Hermite Interpolation Technique-Based Performance Assessment of Coir–Polypropylene Hybrid Fiber-Reinforced Concrete

Fractional differential equations (FDEs) play a fundamental role in modeling complex physical, biological, and engineering phenomena characterized by memory effects and nonlocal dynamics. This paper presents an efficient numerical framework based on a fractional Hermite interpolation formula for solving FDEs. The proposed method extends the classical Hermite interpolation scheme to fractional calculus by embedding fractional derivatives within the interpolation structure, thereby improving approximation precision and convergence behavior. To enhance computational performance, optimized interpolation nodes and refined fractional derivative approximations are introduced, effectively reducing truncation errors and improving numerical stability. The method is systematically formulated and implemented in a computational environment, with numerical experiments verifying its robustness and accuracy. Results confirm that the proposed scheme achieves superior stability and precision compared with conventional numerical techniques, demonstrating its potential for broad application in the solution of fractional-order models across scientific and engineering domains.

Curve reconstruction is the process of estimating a smooth function or curve that fits a given setof data points, either exactly (interpolation) or approximately (fitting). Classical approaches,including global polynomial interpolation, splines, Hermite interpolation, and radial basisfunction fitting, face challenges when data are sparse, irregularly distributed, or noisy. In thispaper, we propose a curve reconstruction method based on the discrete form of the biharmonicequation. The method formulates reconstruction as a constrained quadratic optimizationproblem, incorporating both equality and inequality constraints and producing globallyC1smooth curves. The approach is physically interpretable, penalizing excessive bending, as in thecase of a thin elastic beam, and can be extended to higher-dimensional surface reconstruction.Performanceisevaluatedthroughnumericalexperimentsonknownfunctionsandsyntheticdatawith various distributions and constraints, including small perturbation tests to assess stabilityand robustness. The results demonstrate that the proposed method reproduces the data, enforcesthe prescribed bounds, and remains stable under irregular sampling and noise.

Wafer-level thin-film stress measurement is essential for reliable semiconductor fabrication. However, existing techniques present limitations in practice. Interferometry achieves high precision but at a cost that becomes prohibitive for large wafers. Meanwhile laser-scanning systems are more affordable but can only provide sparse data points. This work develops a phase-measuring deflectometry (PMD) system to bridge this gap and deliver a full-field solution for wafer stress mapping. The implementation addresses three key challenges in adapting PMD. First, screen positioning and orientation are refined using an inverse bundle-adjustment approach, which performs multi-parameter optimization without re-optimizing the camera model and simultaneously uses residuals to quantify screen deformation. Second, a backward-propagation ray-tracing framework benchmarks two iterative strategies to resolve the slope-height ambiguity which is a fundamental challenge in PMD caused by the absence of a fixed optical center on the source side. The reprojection constraint strategy is selected for its superior convergence precision. Third, this strategy is integrated with regional wavefront reconstruction based on Hermite interpolation to effectively eliminate edge artifacts. Experimental results demonstrate a peak-to-valley error in the reconstructed topography of 0.48 µm for a spherical mirror with a radius of 500 mm. The practical utility of the system is confirmed through curvature mapping of a 12-inch patterned wafer and further validated by stress measurements on an 8-inch bare wafer, which show less than 5% deviation from industry-standard instrumentation. These results validate the proposed PMD method as an accurate and cost-effective approach for production-scale thin-film stress inspection.

Distributed optimal consensus of nonlinear multi-agent systems under intermittent communication networks.

Accurate generation of gait patterns is essential for advancing robotic gait rehabilitation. This study presents GSAHermNet, a novel two-stage framework that combines a GraphSAGE-based neural network for predicting key gait events with Hermite interpolation to reconstruct full joint trajectories. Unlike conventional methods that generate the entire gait cycle directly, GSAHermNet focuses on predicting key gait events using only seven body and walking parameters, thereby reducing over fitting and enhancing generalizability across diverse walking speeds and conditions. The model was trained on a public dataset of 42 healthy subjects using 5-fold cross-validation on 40 individuals, while the remaining two subjects were reserved for independent testing. Experimental results demonstrate that GSAHermNet achieves mean absolute deviations (MAD) below 4.58° and correlation coefficients (r) of 0.99 for hip and knee joints, and MAD below 3.69° with r = 0.85 for the ankle. Comparative analyses confirm that GSAHermNet outperforms conventional statistical and machine learning approaches in both accuracy and robust ness. The proposed approach has great potential for real word applications, such as adaptive control in functional electrical stimulation systems and personalized motion planning in lower-limb exoskeletons. An online framework for real-time gait trajectory generation will be established using wearable sensor inputs in future.

