Spline Kernel Research Articles

Applied machine learning: Performance prediction of heat pipe with mesh wick

This study presents an investigation of a heat pipe with a mesh wick, utilizing machine learning (ML) techniques. The model including radial basis function interpolation (RBF), Kriging model (KRG), and the k-nearest neighborhood model (K-NN) were studied and compared. A set of training and validating populations were classified using a k-means clustering technique. The design variable included the geometric shape of heat pipe such as its diameter, the properties and percentage used of working fluid, and the temperature at the evaporator. The prediction case study included the heat transfer rate (q), and total difference temperature between evaporator and condenser section (ΔT). The prediction results found that the ΔT gave the most accurate indicator while the q is passable to applied. The Kriging model proved to be the most accurate, achieving an RMSE of 0.9896 and R2 of 0.9149 for heat transfer rate prediction, and an RMSE of 0.1902 and R2 of 0.9398 for total temperature difference prediction with 90 % training data. The second-best accuracy was achieved by the RBF model, with the linear, thin plate, and cubic spline kernels performing reasonably well.

Oracle-efficient estimation and global inferences for variance function of functional data

A new two-step reconstruction-based moment estimator and an asymptotically correct smooth simultaneous confidence band as a global inference tool are proposed for the heteroscedastic variance function of dense functional data. Step one involves spline smoothing for individual trajectory reconstructions and step two employs kernel regression on the individual squared residuals to estimate each trajectory variability. Then by the method of moment an estimator for the variance function of functional data is constructed. The estimation procedure is innovative by synthesizing spline smoothing and kernel regression together, which allows one not only to apply the fast computing speed of spline regression but also to employ the flexible local estimation and the extreme value theory of kernel smoothing. The resulting estimator for the variance function is shown to be oracle-efficient in the sense that it is uniformly as efficient as the ideal estimator when all trajectories were known by “oracle”. As a result, an asymptotically correct simultaneous confidence band for the variance function is established. Simulation results support our asymptotic theory with fast computation. As an illustration, the proposed method is applied to the analyses of two real data sets leading to a number of discoveries.

Parametric analysis of the performance of the SPH solutions of unsteady free-surface flow

ABSTRACT In this article, the performances of the SPH method to solve Shallow Water Equations SWEs with three investigation parameters were studied, such as the type of kernel functions, namely: cubic spline, Gaussian and quintic spline kernels, the number of particles used and the stabilization terms injected, specifically: Lax Friedrichs flux, artificial viscosity and two shocks Riemann solver. Three benchmarking tests make the subject of unsteady free surface flow in this study. It is 1D typical dam-break on wet and dry bottom; 2D partial dam-break on a dry floodplain and 2D partial dam-break on channel with 90° bend. The analysis of the different errors between the numerical and analytical solutions and/or the experimental data shows that the SPH method gives reliable values with the selected optimal parameters which are the cubic kernel function and the artificial viscosity term. The increase in the number of particles increases the precision but also the calculation time.

Associations between maternal exposure to multiple metals and metalloids and blood pressure in preschool children: A mixture-based approach

