Interpolation Process Research Articles

Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws

ABSTRACTThe fifth‐order alternative finite difference weighted essentially non‐oscillatory (A‐WENO5) scheme is dominated by the truncation error of interpolation, resulting in a loss of one order of accuracy, despite the sixth‐order Taylor expansion of flux terms. In this study, we introduce the central WENO (CWENO) interpolation process in the A‐WENO5 framework to recover the optimal order and design fifth‐ and sixth‐order alternative CWENO schemes for solving the hyperbolic conservation laws. The key point is to enhance the interpolation procedure of the central stencil to realize the optimal sixth‐order accuracy. The linear weights are determined through approximate dispersion relation analysis, which also indicates a significant reduction in numerical dissipation compared with the A‐WENO5 scheme. Combining affine‐invariant WENO operators and Taylor analysis, the new local and global smoothness indicators are designed. The proposed schemes present many benefits, including lower dissipation, optimal order in truncation error, flexibility in choosing linear weights, and fewer CPU timings besides capturing the discontinuous solutions without numerical oscillations in contrast to the classical A‐WENO5 scheme.

Leveraging Attention Mechanisms in Neural Networks for High‐Order Accuracy in Particle‐in‐Cell Simulations

This paper introduces a novel approach to enhance the accuracy of charge density calculations in particle‐in‐cell (PIC) simulations by leveraging attention mechanisms in neural networks (NNs). We propose a three‐network architecture comprising a 1st‐order‐pre‐trainer, a 2nd‐order‐improver, and a discriminator network. The 1st‐order‐pre‐trainer is initially trained on a large dataset to predict charge densities from particle positions and charges. Subsequently, it is fine‐tuned with the 2nd‐order‐improver and discriminator network using a smaller dataset to achieve near 2nd‐order accuracy. Our approach substitutes the traditional particle interpolation process in JefiPIC with a meticulously trained NN. The results demonstrate that PIC simulations enhanced by NNs can simulate plasmas and electromagnetic (EM) fields with significantly enhanced accuracy, achieving an absolute accuracy improvement exceeding 10% when compared to a 1st‐order PIC simulator and a relative accuracy improvement of over 50% in comparison to other direct training techniques. Furthermore, our method has the potential to diminish the reliance on acquiring real labels, which are often difficult to observe. This work highlights the potential of integrating artificial intelligence (AI) techniques to improve the precision and efficiency of PIC simulations, paving the way for future advancements in plasma and nuclear physics research.

An explainable spatial interpolation method considering spatial stratified heterogeneity

Spatial interpolation is essential for handling sparsity and missing spatial data. Current machine learning-based spatial interpolation methods are subject to the statistical constraints of spatial stratified heterogeneity (SSH), normally involving separate modeling of each stratum and simple weighted averaging to integrate intra-stratum and inter-strata features. However, these models overlook the different contributions of inter-strata features to different locations within a stratum (heterogeneous inter-strata associations, HIA) and the explanation of spatial effects on the interpolation process, leading to suboptimal and unreliable interpolation outcomes. This article proposes a novel explainable spatial interpolation method considering SSH (X-SSHM). Spatial and environmental features are utilized to describe intra-stratum and inter-strata information, which are fed into random forest-based learners to achieve high-level semantic feature mapping. Geographically weighted regression is employed to integrate intra-stratum and inter-strata features to achieve a unified expression of SSH and HIA, obtaining the final interpolation result. Geographically weighted Shapley (GSHAP) is proposed to decompose the marginal contributions of intra-stratum and inter-strata features. Model performance is evaluated on simulated and soil organic matter datasets. X-SSHM outperformed five baselines regarding interpolation accuracy. Moreover, statistical methods validated X-SSHM’s ability to elucidate the mechanisms by which SSH, spatial autocorrelation and HIA affect the model interpolation process.