Uniaxial compressive strength (UCS) is a fundamental indicator of formation hardness, playing a vital role in evaluating geomechanical properties during drilling process. Accurate UCS prediction enables real-time assessment of formation conditions, contributing to improved drilling safety and efficiency. This study proposes a multi-source data fusion approach that integrates vibration data with conventional drilling parameters to enhance UCS prediction accuracy. To address the inconsistency in time scales between the two data sources, a piecewise cubic Hermite interpolation method is applied for temporal alignment. The fused dataset is then used to retrain an extreme learning machine model. Experimental validation is conducted using data collected from a surface drilling test site. Results demonstrate that the proposed method significantly outperforms single-source prediction models, highlighting the effectiveness of vibration-assisted data fusion in real-time UCS estimation.

The wind fields in extreme wind areas have highly nonstationary characteristics, so the accurate simulation of nonstationary wind fields is a fundamental concern in the buffeting analysis of large-span bridges in these areas. Due to the time-varying coherence, classical spectral representation method (SRM) needs for extensive Cholesky decomposition and harmonic superposition. To improve efficiency, interpolation schemes are introduced into the decomposition, and time–frequency decoupling methods are employed to apply the fast Fourier transform. However, the frequency and time interpolation node distribution schemes are complicated and lack adaptive ability. Meanwhile, the traditional two-dimensional (2D) time–frequency interpolation method is less efficient. Therefore, new adaptive frequency and time interpolation-enhanced schemes and an improved 2D Hermite interpolation method are proposed in this study, aimed to improve the accuracy and efficiency of simulating nonstationary wind fields. The frequency interpolation scheme takes the wind spectrum derivative as an index and sets the interpolation node distribution adaptively. In addition, the time interpolation scheme sets time interpolation nodes based on the peak and trough locations in time-varying mean wind speed. Then, the improved 2D Hermite interpolation method is conducted to decrease the Cholesky decomposition and decouple the time–frequency spectrum, and time-domain basis functions in the same frequency-domain region are summed, to further reduce the computational effort of this interpolation method. Finally, the interpolation scheme and the proposed method are validated through parametric analysis and numerical examples to assess their accuracy and efficiency.

ABSTRACT This paper introduces a novel and efficient numerical method for pricing European options. Our approach leverages the characteristic function framework and approximates the risk‐neutral density of the underlying asset price process using a series expansion in cardinal Hermite interpolant multiwavelets. We first detail the construction and key properties of these multiwavelets, including their interpolation capabilities and suitability for function approximation on bounded intervals. A primary challenge in collocation methods is their inherent sensitivity to the selection of collocation points. To address this, we formulate the pricing problem as a rectangular system of linear equations, which is then solved robustly using a least squares technique, thereby enhancing the method's stability and accuracy. We provide a rigorous theoretical analysis of the proposed scheme, establishing its convergence and deriving the associated order of convergence. The analytical findings are strongly supported by extensive numerical experiments. These results not only validate the theoretical convergence rates but also demonstrate the high computational efficiency and accuracy of our method compared to established benchmarks.

Abstract Accurate estimation of individual dry matter intake (DMI) in pastured beef cattle is crucial for grassland management, genetic improvement, and sustainable animal agriculture. Current methods for measuring DMI are labor-intensive, costly, and spatially demanding, with limited options for cattle producers. To address this, we developed a machine learning approach to predict DMI using only body weight, water intake, and open-source climate variables. Pasture data were collected from 2021 to 2023 in Wardensville, WV at the West Virginia University Research, Outreach, and Education Center. Each year, 36 crossbred steers were phenotyped for Residual Feed Intake (RFI) in a drylot, and after a grazing acclimation period, were rotationally grazed through seven 0.05 ha plots. Daily weights and water intake data were collected throughout the experiment using an RFID-equipped front-end scale and metered waterers. Fecal samples were collected to estimate individual DMI using an inert marker. This process was repeated as often as forage growth allowed from May–November, with four grazing tests in 2021, five in 2022, and three in 2023. A pasture training dataset was created from daily bodyweight, water intake, marker-derived intakes, and local climate data. This dataset was combined with a corresponding dataset containing the same features, but with ground truth DMI measured at a Growsafe 800 feed bunk, to train a Gaussian Process Boosting (GPBoost) model—a machine learning approach—for predicting individual DMI. The model was initialized, trained, and optimized in MLflow and Docker. Missing data were handled through a robust imputation strategy, including linear interpolation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), K-Nearest Neighbors (KNN), and forward/backward filling techniques. Data were standardized and outliers were detected using interquartile range (IQR) and Z-score methods. An 80:20 train-test split was used for model validation. Model complexity was controlled by optimizing tree depth, number of leaves, learning rate, and regularization parameters, ensuring balance between generalization and predictive accuracy. The Gaussian process component enabled structured residual modeling, capturing latent dependencies across repeated measures for individual animals. Our GPBoost model trained on both drylot and pasture data was able to predict individual grazing DMI with an RMSE of 1.65 kg and an MAE of 1.2. Our model outperformed the current NASEM equations for pasture intake by 70%, demonstrating that this machine learning approach provides a more efficient and accurate method for predicting individual DMI in pastured beef cattle. This work represents a novel, scalable solution for researchers and producers seeking to estimate individual DMI with greater accuracy, improving both efficiency and sustainability in animal agriculture. Our model can be applied to season-long grazing datasets, allowing access into questions regarding differences in barn and pasture-derived RFIs, grazing efficiency and methane emissions, and lifetime ecological impacts of grazing cattle.

