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Search Results (325)

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Keywords = optimizations on manifolds

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23 pages, 21197 KiB  
Article
DLPLSR: Dual Label Propagation-Driven Least Squares Regression with Feature Selection for Semi-Supervised Learning
by Shuanghao Zhang, Zhengtong Yang and Zhaoyin Shi
Mathematics 2025, 13(14), 2290; https://doi.org/10.3390/math13142290 - 16 Jul 2025
Viewed by 140
Abstract
In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient [...] Read more.
In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient use of unlabeled data, low pseudo-label accuracy, and inefficient label propagation. To address these issues, this paper proposes dual label propagation-driven least squares regression with feature selection, named DLPLSR, which is a pseudo-label-free SSL framework. DLPLSR employs a fuzzy-graph-based clustering strategy to capture global relationships among all samples, and manifold regularization preserves local geometric consistency, so that it implements the dual label propagation mechanism for comprehensive utilization of unlabeled data. Meanwhile, a dual-feature selection mechanism is established by integrating orthogonal projection for maximizing feature information with an 2,1-norm regularization for eliminating redundancy, thereby jointly enhancing the discriminative power. Benefiting from these two designs, DLPLSR boosts learning performance without pseudo-labeling. Finally, the objective function admits an efficient closed-form solution solvable via an alternating optimization strategy. Extensive experiments on multiple benchmark datasets show the superiority of DLPLSR compared to state-of-the-art LSR-based SSL methods. Full article
(This article belongs to the Special Issue Machine Learning and Optimization for Clustering Algorithms)
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23 pages, 4119 KiB  
Article
Cross-Scenario Interpretable Prediction of Coal Mine Water Inrush Probability: An Integrated Approach Driven by Gaussian Mixture Modeling with Manifold Learning and Metaheuristic Optimization
by Qiushuang Zheng and Changfeng Wang
Symmetry 2025, 17(7), 1111; https://doi.org/10.3390/sym17071111 - 10 Jul 2025
Viewed by 217
Abstract
Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and [...] Read more.
Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and struggle with interpretability, leading to insufficient predictive accuracy and engineering applicability under complex geological conditions. This study addresses these limitations by integrating Gaussian mixture modeling (GMM), manifold learning, and data augmentation to effectively capture multimodal hydrological data distributions and reveal their intrinsic symmetrical configurations and manifold structures, thereby reducing feature dimensionality. We then apply a whale optimization algorithm (WOA)-enhanced XGBoost model to forecast water inrush probabilities. Our model achieved an R2 of 0.92, demonstrating a greater than 60% error reduction across various metrics. Validation at the Yangcheng Coal Mine confirmed that this balanced approach significantly enhances predictive accuracy, interpretability, and cross-scenario applicability. The synergy between high accuracy and transparency provides decision makers with reliable risk insights, enabling bidirectional validation with geological mechanisms and supporting the implementation of targeted, proactive safety measures. Full article
(This article belongs to the Section Mathematics)
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22 pages, 5548 KiB  
Article
Novel Data-Driven PDF Modeling in FGM Method Based on Sparse Turbulent Flame Data
by Guihua Zhang, Jiayue Liu, Yuxin Wu and Guangxi Yue
Energies 2025, 18(13), 3546; https://doi.org/10.3390/en18133546 - 4 Jul 2025
Viewed by 305
Abstract
The Flamelet Generated Manifold (FGM) method is widely employed in turbulent combustion simulations due to its high accuracy and computational efficiency. However, the model’s ability to capture turbulent combustion interactions is limited by the shape of the presumed probability density function (PDF) of [...] Read more.