BackgroundExposure to metals during pregnancy can potentially influence blood pressure (BP) in children, but few studies have examined the mixed effects of prenatal metal exposure on childhood BP. We aimed to assess the individual and combined effects of prenatal metal and metalloid exposure on BP in preschool children. MethodsA total of 217 mother–child pairs were selected from the Zhuang Birth Cohort in Guangxi, China. The maternal plasma concentrations of 20 metals [e.g. lead (Pb), rubidium (Rb), cesium (Cs), and zinc (Zn)] in early pregnancy were measured by inductively coupled plasmamass spectrometry. Childhood BP was measured in August 2021. The effects of prenatal metal exposure on childhood BP were explored by generalized linear models, restricted cubic spline and Bayesian kernel machine regression (BKMR) models. ResultsIn total children, each unit increase in the log10-transformed maternal Rb concentration was associated with a 10.82-mmHg decrease (95% CI: −19.40, −2.24) in childhood diastolic BP (DBP), and each unit increase in the log10-transformed maternal Cs and Zn concentrations was associated with a 9.67-mmHg (95% CI: −16.72, −2.61) and 4.37-mmHg (95% CI: −8.68, −0.062) decrease in childhood pulse pressure (PP), respectively. The log10-transformed Rb and Cs concentrations were linearly related to DBP (P nonlinear=0.603) and PP (P nonlinear=0.962), respectively. Furthermore, an inverse association was observed between the log10-transformed Cs concentration and PP (β =-12.18; 95% CI: −22.82, −1.54) in girls, and between the log10-transformed Rb concentration and DBP (β =-12.54; 95% CI: −23.87, −1.21) in boys, while there was an increasing association between the log10-transformed Pb concentration and DBP there was an increasing in boys (β =6.06; 95% CI: 0.36, 11.77). Additionally, a U-shaped relationship was observed between the log10-transformed Pb concentration and SBP (P nonlinear=0.015) and DBP (P nonlinear=0.041) in boys. Although there was no statistically signiffcant difference, there was an inverse trend in the combined effect of maternal metal mixture exposure on childhood BP among both the total children and girls in BKMR. ConclusionsPrenatal exposure to both individual and mixtures of metals and metalloids influences BP in preschool children, potentially leading to nonlinear and sex-specific effects.

Numerical simulation of coupled Klein–Gordon–Schrödinger equations: RBF partition of unity

The coupled Klein–Gordon–Schrödinger equations have significant implications in quantum field theory, particle physics, cosmology, and nonlinear dynamics. In this study, we propose an efficient method for numerically simulating this system. The proposed approach involves employing the radial basis function partition of unity for spatial discretization. This method utilizes scaled Lagrange basis functions with polyharmonic spline kernels, taking advantage of the scalability property of the polyharmonic kernel to ensure stability in the approximation process. The resulting spatially discretized system yields a nonlinear time-dependent set of differential equations. To solve this system, we combine an implicit central finite difference scheme with a predictor–corrector procedure to overcome the nonlinearity. In the numerical results section, we assess the efficiency, accuracy, and versatility of the proposed method by conducting several simulations in large domains over extended periods. We present and compare these results with those obtained using alternative methods, demonstrating the effectiveness of the proposed approach in accurately solving the coupled Klein–Gordon–Schrödinger equations.

Association between polycyclic aromatic hydrocarbon exposure and cognitive performance in older adults: a cross-sectional study from NHANES 2011-2014.

Background: polycyclic aromatic hydrocarbons (PAHs) are classified as neurotoxins, but the relationship between exposure to PAHs and cognition in adults is unclear, and their non-linear and mixed exposure association hasn't been explored. Objective: to evaluate the non-linear and joint association between co-exposure to PAHs and multiple cognitive tests in U.S. older people. Methods: restricted cubic spline (RCS) and Bayesian kernel machine regression (BKMR) were conducted to evaluate the non-linear and mixed exposure association, based on the cross-sectional data from NHANES 2011-2014: 772 participants over 60 years old, 4 cognitive test scores, including the Immediate Recall Test (IRT), Delayed Recall Test (DRT), Animal Fluency Test (AFT), and Digit Symbol Substitution test (DSST), and 5 urinary PAH metabolites. Results: a V-shaped nonlinear relationship was found between 3-hydroxyfluorene (3-FLUO), 2-hydroxyfluorene (2-FLUO), and DRT. Negative trends between mixed PAH exposure and IRT, DRT, and DSST scores were observed. 2-FLUO contributed the most to the negative association of multiple PAHs with IRT and DRT scores and 2-hydroxynaphthalene (2-NAP) played the most important role in the decreasing relationship between mixed PAH exposure and DSST scores. Conclusion: our study suggested that PAH exposure in the U.S. elderly might be related to their poor performances in IRT, DRT and DSST. Further prospective studies are needed to validate the association.

Exploration of Kernel Parameters in Signal GBF-PUM Approximation on Graphs

Abstract The application of the Partition of Unity Method (PUM) to signal approximation on graphs represents a recent advancement of this versatile and efficient interpolation technique. Given the novelty of this approach, little is yet known regarding the role of kernel parameters employed in constructing the associated Graph Basis Functions (GBFs). In order to shed light on this aspect, this study proposes several numerical tests obtained using GBFs generated by heat kernels and variational spline kernels.