Abstract Phase unwrapping is a fundamental procedure in optical metrology and image processing. The least-squares (LS) method has been widely adopted in phase unwrapping (PU) tasks due to its computational efficiency and mathematical elegance.Since PU-LS issues can be formulated as a two-dimensional integration, modal wavefront (MW) integration techniques have been extensively employed for the numerical solution. Although regional wavefront (RW) integration methods preserve the independence of measurement points through a distinctive geometric structure and offer improved robustness in the presence of incomplete data, they have not yet been applied to PU-LS issues. Therefore, this study introduces a Southwell RW integration approach based on Hermite interpolation and applies it to the PU-LS framework.Compared with existing MW and discrete cosine transform (DCT) methods, the proposed RW approach achieves a reduction of approximately 50% in peak-to-valley (PV) error. It exhibits superior robustness to phase occlusion. Experimental results validate the practical feasibility and effectiveness of the RW-based strategy for PU-LS applications.

LMAPS incorporating Hermite interpolation for solving convection–reaction–diffusion equations

Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods involving only four smooth standard shape functions, which results in a spline function fitting the given value and gradient data value with $\mathcal{C}^1$-coupling along the edges of the triangles. We characterize their invariance properties with relevance for the construction of interpolation surfaces over triangularizations of scanned 3D data. The numerically simplest procedures among them leaving invariant all polynomials of 2-variables with degree 0 (resp. 1) involve only polynomials of 5-th (resp. 6-th) degree, but the characterizations give rise to a huge variety of procedures with non-polynomial shape functions.

Data from earth observation satellites provide unique and valuable information about water quality conditions in freshwater lakes but require significant processing before they can be used, even with the use of tools like Google Earth Engine. We use imagery from Sentinel 2 and MODIS and in situ data from the State of Utah Ambient Water Quality Management System (AQWMS) database to develop models and to generate a highly accessible, easy-to-use CSV file of chlorophyll-a (which is an indicator of algal biomass), turbidity, and water temperature measurements on Utah Lake. From a collection of 937 Sentinel 2 images spanning the period from January 2019 to May 2025, we generated 262,081 estimates each of chlorophyll-a and turbidity, with an additional 1,140,777 data points interpolated from those estimates to provide a dataset with a consistent time step. From a collection of 2333 MODIS images spanning the same time period, we extracted 1,390,800 measurements each of daytime water surface temperature and nighttime water surface temperature and interpolated or imputed an additional 12,058 data points from those estimates. We interpolated the data using piecewise cubic Hermite interpolation polynomials to preserve the original distribution of the data and provide the most accurate estimates of measurements between observations. We demonstrate the processing steps required to extract usable, accurate estimates of these three water quality parameters from satellite imagery and format them for analysis. We include summary statistics and charts for the resulting dataset, which show the usefulness of this data for informing Utah Lake management issues. We include the Jupyter Notebook with the implemented processing steps and the formatted CSV file of data as supplemental materials. The Jupyter Notebook can be used to update the Utah Lake data or can be easily modified to generate similar data for other waterbodies. We provide this method, tool set, and data to make remotely sensed water quality data more accessible to researchers, water managers, and others interested in Utah Lake and to facilitate the use of satellite data for those interested in applying remote sensing techniques to other waterbodies.

Abstract We describe a representation of C 1 piecewise polynomials defined using generalized Hermite elements in two dimensions. This provides a way to generate C 1 piecewise polynomials using nodal variables that are the same at all vertices for degree n ⩾ 5. From this, one obtains both the dimension of the space and an interpolant.