The Flamelet Generated Manifold (FGM) method is widely employed in turbulent combustion simulations due to its high accuracy and computational efficiency. However, the model’s ability to capture turbulent combustion interactions is limited by the shape of the presumed probability density function (PDF) of the mixture fraction and progress variable. To construct a conditional β PDF with better performance, a systematic PDF modeling and analysis framework coupled with machine learning methods based on the sparse experimental data was proposed. A comparative analysis was conducted for five machine learning methods across two experimental datasets using this framework. The results demonstrate that the random forest algorithm represents the optimal choice when both training complexity and predictive performance are comprehensively considered. To expand the model’s applicable range, a data fusion strategy was applied in different machine learning methods. The effectiveness of data fusion is demonstrated by comparative analysis between single-dataset and fused-dataset models. The analysis of convex hull in low-dimensional space reveals the fundamental mechanism of data fusion in the FGM-PDF method, which is significantly important to construct a data-driven PDF model in sparse-data scenarios with much better performance. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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28 pages, 25499 KiB  
Article
A Combined CFD, Theoretical, and Experimental Approach for Improved Hydrodynamic Performance of a Clam Dredge System
by Rui You and Nathan H. Kennedy
J. Mar. Sci. Eng. 2025, 13(7), 1305; https://doi.org/10.3390/jmse13071305 - 4 Jul 2025
Viewed by 664
Abstract
This paper addresses the need for an integrated approach to develop an improved clam dredge system. Current designs often rely on empirical methods, resulting in a disconnect between theoretical models, computational simulations, and experimental validation. To bridge this gap, the study integrates computational [...] Read more.
This paper addresses the need for an integrated approach to develop an improved clam dredge system. Current designs often rely on empirical methods, resulting in a disconnect between theoretical models, computational simulations, and experimental validation. To bridge this gap, the study integrates computational fluid dynamics (CFD), experimental tests, and analytical methods to develop a clam dredge system. Firstly, the paper introduces an analytical tool that facilitates decision making by evaluating pump parameters, and to determine the operating point for various hose and nozzle parameters. This guides the parameter selection of pump, hose and jets for maximum performance. Secondly, CFD is utilized to analyze flow behavior, enabling the design of internal nozzle geometries that minimize head losses and maximize the scouring effect. A full-scale experimental measurement was conducted to validate computational results. Furthermore, a replica manifold is constructed using 3D printing and tested, demonstrating improvements in jet speed with both original and new nozzle designs. Analytical results indicate that increasing hose length reduces BHP, flow rate, and jet velocity, while increasing hose or jet diameter boosts BHP and flow but reduces jet speed due to pressure drops. Switching pumps reduced power consumption by 10.5% with minimal speed loss. The CFD analysis optimized nozzle design, reducing jet loss and enhancing efficiency. The proposed slit nozzle design reduces the loss coefficient by 85.24% in small-scale runs and by 83% in full-scale runs compared to the original circular jet design. The experiments confirmed the pressure differences between the CFD and experimental tests are within 10%, and demonstrated that rectangular jets increase speed by 9% and seafloor force by 19%. This paper improved the hydrodynamic design of the clam dredge system, and provides a framework for future dredge system designs. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 5808 KiB  
Article
Hyperbolic Spatial Covariance Modeling with Adaptive Signal Filtering for Robust Wi-Fi Indoor Positioning
by Wenxu Wang and Mingxiang Liu
Sensors 2025, 25(13), 4125; https://doi.org/10.3390/s25134125 - 2 Jul 2025
Viewed by 274
Abstract
Robust indoor positioning, crucial to modern location-based services, increasingly leverages Channel State Information (CSI) for its superior multipath resolution over the traditional RSSI. However, current CSI-based methods are hampered by three key limitations: susceptibility to skewed, non-Gaussian noise; informational redundancy from multi-AP configurations; [...] Read more.