Comparison of Inverse Distance Weighted and Thin Plate Spline Interpolation Methods in Projecting the Strength of the West Sumatra Earthquake

The Indonesian archipelago is situated in a highly active geological zone, making it prone to frequent earthquakes. West Sumatra, located on the west coast of central Sumatra, comprises lowland coastal areas and volcanic plateaus formed by the Barisan Mountains, covering a land area of 42,297.30 km² (2.17% of Indonesia's territory). This research aims to determine which interpolation method—Inverse Distance Weighted (IDW) and Thin Plate Spline (TPS)—provides more accurate predictions of earthquake strength in West Sumatra. The dataset consists of 229 earthquake events, divided into 90% for training (206 points) and 10% for testing (23 points). The training data was further subdivided into 80% training data 2 (164 points) and 20% validation data (42 points). The interpolation processes using the IDW and TPS methods were repeated 100 times, with the training 2 and validation data randomly shuffled in each iteration. Visualization of the interpolation results indicated that the earthquake magnitudes ranged from 2.0 to 4.5. Although the Mean Absolute Percentage Error (MAPE) values for the TPS method on the test and validation datasets were 16.42 and 14.29, respectively—slightly lower than the MAPE values for the IDW method—the t-test results showed no statistically significant difference between the two methods. Statistically, there is no significant difference between IDW and TPS in terms of predictive accuracy. However, researchers prefer the IDW method due to its computational efficiency and simplicity. Therefore, IDW is considered the most suitable method for analyzing earthquake strength in the West Sumatra region

A Boolean sum interpolation for multivariate functions of bounded variation

This paper deals with the approximation error of trigonometric interpolation for multivariate functions of bounded variation in the sense of Hardy-Krause. We propose interpolation operators related to both the tensor product and sparse grids on the multivariate torus. For these interpolation processes, we investigate the corresponding error estimates in the Lp norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches.

Secure smart grid implementation with automatic data integrity attack location prediction and exalted energy theft detection

Smart grid systems use digital communication technology to efficiently monitor and manage electricity distribution. However, there is a need for improve the robustness of smart grid systems. Hence a novel “Secure Smart Grid Implementation with Automatic Data Integrity Attack Location Prediction and Exalted Energy Theft Detection” has been proposed. Current detection methods are not good at identifying data integrity attacks. So a novel Automatic Deterministic Attack Location Prediction Model detects data integrity attacks using a Stacked Watermarking BiGRU-based Deep Deterministic Q network, extracting system matrix and state time series variation. Moreover, Energy theft detection algorithms, which are intended to detect dishonest clients, provide erroneous findings because of linear interpolation processes and randomised near misses, which ignore important data points. Thus a novel Exalted Energy Theft Detector with Secure Encoding is introduced where Amortized Multicode GAN method secures smart grids by detecting energy theft and preventing firmware code modifications, utilising fractional multi-level quantum encoding to identify injection locations. As a result, the proposed model has an accuracy of 97.1%, recall of 96.25%, error rate is 1.36%, F1-score is 96.20%, sensitivity is 96.10%, specificity is 96.10%, MAPE is 0.48%, MSE is 0.0001 and RMSE is 0.017.

Spatial interpolation of global DEM using federated deep learning

The digital elevation model (DEM) provides important data support for 3D terrain modeling. However, due to the complex and changeable terrain in the real world and the high cost of field measurement, it is extremely difficult to obtain continuous and high-density elevation data directly. Therefore, it is necessary to rely on spatial interpolation technology to restore the DEM overall picture in the original sampling area. The traditional spatial interpolation method usually has the characteristics of low model complexity and high computational cost, which leads to low real-time performance and low precision of the interpolation process. The interpolation operation based on DEM data can be considered as a special image generation process where the input is a DEM image with missing values and the output is a complete DEM image. At present, a large number of studies have proved that deep learning methods are very effective in image generation tasks. However, the training of deep learning models requires the support of a large number of high-quality data sets. DEM data in various countries, especially in key regions, are usually restricted by privacy protection regulations and cannot be disclosed. The emergence of Federated Learning (FL) provides a new solution, which supports local training on multiple end nodes, without sending local data to a remote center server for centralized training, effectively protecting data privacy. In this study, we propose a DEM interpolation model based on FL and multiScale U-Net. The experimental results show that compared with the traditional method, this model has faster processing speed and lower interpolation precision. At the same time, this research result provides a new way for efficient and secure use of terrain information, especially in those application scenarios that have strict requirements for DEM data privacy and security.