The cislunar space navigation satellite system is essential infrastructure for lunar exploration in the next phase. It relies on high-precision orbit determination to provide the reference of time and space. This paper focuses on constructing a navigation constellation using special orbital locations such as Earth–Moon libration points and distant retrograde orbits (DRO), and it discusses the simplification of planetary perturbation models for their autonomous orbit determination on board. The gravitational perturbations exerted by major solar system bodies on spacecraft are first analyzed. The minimum perturbation required to maintain a precision of 10 m during a 30-day orbit extrapolation is calculated, followed by a simulation analysis. The results indicate that considering only gravitational perturbations from the Moon, Sun, Venus, Saturn, and Jupiter is sufficient to maintain orbital prediction accuracy within 10 m over 30 days. Based on these findings, a method for simplifying the ephemeris is proposed, which employs Hermite interpolation for the positions of the Sun and Moon at fixed time intervals, replacing the traditional Chebyshev polynomial fitting used in the JPL DE ephemeris. Several simplified schemes with varying time intervals and orders are designed. The simulation results of the inter-satellite links show that, with a 6-day orbit arc length, a 1-day lunar interpolation interval, and a 5-day solar interpolation interval, the accuracy loss for cislunar space navigation satellites remains within the meter level, while memory usage is reduced by approximately 60%.

Pupillometry is commonly used to evaluate cognitive effort, attention, and facial expression response, offering valuable insights into human performance. The combination of eye tracking and facial expression data under the iMotions platform provides great opportunities for multimodal research. However, there is a lack of standardized pipelines for managing pupillometry data on a multimodal platform. Preprocessing pupil data in multimodal platforms poses challenges like timestamp misalignment, missing data, and inconsistencies across multiple data sources. To address these challenges, the authors introduced a systematic preprocessing pipeline for pupil diameter measurements collected using iMotions 10 (version 10.1.38911.4) during an endoscopy simulation task. The pipeline involves artifact removal, outlier detection using advanced methods such as the Median Absolute Deviation (MAD) and Moving Average (MA) algorithm filtering, interpolation of missing data using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), and mean pupil diameter calculation through linear regression, as well as normalization of mean pupil diameter and integration of the pupil diameter dataset with facial expression data. By following these steps, the pipeline enhances data quality, reduces noise, and facilitates the seamless integration of pupillometry other multimodal datasets. In conclusion, this pipeline provides a detailed and organized preprocessing method that improves data reliability while preserving important information for further analysis.

We propose the Epsilon Difference Gradient Evolution (EDGE) method for accurate flow-map calculation on grids via Hermite interpolation without using velocity buffers. Our key idea is to integrate Gradient Evolution for accurate first-order derivatives and a tetrahedron-based Epsilon Difference scheme to compute higher-order derivatives with reduced memory consumption. EDGE achieves O (1) memory usage, independent of flow map length, while maintaining vorticity preservation comparable to buffer-based methods. We validate our methods across diverse vortical flow scenarios, demonstrating up to 90% backward map memory reduction and significant computational efficiency, broadening the applicability of flow-map methods to large-scale and complex fluid simulations.

In this paper, we present a rigorous analysis for root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and satisfy certain restrictions on the asymptotic behavior at infinity within this strip. The key ingredients of our analysis are some new and remarkable contour integral representations for the Hermite coefficients and the remainder of Hermite spectral interpolations with which sharp error estimates for Hermite approximations in the weighted and maximum norms are established. Further extensions to Gauss-Hermite quadrature and the scaling factor are also discussed. Particularly, we prove the root-exponential convergence of Gauss–Hermite quadrature under explicit conditions on the integrands. Numerical experiments confirm our theoretical results.

The article presents a new approach to the construction of integrators based on the use of multi-step block methods, aimed at solving hard dynamic problems. The main focus is on integration step adaptation schemes, where the restoration of new values in the support blocks is performed using Hermitian interpolation. The use of interpolants with multiple nodes ensures the preservation of the approximation orders of the restored values, corresponding to the orders of the main computational scheme. Several algorithms for step control are proposed, based on the estimation of local errors at coinciding points within the computational block. Comparison of values at these coinciding points allows for accurate adjustment of the integration step, minimizing error while maintaining the required accuracy. The main theoretical aspects are discussed, including the coordination of approximation orders during step adaptation and the computational advantages of applying the method to hard problems. Results of numerical experiments are presented, demonstrating the effectiveness of the proposed algorithms compared to traditional methods, as well as their applicability to solving hard problems with a high degree of accuracy. Figs.: 18. Tabl.: 2. Refs.: 27 item.