Robust indoor positioning, crucial to modern location-based services, increasingly leverages Channel State Information (CSI) for its superior multipath resolution over the traditional RSSI. However, current CSI-based methods are hampered by three key limitations: susceptibility to skewed, non-Gaussian noise; informational redundancy from multi-AP configurations; and spatial discontinuities arising from Euclidean-based modeling. To address these challenges, we propose a unified framework that synergistically combines three innovations: (1) an adaptive filtering pipeline that uses wavelet decomposition and dynamic Kalman updates to suppress skewed noise; (2) a graph attention network that optimizes AP selection by modeling spatiotemporal correlations; and (3) a hyperbolic covariance model that captures the intrinsic non-Euclidean geometry of signal propagation. Evaluations on experimental data demonstrate that our framework achieves superior positioning accuracy and environmental robustness over state-of-the-art methods. Crucially, the hyperbolic representation enhances resilience to obstructions by preserving the signal manifold’s true structure, thereby advancing the practical deployment of fingerprinting systems. Full article
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23 pages, 9748 KiB  
Article
Driving Pattern Analysis, Gear Shift Classification, and Fuel Efficiency in Light-Duty Vehicles: A Machine Learning Approach Using GPS and OBD II PID Signals
by Juan José Molina-Campoverde, Juan Zurita-Jara and Paúl Molina-Campoverde
Sensors 2025, 25(13), 4043; https://doi.org/10.3390/s25134043 - 28 Jun 2025
Viewed by 655
Abstract
This study proposes an automatic gear shift classification algorithm in M1 category vehicles using data acquired through the onboard diagnostic system (OBD II) and GPS. The proposed approach is based on the analysis of identification parameters (PIDs), such as manifold absolute pressure (MAP), [...] Read more.
This study proposes an automatic gear shift classification algorithm in M1 category vehicles using data acquired through the onboard diagnostic system (OBD II) and GPS. The proposed approach is based on the analysis of identification parameters (PIDs), such as manifold absolute pressure (MAP), revolutions per minute (RPM), vehicle speed (VSS), torque, power, stall times, and longitudinal dynamics, to determine the efficiency and behavior of the vehicle in each of its gears. In addition, the unsupervised K-means algorithm was implemented to analyze vehicle gear changes, identify driving patterns, and segment the data into meaningful groups. Machine learning techniques, including K-Nearest Neighbors (KNN), decision trees, logistic regression, and Support Vector Machines (SVMs), were employed to classify gear shifts accurately. After a thorough evaluation, the KNN (Fine KNN) model proved to be the most effective, achieving an accuracy of 99.7%, an error rate of 0.3%, a precision of 99.8%, a recall of 99.7%, and an F1-score of 99.8%, outperforming other models in terms of accuracy, robustness, and balance between metrics. A multiple linear regression model was developed to estimate instantaneous fuel consumption (in L/100 km) using the gear predicted by the KNN algorithm and other relevant variables. The model, built on over 66,000 valid observations, achieved an R2 of 0.897 and a root mean square error (RMSE) of 2.06, indicating a strong fit. Results showed that higher gears (3, 4, and 5) are associated with lower fuel consumption. In contrast, a neutral gear presented the highest levels of consumption and variability, especially during prolonged idling periods in heavy traffic conditions. In future work, we propose integrating this algorithm into driver assistance systems (ADAS) and exploring its applicability in autonomous vehicles to enhance real-time decision making. Such integration could optimize gear shift timing based on dynamic factors like road conditions, traffic density, and driver behavior, ultimately contributing to improved fuel efficiency and overall vehicle performance. Full article
(This article belongs to the Section Vehicular Sensing)
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30 pages, 14473 KiB  
Article
VOX-LIO: An Effective and Robust LiDAR-Inertial Odometry System Based on Surfel Voxels
by Meijun Guo, Yonghui Liu, Yuhang Yang, Xiaohai He and Weimin Zhang
Remote Sens. 2025, 17(13), 2214; https://doi.org/10.3390/rs17132214 - 27 Jun 2025
Viewed by 373
Abstract
Accurate and robust pose estimation is critical for simultaneous localization and mapping (SLAM), and multi-sensor fusion has demonstrated efficacy with significant potential for robotic applications. This study presents VOX-LIO, an effective LiDAR-inertial odometry system. To improve both robustness and accuracy, we propose an [...] Read more.