Neural-Network and Multivariate-Normal-Distribution Hybrid Method for Real-Time Ground-Shaking Reconstruction

ABSTRACT Ground-shaking maps provide a spatial representation of the impact of a seismic event in terms of ground-motion parameters (GMPs), especially useful in the context of seismic monitoring and civil protection operations. Algorithms used to compute these maps usually rely on seismic source parameters to steer the interpolation process and consequently are limited to operate in near-real time. The present work introduces a novel algorithm that combines neural networks with the multivariate normal distribution method to reconstruct ground-shaking maps using only data available in real time, improving on previously proposed algorithms. The core idea of the proposed algorithm is to maintain the structure proposed by ShakeMap while removing the dependence on the source parameters, imposed by the use of ground-motion prediction equations, by replacing them with an appropriate neural network working on the GMPs recorded in real time at the seismic stations. The overall workflow of the method and the details of the neural network architecture and training are described. A model trained on synthetic and recorded data to target seismic events affecting the Italian territory is tested using the 2016 Norcia, Italy, earthquake showing the method reconstruction capabilities, its robustness to noise and to network geometry changes, and its real-time potential.

Study of a Numerical Integral Interpolation Method for Electromagnetic Transient Simulations

In the fixed time-step electromagnetic transient (EMT)-type program, an interpolation process is applied to deal with switching events. The interpolation method frequently reduces the algorithm’s accuracy when dealing with power electronics. In this study, we use the Butcher tableau to analyze the defects of linear interpolation. Then, based on the theories of Runge–Kutta integration, we propose two three-stage diagonally implicit Runge–Kutta (3S-DIRK) algorithms combined with the trapezoidal rule (TR) and backward Euler (BE), respectively, with TR-3S-DIRK and BE2-3S-DIRK for the interpolation and synchronization processes. The proposed numerical integral interpolation scheme has second-order accuracy and does not produce spurious oscillations due to the size change in the time step. The proposed method is compared with the critical damping adjustment method (CDA) and the trapezoidal method, showing that it does not produce spurious numerical oscillations or first-order errors.

STDAN: Deformable Attention Network for Space-Time Video Super-Resolution.

The target of space-time video super-resolution (STVSR) is to increase the spatial-temporal resolution of low-resolution (LR) and low-frame-rate (LFR) videos. Recent approaches based on deep learning have made significant improvements, but most of them only use two adjacent frames, that is, short-term features, to synthesize the missing frame embedding, which cannot fully explore the information flow of consecutive input LR frames. In addition, existing STVSR models hardly exploit the temporal contexts explicitly to assist high-resolution (HR) frame reconstruction. To address these issues, in this article, we propose a deformable attention network called STDAN for STVSR. First, we devise a long short-term feature interpolation (LSTFI) module that is capable of excavating abundant content from more neighboring input frames for the interpolation process through a bidirectional recurrent neural network (RNN) structure. Second, we put forward a spatial-temporal deformable feature aggregation (STDFA) module, in which spatial and temporal contexts in dynamic video frames are adaptively captured and aggregated to enhance SR reconstruction. Experimental results on several datasets demonstrate that our approach outperforms state-of-the-art STVSR methods. The code is available at https://github.com/littlewhitesea/STDAN.

Prediction of personalised postprandial glycaemic response in type 1 diabetes mellitus.