Nataf-KernelDensity-Spline-based point estimate method for handling wind power correlation in probabilistic load flow

Modern power systems integrated with renewable energies (REs) contain many uncertainties. The proposed method introduces a novel approach to address the challenges associated with wind power generation uncertainty in probabilistic load flow (PLF) studies. Unlike conventional methods that use wind speed as an input, the paper advocates for utilizing wind generator output power (WGOP) as an input to the point estimate method (PEM) in solving PLF. The uniqueness lies in recognizing the distinct behavior of wind power uncertainty, where not all random samples of wind speed contribute to actual wind power production. The paper suggests a Nataf-KernelDensity-Spline-based PEM, combining the Nataf transformation, Kernel density estimation (KDE), and cubic spline interpolation. This innovative integration effectively manages wind power correlation within the analytical framework. By incorporating spline interpolation and kernel density estimation into the traditional PEM, the proposed method significantly enhances accuracy. To validate the effectiveness of the proposed approach, the method is applied to IEEE-9 and IEEE-57 bus test systems, considering uncertainties related to load, wind power generation (WPG), solar power generation (SPG), and conventional generator (CoG) outages. Comparative analysis with Monte Carlo simulation (MCS) results demonstrates that the proposed method outperforms the conventional PEM in terms of accuracy. Overall, the paper contributes a pioneering solution that not only highlights the importance of using WGOP as an input in PLF but also introduces a sophisticated method that surpasses traditional approaches, improving accuracy in power system studies involving renewable energy integration. The accuracy of the proposed method is validated by comparing its results with those obtained through Monte Carlo simulation (MCS), where the proposed method yields more accurate results than the conventional PEM.

MIXED ESTIMATORS OF TRUNCATED SPLINE-EPANECHNIKOV KERNEL ON NONPARAMETRIC REGRESSION AND ITS APPLICATIONS

Research on innovations in the statistics and statistical computing program systems implemented in the health sector. The development of a mixed estimator model is an innovation of nonparametric regression analysis by combining two approaches in nonparametric regression, namely the truncated spline estimator and the Epanechnikov kernel. The urgency of this study is that there are often cases where there are different data patterns from each predictor variable. In addition, by using only one form of the estimator in estimating a multivariable regression curve, the result is that the estimator obtained will not match the data pattern. The research objective was to find a mixed estimator between the truncated spline and the Epanechnikov kernel and the estimator results were applied to Dengue Hemorrhagic Fever case data. The unit of observation is a province in Indonesia and This study relied on secondary data received from the Central Statistical Agency (BPS) and the Health Office. Based on the analysis results, it was found that the best model of nonparametric regression with a mixed estimator of the truncated spline and Epanechnikov Kernel is a model with 3 knots with a combination of variables. The coefficient of determination (R2) is 98.11%. We can conclude that the mixed estimator tends to follow actual data and represents a nonparametric regression model with a mixed estimator that can predict the number of Dengue Hemorrhagic Fever Cases in Indonesia

Prediction of seawater salinity based on comparison of truncated spline estimators, Fourier Series and Kernel

Salinity is one of the factors that affect salt production. Salinity is defined as the level of saltiness or too much salt in water. The salt in question is a variety of ions dissolved in water, including table salt (NaCl). The higher the level of NaCl contained, the better the quality of the salt formed. This low quality causes Indonesia to import salt, both consumption salt and industrial salt. Because most of the quality of salt still does not meet the criteria of SNI. For this reason, it is necessary to predict the salinity of seawater to help determine the next steps or policies in improving the quality of salt in Indonesia, especially in the Madura area. This research is examined in the form of a nonparametric regression curve estimator with a truncated spline estimator approach, Fourier series and kernel. From the comparison results, the best model for predicting seawater salinity is the estimator of the Fourier series base sine cosine with an oscillation parameter (k) of 2 with a GCV value of 5.017987 and MSE and a coefficient of determination of 0.06299933 and 94.64373%. So the prediction results obtained in this study are close to accurate with MAPE values of 0.07225208%, MSE of 0.0001441417 and coefficient of determination of 99.99%.