Accurate and robust pose estimation is critical for simultaneous localization and mapping (SLAM), and multi-sensor fusion has demonstrated efficacy with significant potential for robotic applications. This study presents VOX-LIO, an effective LiDAR-inertial odometry system. To improve both robustness and accuracy, we propose an adaptive hash voxel-based point cloud map management method that incorporates surfel features and planarity. This method enhances the efficiency of point-to-surfel association by leveraging long-term observed surfel. It facilitates the incremental refinement of surfel features within classified surfel voxels, thereby enabling precise and efficient map updates. Furthermore, we develop a weighted fusion approach that integrates LiDAR and IMU data measurements on the manifold, effectively compensating for motion distortion, particularly under high-speed LiDAR motion. We validate our system through experiments conducted on both public datasets and our mobile robot platforms. The results demonstrate that VOX-LIO outperforms the existing methods, effectively handling challenging environments while minimizing computational cost. Full article
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20 pages, 6063 KiB  
Article
A Hierarchical Evolutionary Search Framework with Manifold Learning for Powertrain Optimization of Flying Vehicles
by Chenghao Lyu, Nuo Lei, Chaoyi Chen and Hao Zhang
Energies 2025, 18(13), 3350; https://doi.org/10.3390/en18133350 - 26 Jun 2025
Viewed by 257
Abstract
Hybrid electric vertical take-off and landing (HEVTOL) flying vehicles serve as effective platforms for efficient transportation, forming a cornerstone of the emerging low-altitude economy. However, the current lack of co-optimization methods for powertrain component sizing and energy controller design often leads to suboptimal [...] Read more.
Hybrid electric vertical take-off and landing (HEVTOL) flying vehicles serve as effective platforms for efficient transportation, forming a cornerstone of the emerging low-altitude economy. However, the current lack of co-optimization methods for powertrain component sizing and energy controller design often leads to suboptimal HEVTOL performance. To address this, this paper proposes a hierarchical manifold-enhanced Bayesian evolutionary optimization (HM-BEO) approach for HEVTOL systems. This framework employs lightweight manifold dimensionality reduction to compress the decision space, enabling Bayesian optimization (BO) on low-dimensional manifolds for a global coarse search. Subsequently, the approximate Pareto solutions generated by BO are utilized as initial populations for a non-dominated sorting genetic algorithm III (NSGA-III), which performs fine-grained refinement in the original high-dimensional design space. The co-optimization aims to minimize fuel consumption, battery state-of-health (SOH) degradation, and manufacturing costs while satisfying dynamic and energy management constraints. Evaluated using representative HEVTOL duty cycles, the HM-BEO demonstrates significant improvements in optimization efficiency and solution quality compared to conventional methods. Specifically, it achieves a 5.3% improvement in fuel economy, a 7.4% mitigation in battery SOH degradation, and a 1.7% reduction in system manufacturing cost compared to standard NSGA-III-based optimization. Full article
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44 pages, 65610 KiB  
Article
scRL: Utilizing Reinforcement Learning to Evaluate Fate Decisions in Single-Cell Data
by Zeyu Fu, Chunlin Chen, Song Wang, Junping Wang and Shilei Chen
Biology 2025, 14(6), 679; https://doi.org/10.3390/biology14060679 - 11 Jun 2025
Viewed by 1533
Abstract
Single-cell RNA sequencing now profiles whole transcriptomes for hundreds of thousands of cells, yet existing trajectory-inference tools rarely pinpoint where and when fate decisions are made. We present single-cell reinforcement learning (scRL), an actor–critic framework that recasts differentiation as a sequential decision process [...] Read more.
