics 2026, 15(9), 1868; https://doi.org/10.3390/electronics15091868 - 28 Apr 2026
Viewed by 362
Abstract
The increasing electrification of urban transportation has formulated a tightly coupled energy-mobility nexus. Under extreme disaster events or grid faults, rapidly restoring power supply capacity and re-dispatching shared electric vehicle (EV) fleets are critical for enhancing system resilience. Existing co-optimization methods face the [...] Read more.
The increasing electrification of urban transportation has formulated a tightly coupled energy-mobility nexus. Under extreme disaster events or grid faults, rapidly restoring power supply capacity and re-dispatching shared electric vehicle (EV) fleets are critical for enhancing system resilience. Existing co-optimization methods face the curse of dimensionality when dealing with high-dimensional discrete grid reconfigurations and continuous spatio-temporal EV queuing dynamics. While multi-agent deep reinforcement learning (MADRL) offers real-time responsiveness, it inherently struggles to satisfy strict physical constraints, frequently generating infeasible and unsafe actions. To bridge this gap, this paper proposes a heuristic-guided safe multi-agent reinforcement learning (Safe-MADRL) framework for the resilient dispatch of the energy-mobility nexus. Instead of relying solely on black-box neural networks, the framework structurally embeds physical models and heuristic solvers into the learning loop. A quantum particle swarm optimization (QPSO) algorithm acts as a heuristic action refiner to ensure that grid topology actions strictly comply with non-linear power flow and voltage constraints. Simultaneously, a mixed-integer linear programming (MILP) model coupled with a single-queue multi-server (SQMS) model serves as a safety projection layer. This layer mathematically guarantees EV battery energy continuity and accurately quantifies spatio-temporal queuing delays at charging stations. Case studies on a coupled IEEE 33-node distribution system and a regional transportation network demonstrate that the proposed Safe-MADRL framework achieves zero physical violations during training and significantly outperforms traditional mathematical optimization and pure learning-based methods in computational efficiency, system power loss reduction, and overall operational economy. Full article
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14 pages, 1640 KB  
Article
Small-Data Neural Computing Outperforms RSM: Low-Cost Smart Optimization in Injection Molding
by Ming-Lang Yeh, Wen Pei and Han-Ching Huang
Appl. Sci. 2026, 16(9), 4288; https://doi.org/10.3390/app16094288 - 28 Apr 2026
Viewed by 305
Abstract
In smart manufacturing, the injection molding industry faces a “data scarce environment” due to prohibitive physical trial costs. Processing recycled polypropylene (rPP) exacerbates this challenge, as traditional response surface methodology (RSM) fails to capture complex non-linear rheological behaviors induced by material variability. This [...] Read more.
In smart manufacturing, the injection molding industry faces a “data scarce environment” due to prohibitive physical trial costs. Processing recycled polypropylene (rPP) exacerbates this challenge, as traditional response surface methodology (RSM) fails to capture complex non-linear rheological behaviors induced by material variability. This study proposes a “domain-knowledge guided data augmentation framework,” integrating Taguchi experimental data (L25) with Moldex3D digital twin simulations to construct a 300-sample hybrid dataset. A back-propagation neural network (BPNN) with L2 regularization was employed for small-sample learning, providing a continuous differentiable physical mapping. To rigorously prevent neighborhood data leakage, the model was evaluated via a strict nested group-based 5-fold cross-validation. Particle swarm optimization (PSO) was coupled to overcome the local minima of gradient descent. Comparative analysis demonstrates that BPNN significantly outperforms both traditional RSM and a newly introduced Random Forest (RF) baseline, achieving a testing mean squared error (MSE) of 0.001 (±0.0002) and a testing R2 of 0.95. PSO minimized the shrinkage rate to 3.079%, validated via Moldex3D digital twin simulation with a 0.19% relative error. Synergizing virtual–physical integration with robust neural computing enables superior process control precision in small-data regimes, offering small and medium-sized enterprises (SMEs) a cost-effective pathway for smart optimization. Full article
(This article belongs to the Section Applied Industrial Technologies)
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