Assessment of radial basis function method with thin plate spline kernel for evaluable precipitable water vapor interpolation from GPS observations over state of California, USA

Assessment of radial basis function method with thin plate spline kernel for evaluable precipitable water vapor interpolation from GPS observations over state of California, USA

The association between multi-heavy metals exposure and lung function in a typical rural population of Northwest China

Heavy metal exposure is acknowledged to be associated with decrease oflung function, but the relationship between metals co-exposure and lung function in rural areas of Northwest China remains unclear, particularly in an area famous for heavy metal pollution and solid fuel use. Therefore, the purpose of this study is to explore the effects of heavy metal exposure on lung function and the potential impacts of living habit in a rural cohort of Northwest China. The study area included five villages of two regions in Northwestern China-Gansu province. All participants were recruited from the Dongdagou-Xinglong (DDG-XL) rural cohort in the study area. Urine levels of 10 common and representative heavy metals were detected by ICP-MS, including Cobalt (Co), Nickel (Ni), Molybdenum (Mo), Cadmium (Cd), Stibium (Sb), Copper (Cu), Zinc (Zn), Mercury (Hg), Lead (Pb), and Manganese (Mn). The lung function was detected by measuring percentages of predicted forced vital capacity (FVC%) and predictedforced expiratory volume in one second (FEV1%) as well as the ratio of FEV1/FVC. We also analyzed the association between heavy metals and pulmonary ventilation dysfunction (PVD). Restricted cubic spline, logistic regression, linear regression, and bayesian kernel machine regression (BKMR) model were used to analyze the relationship between heavy metal exposure and lung function. Finally, a total of 382 participants were included in this study with an average age of 56.69 ± 7.32years, and 82.46% of them used solid fuels for heating and cooking. Single metal exposure analysis showed that the higher concentration of Hg, Mn, Sb, and lower Mo may be risk factors for PVD. We also found that FEV1% and FVC% were negatively correlated with Sb, Hg, and Mn, but positively correlated with Mo. The effect of mixed heavy metals exposure could be observed through BKMR model, through which we found the lung function decreased with the increase of heavy metal concentration. Furthermore, the males, BMI ≥ 24kg/m2 and who used solid fuels showed a higher risk of PVD when exposed to Co, Zn, and Hg. Our results suggested that heavy metal exposure was associated with decrease of lung function regardless of single exposure or mixed exposure, particularly for Sb, Hg, Mn and those who use solid fuels.

Spline and kernel mixed estimators in multivariable nonparametric regression for dengue hemorrhagic fever model

This article discusses statistical innovations implemented in the health sector. The research is being conducted on the treatment and prevention of Dengue Hemorrhagic Fever (DHF), focusing on the factors contributing to the increase in DHF. Create a nonparametric regression model with a mixed estimator, truncated spline, and Gaussian Kernel to estimate the regression curve. In multiple nonparametric regression, this method can handle differences in data patterns between predictors. Truncated splines are polynomial segments with segmented and continuous properties. Truncated splines contain knot points that can locate their estimated data no matter where the data pattern moves. In addition, the Gaussian Kernel estimator is dependent on bandwidth, which regulates the regression curve's smoothness. The mixed estimators of truncated spline and Gaussian Kernel could model DHF cases according to an empirical analysis of DHF data. The most effective model has a Coefficient of Determination (R2) of 88.46%. Simultaneous hypothesis testing indicates that the model contains at least one significant predictor variable.

A compact radial basis function partition of unity method

In this work we develop the standard Hermite interpolation based RBF-generated finite difference (RBF-HFD) method into a new faster and more accurate technique based on partition of unity (PU) method. In the new approach, much fewer number of local linear systems needs to be solved for calculating the stencil weights. This reduces the computational cost of the method, remarkably. In addition, the method is flexible in using different types of PU weight functions, smooth or discontinuous, each results in a different scheme with additional nice properties. We also investigate the scaling property of polyharmonic spline (PHS) kernels to develop a simple and stable algorithm for computing local approximants in PU patches. Experimental results confirm the efficiency and applicability of the proposed method.