Single-cell RNA sequencing now profiles whole transcriptomes for hundreds of thousands of cells, yet existing trajectory-inference tools rarely pinpoint where and when fate decisions are made. We present single-cell reinforcement learning (scRL), an actor–critic framework that recasts differentiation as a sequential decision process on an interpretable latent manifold derived with Latent Dirichlet Allocation. The critic learns state-value functions that quantify fate intensity for each cell, while the actor traces optimal developmental routes across the manifold. Benchmarks on hematopoiesis, mouse endocrinogenesis, acute myeloid leukemia, and gene-knockout and irradiation datasets show that scRL surpasses fifteen state-of-the-art methods in five independent evaluation dimensions, recovering early decision states that precede overt lineage commitment and revealing regulators such as Dapp1. Beyond fate decisions, the same framework produces competitive measures of lineage-contribution intensity without requiring ground-truth probabilities, providing a unified and extensible approach for decoding developmental logic from single-cell data. Full article
(This article belongs to the Special Issue AI Deep Learning Approach to Study Biological Questions (2nd Edition))
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16 pages, 2686 KiB  
Article
An Equivalence Theorem and A Sequential Algorithm for A-Optimal Experimental Designs on Manifolds
by Jingwen Zhang and Yaping Wang
Axioms 2025, 14(6), 436; https://doi.org/10.3390/axioms14060436 - 2 Jun 2025
Viewed by 288
Abstract
Selecting input data points in the context of high-dimensional, nonlinear, and complex data in Riemannian space is challenging. While optimal experimental design theory is well-established in Euclidean space, its extension to Riemannian manifolds remains underexplored. Li and Del Castillo recently obtained new theoretical [...] Read more.
Selecting input data points in the context of high-dimensional, nonlinear, and complex data in Riemannian space is challenging. While optimal experimental design theory is well-established in Euclidean space, its extension to Riemannian manifolds remains underexplored. Li and Del Castillo recently obtained new theoretical results on D-optimal and G-optimal designs on Riemannian manifolds. This paper follows their framework to investigate A-optimal designs on such manifolds. We prove an equivalence theorem for A-optimality under the manifold regularization model. Based on this result, a sequential algorithm for identifying A-optimal designs on manifold data is developed. Numerical studies using both synthetic and real datasets show the validity of the proposed method. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
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21 pages, 5887 KiB  
Article
Meta-Features Extracted from Use of kNN Regressor to Improve Sugarcane Crop Yield Prediction
by Luiz Antonio Falaguasta Barbosa, Ivan Rizzo Guilherme, Daniel Carlos Guimarães Pedronette and Bruno Tisseyre
Remote Sens. 2025, 17(11), 1846; https://doi.org/10.3390/rs17111846 - 25 May 2025
Viewed by 512
Abstract
Accurate crop yield prediction is essential for sugarcane growers, as it enables them to predict harvested biomass, guiding critical decisions regarding acquiring agricultural inputs such as fertilizers and pesticides, the timing and execution of harvest operations, and cane field renewal strategies. This study [...] Read more.
Accurate crop yield prediction is essential for sugarcane growers, as it enables them to predict harvested biomass, guiding critical decisions regarding acquiring agricultural inputs such as fertilizers and pesticides, the timing and execution of harvest operations, and cane field renewal strategies. This study is based on an experiment conducted by researchers from the Commonwealth Scientific and Industrial Research Organisation (CSIRO), who employed a UAV-mounted LiDAR and multispectral imaging sensors to monitor two sugarcane field trials subjected to varying nitrogen (N) fertilization regimes in the Wet Tropics region of Australia. The predictive performance of models utilizing multispectral features, LiDAR-derived features, and a fusion of both modalities was evaluated against a benchmark model based on the Normalized Difference Vegetation Index (NDVI). This work utilizes the dataset produced by this experiment, incorporating other regressors and features derived from those collected in the field. Typically, crop yield prediction relies on features derived from direct field observations, either gathered through sensor measurements or manual data collection. However, enhancing prediction models by incorporating new features extracted through regressions executed on the