Patients with type 1 diabetes (T1D) face unique challenges in glycaemic control due to the complexity and uniqueness of the dietary structure in China, especially in terms of postprandial glycaemic response (PPGR). This study aimed to establish a personalized model for predicting PPGR in patients with T1D. Data provided by the First People's Hospital of Yunnan Province, 13 patients with T1D, were recruited and provided with an intervention for at least two weeks. All patients were asked to wear a continuous glucose monitoring (CGM) device under free-living conditions during the study period. To tackle the challenge of incomplete data from wearable devices for CGM measurements, the GAIN method was used in this paper to achieve a more rational interpolation process. In this study, patients' PPGRs were calculated, and a LightGBM prediction model was constructed based on a Bayesian hyperparameter optimisation algorithm and a random search algorithm, which integrated glucose measurement, insulin dose, dietary nutrient content, blood measurement and anthropometry as inputs. The experimental outcomes revealed that the PPGR prediction model presented in this paper demonstrated superior accuracy (R=0.63) compared to both the carbohydrate content only model (R=0.14) and the baseline model emulating the standard of care for insulin administration (R=0.43). In addition, the interpretation of the model using the SHAP method showed that blood glucose levels at meals and blood glucose trends 30 minutes before meals were the most important features of the model. The proposed model offers a heightened precision in predicting PPGR in patients with T1D, so it can better guide the diet plan and insulin intake dose of patients with T1D.

A spatial model for the representation of emotional landscapes

AbstractThis article proposes a cartographic solution to represent the emotional landscapes of evasion for a Holocaust survivor, specifically his perceptions of safety or danger during his escape. The victim's emotional landscapes are spatially interpolated using techniques for vectors of both travel direction and magnitude (of perceptions of safety or danger). The implications for the spatial representation of emotions are that emotional landscapes might be better understood by going through an interpolation process, as the statistical analysis reveals spatial trends and autocorrelation. This may help in understanding how the abstract notion of space and the human valence of place vary in relation to each other (or not), and whether and how that variation differs based on distance and direction.

Real-time representation and rendering of high-resolution 3D light field based on texture-enhanced optical flow prediction.

Three-dimensional (3D) light field displays can provide an immersive visual perception and have attracted widespread attention, especially in 3D light field communications, where 3D light field displays can provide face-to-face communication experiences. However, due to limitations in 3D reconstruction and dense views rendering efficiency, generating high-quality 3D light field content in real-time remains a challenge. Traditional 3D light field capturing and reconstruction methods suffer from high reconstruction complexity and low rendering efficiency. Here, a Real-time optical flow representation for the high-resolution light field is proposed. Based on the principle of 3D light field display, we use optical flow to ray trace and multiplex sparse view pixels. We simultaneously synthesize 3D light field images during the real-time interpolation process of views. In addition, we built a complete capturing-display system to verify the effectiveness of our method. The experiments' results show that the proposed method can synthesize 8 K 3D light field videos containing 100 views in real-time. The PSNR of the virtual views is around 32 dB and SSIM is over 0.99, and the rendered frame rate is 32 fps. Qualitative experimental results show that this method can be used for high-resolution 3D light field communication.

Geographic principles applied to population dynamics: A spatially interpolated integrated population model