Predictions of Geological Interface Using Relevant Vector Machine with Borehole Data

Due to the discreteness, sparsity, multidimensionality, and incompleteness of geotechnical investigation data, traditional methods cannot reasonably predict complex stratigraphic profiles, thus hindering the three-dimensional (3D) reconstruction of geological formation that is vital to the visualization and digitization of geotechnical engineering. The machine learning method of relevant vector machine (RVM) is employed in this work to predict the 3D stratigraphic profile based on limited geotechnical borehole data. The hyper-parameters of kernel functions are determined by maximizing the marginal likelihood using the particle swarm optimization algorithm. Three kinds of kernel functions are employed to investigate the prediction performance of the proposed method in both 2D analysis and 3D analysis. The 2D analysis shows that the Gauss kernel function is more suitable to deal with nonlinear problems but is more sensitive to the number of training data and it is better to use spline kernel functions for RVM model trainings when there are few geotechnical investigation data. In the 3D analysis, it is found that the prediction result of the spline kernel function is the best and the relevant vector machine model with a spline kernel function performs better in the area with a fast change in geological formation. In general, the RVM model can be used to achieve the purpose of 3D stratigraphic reconstruction.

ESTIMATION OF SEMIPARAMETRIC REGRESSION CURVE WITH MIXED ESTIMATOR OF MULTIVARIABLE LINEAR TRUNCATED SPLINE AND MULTIVARIABLE KERNEL

The response variable of the regression analysis has a linear relationship with one of the variable predictors, however the unknown relationship pattern with the other predictor variables. Consequently, it can be approached by using semiparametric regression model. The predictor variable that has a linear relationship with the response variable can be approached by using linear parametric curve called parametric component. Meanwhile, the unknown relationship between the response variable with another predictor variable can be approached by using nonparametric curve called nonparametric component. If the predictor variable in nonparametric component is more than one, then it can be approached by using a different nonparametric curve named combined or mixed estimator. In this research, nonparametric component is approached using mixed estimator of multivariable linear truncated spline and multivariable kernel. The objective of this research is to estimate the model of semiparametric regression curve with mixed estimator of multivariable truncated spline and multivariable kernel. Estimation of this mixed model using ordinary least square method.

A fully explicit incompressible Smoothed Particle Hydrodynamics method for multiphase flow problems

Multiphase flow is a challenging area of computational fluid dynamics (CFD) due to their potential large topological change and close coupling between the interface and fluid flow solvers. As such, Lagrangian meshless methods are very well suited for solving such problems. In this paper, we present a new fully explicit incompressible Smoothed Particle Hydrodynamics approach (EISPH) for solving multiphase flow problems. Assuming that the change in pressure between consecutive time-steps is small, due to small time steps in explicit solvers, an approximation of the pressure for following time-steps is derived. To verify the proposed method, several test cases including both single-phase and multi-phase flows are solved and compared with either analytical solutions or available literature. Additionally, we introduce a novel kernel function, which improves accuracy and stability of the solutions, and the comparison with a well-established quintic spline kernel function is discussed. For the presented benchmark problems, results show very good agreements in velocity and pressure fields and the interface-capturing with those in the literature. To the best knowledge of the authors, the EISPH method is presented for the first time for multiphase flow simulations.

Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts. We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains. We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster.

Linear system identification using the sequential stabilizing spline algorithm

Paradoxically, even if stability (with its many facets) is the key concept in control, including system stability constraints in an identification procedure is still an unresolved puzzle under many aspects. In fact, also in the linear setting there is no procedure proposed in the literature able to estimate the dominant pole of a dynamic system ensuring stability. In this paper, we design a new algorithm, namely the sequential stabilizing spline (SSS) algorithm, which fills this gap. Our approach determines the system’s stability radius by combining Gaussian regression and stochastic simulation, using stable spline kernels to model the one-step ahead predictor impulse responses. Then, a stable model is recovered through a novel sequential convex optimization procedure whose computational time is orders of magnitude faster than approaches based on linear matrix inequalities (LMI). Numerical experiments are included and show that SSS can return models with high long-term predictive capability. SSS performance is comparable to that achieved by classical prediction error methods equipped with an oracle that has access to the test set to tune the best model order for any prediction horizon.

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

<p class='IJASEITAbtract'>Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R²) value and better accuracy for each combination of sample sizes and variance variations.