original dataset features can potentially improve predictive outcomes. These extracted features, nominated in this work as meta-features (MFs), extracted through regressions with different regressors on original features, and incorporated into the dataset as new feature predictors, can be utilized in further regression analyses to optimize crop yield prediction. This study investigates the potential of generating MFs as an innovation to enhance sugarcane crop yield predictions. MFs were generated based on the values obtained by different regressors applied to the features collected in the field, allowing for evaluating which approaches offered superior predictive performance within the dataset. The kNN meta-regressor outperforms other regressors because it takes advantage of the proximity of MFs, which was checked through a projection where the dispersion of points can be measured. A comparative analysis is presented with a projection based on the Uniform Manifold Approximation and Projection (UMAP) algorithm, showing that MFs had more proximity than the original features when projected, which demonstrates that MFs revealed a clear formation of well-defined clusters, with most points within each group sharing the same color, suggesting greater uniformity in the predicted values. Incorporating these MFs into subsequent regression models demonstrated improved performance, with R¯2 values higher than 0.9 for MF Grad Boost M3, MF GradientBoost M5, and all kNN MFs and reduced error margins compared to field-measured yield values. The R¯2 values obtained in this work ranged above 0.98 for the AdaBoost meta-regressor applied to MFs, which were obtained from kNN regression on five models created by the researchers of CSIRO, and around 0.99 for the kNN meta-regressor applied to MFs obtained from kNN regression on these five models. Full article
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23 pages, 2319 KiB  
Article
Codesign of Transmit Waveform and Receive Filter with Similarity Constraints for FDA-MIMO Radar
by Qiping Zhang, Jinfeng Hu, Xin Tai, Yongfeng Zuo, Huiyong Li, Kai Zhong and Chaohai Li
Remote Sens. 2025, 17(10), 1800; https://doi.org/10.3390/rs17101800 - 21 May 2025
Viewed by 389
Abstract
The codesign of the receive filter and transmit waveform under similarity constraints is one of the key technologies in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar systems. This paper discusses the design of constant modulus waveforms and filters aimed at maximizing the signal-to-interference-and-noise [...] Read more.
The codesign of the receive filter and transmit waveform under similarity constraints is one of the key technologies in frequency diverse array multiple-input multiple-output (FDA-MIMO) radar systems. This paper discusses the design of constant modulus waveforms and filters aimed at maximizing the signal-to-interference-and-noise ratio (SINR). The problem’s non-convexity renders it challenging to solve. Existing studies have typically employed relaxation-based methods, which inevitably introduce relaxation errors that degrade system performance. To address these issues, we propose an optimization framework based on the joint complex circle manifold–complex sphere manifold space (JCCM-CSMS). Firstly, the similarity constraint is converted into the penalty term in the objective function using an adaptive penalty strategy. Then, JCCM-CSMS is constructed to satisfy the waveform constant modulus constraint and filter norm constraint. The problem is projected into it and transformed into an unconstrained optimization problem. Finally, the Riemannian limited-memory Broyden–Fletcher–Goldfarb–Shanno (RL-BFGS) algorithm is employed to optimize the variables in parallel. Simulation results demonstrate that our method achieves a 0.6 dB improvement in SINR compared to existing methods while maintaining competitive computational efficiency. Additionally, waveform similarity was also analyzed. Full article
(This article belongs to the Special Issue Array Digital Signal Processing for Radar)
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39 pages, 14011 KiB  
Article
Comparing Geodesic Filtering to State-of-the-Art Algorithms: A Comprehensive Study and CUDA Implementation
by Pierre Boulanger and Sadid Bin Hasan
J. Imaging 2025, 11(5), 167; https://doi.org/10.3390/jimaging11050167 - 20 May 2025
Viewed by 515
Abstract
This paper presents a comprehensive investigation into advanced image processing using geodesic filtering within a Riemannian manifold framework. We introduce a novel geodesic filtering formulation that uniquely integrates spatial and intensity relationships through minimal path computation, demonstrating significant improvements in edge preservation and [...] Read more.
This paper presents a comprehensive investigation into advanced image processing using geodesic filtering within a Riemannian manifold framework. We introduce a novel geodesic filtering formulation that uniquely integrates spatial and intensity relationships through minimal path computation, demonstrating significant improvements in edge preservation and noise reduction compared to conventional methods. Our quantitative analysis using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) metrics across diverse image types reveals that our approach outperforms traditional techniques in preserving fine details while effectively suppressing both Gaussian and non-Gaussian noise. We developed an automatic parameter optimization methodology that eliminates manual tuning by identifying optimal filtering parameters based on image characteristics. Additionally, we present a highly optimized GPU implementation featuring innovative wave-propagation algorithms and memory access optimization techniques that achieve a 200× speedup, making geodesic filtering practical for real-time applications. Our work bridges the gap between theoretical elegance and computational practicality, establishing geodesic filtering as a superior solution for challenging image processing tasks in fields ranging from medical imaging to remote sensing. Full article
(This article belongs to the Section Image and Video Processing)
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36 pages, 900 KiB  
Article
Discrete Physics-Informed Training for Projection-Based Reduced-Order Models with Neural Networks
by Nicolas Sibuet, Sebastian Ares de Parga, Jose Raul Bravo and Riccardo Rossi
Axioms 2025, 14(5), 385; https://doi.org/10.3390/axioms14050385 - 20 May 2025
Viewed by 1038
Abstract
This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional [...] Read more.
This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Our key contributions include the following: (1) a parameter-agnostic, discrete residual loss applicable to nonlinear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics-informed training process for ROMs. The method is demonstrated on a nonlinear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on nonlinear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use case. Finally, the application of physics-informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy; however, it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN. Full article
(This article belongs to the Section Mathematical Physics)
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15 pages, 3352 KiB  
Article
Analysis of High-Dimensional Coordination in Human Movement Using Variance Spectrum Scaling and Intrinsic Dimensionality
by Dobromir Dotov, Jingxian Gu, Philip Hotor and Joanna Spyra
Entropy 2025, 27(4), 447; https://doi.org/10.3390/e27040447 - 21 Apr 2025
Viewed by 850
Abstract
Full-body movement involving multi-segmental coordination has been essential to our evolution as a species, but its study has been focused mostly on the analysis of one-dimensional data. The field is poised for a change by the availability of high-density recording and data sharing. [...] Read more.
Full-body movement involving multi-segmental coordination has been essential to our evolution as a species, but its study has been focused mostly on the analysis of one-dimensional data. The field is poised for a change by the availability of high-density recording and data sharing. New ideas are needed to revive classical theoretical questions such as the organization of the highly redundant biomechanical degrees of freedom and the optimal distribution of variability for efficiency and adaptiveness. In movement science, there are popular methods that up-dimensionalize: they start with one or a few recorded dimensions and make inferences about the properties of a higher-dimensional system. The opposite problem, dimensionality reduction, arises when making inferences about the properties of a low-dimensional manifold embedded inside a large number of kinematic degrees of freedom. We present an approach to quantify the smoothness and degree to which the kinematic manifold of full-body movement is distributed among embedding dimensions. The principal components of embedding dimensions are rank-ordered by variance. The power law scaling exponent of this variance spectrum is a function of the smoothness and dimensionality of the embedded manifold. It defines a threshold value below which the manifold becomes non-differentiable. We verified this approach by showing that the Kuramoto model obeys the threshold when approaching global synchronization. Next, we tested whether the scaling exponent was sensitive to participants’ gait impairment in a full-body motion capture dataset containing short gait trials. Variance scaling was highest in healthy individuals, followed by osteoarthritis patients after hip replacement, and lastly, the same patients before surgery. Interestingly, in the same order of groups, the intrinsic dimensionality increased but the fractal dimension decreased, suggesting a more compact but complex manifold in the healthy group. Thinking about manifold dimensionality and smoothness could inform classic problems in movement science and the exploration of the biomechanics of full-body action. Full article
(This article belongs to the Section Entropy and Biology)
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