Abstract A major impediment to wildlife conservation and management, from a quantitative perspective, is dealing with high degrees of uncertainty associated with population estimates. Integrated population models (IPMs) can help alleviate that challenge, but they are often limited to narrow spatial or temporal windows owing to the financial and logistical burdens of acquiring requisite datasets. To expand the spatiotemporal scope of practical IPM implementation, we developed a novel method that expresses demographic relatedness among sampled and unsampled locations using geographic principles of spatial autocorrelation. We interpolated demographic parameters at unsampled locations using parameter estimates from data‐informed locations. Errors attributable to the interpolative process were corrected using a joint likelihood and locally recorded count data (‘cheaper’ and broadly distributed). We evaluated the spatially interpolated IPM (SIIPM) for precision and accuracy under variable levels of spatial autocorrelation using simulated data and a Leave‐One‐Out Cross‐Validation (LOOCV) technique. Conventional IPMs and state‐space models (SSM) were fit to the same simulated datasets to provide a comparative assessment of the novel method. In a final, empirical demonstration we fit the SIIPM to data collected from Greater Sage‐Grouse (Centrocercus urophasianus; sage‐grouse) populations located in Nevada, U.S.A. during 2013–2021. SIIPMs outperformed conventional IPMs when fit to data possessing moderate‐to‐high levels of spatial autocorrelation. Under moderate levels of autocorrelation, the average improvement in parameter estimation was 13.6% for survival, 65.3% for recruitment and 23.7% for rate of population change (). When spatial autocorrelation was low, the SIIPM still outperformed contemporary approaches in areas that were geographically close (<67 km) to sampling locations. Under low autocorrelation‐near distance scenarios, we observed SIIPM parameters that were 30.8% (recruitment), 32.5% (; IPM comparison) and 54.0% (; SSM comparison) more precise than contemporary models. Spatial autocorrelation is often assumed but rarely tested when comparing population dynamics across regions of large geographic extent. We demonstrated that SIIPMs can improve precision of species' vital rate estimation when extrapolating model inference beyond populations for which long‐term monitoring data exists. Specific to sage‐grouse, these results support previous conclusions of broad‐scale spatial autocorrelation in population dynamics and a reproductive‐survival trade‐off previously documented at smaller scales.

Motion-Aware Video Frame Interpolation

Video frame interpolation methodologies endeavor to create novel frames betwixt extant ones, with the intent of augmenting the video’s frame frequency. However, current methods are prone to image blurring and spurious artifacts in challenging scenarios involving occlusions and discontinuous motion. Moreover, they typically rely on optical flow estimation, which adds complexity to modeling and computational costs. To address these issues, we introduce a Motion-Aware Video Frame Interpolation (MA-VFI) network, which directly estimates intermediate optical flow from consecutive frames by introducing a novel hierarchical pyramid module. It not only extracts global semantic relationships and spatial details from input frames with different receptive fields, enabling the model to capture intricate motion patterns, but also effectively reduces the required computational cost and complexity. Subsequently, a cross-scale motion structure is presented to estimate and refine intermediate flow maps by the extracted features. This approach facilitates the interplay between input frame features and flow maps during the frame interpolation process and markedly heightens the precision of the intervening flow delineations. Finally, a discerningly fashioned loss centered around an intermediate flow is meticulously contrived, serving as a deft rudder to skillfully guide the prognostication of said intermediate flow, thereby substantially refining the precision of the intervening flow mappings. Experiments illustrate that MA-VFI surpasses several representative VFI methods across various datasets, and can enhance efficiency while maintaining commendable efficacy.

Enhancing five-axis CNC toolpath smoothing: Overlap elimination with asymmetrical B-splines

In the realm of five-axis Computer Numerical Control (CNC) machining, the challenge of minimizing velocity, acceleration, and jerk fluctuations has prompted the development of various local corner smoothing methods. However, existing techniques often rely on symmetrical spline curves or impose pre-set transition length constraints, limiting their effectiveness in reducing curvature and maintaining velocity at critical corners. To comprehensively address these limitations comprehensively, a novel approach for local smoothing of five-axis linear toolpaths is presented in this paper. The proposed method introduces two asymmetrical B-splines at corners, effectively smoothing both the tool-tip position in the workpiece coordinate system and the tool orientation in the machine coordinate system. To fine-tune transition curve scales and minimize velocity disparities between adjacent corners, an overlap elimination scheme is employed. Furthermore, the two-step strategy emphasizes the synchronization of tool-tip position and tool orientation while considering maximal approximation error. The outcome is a blended five-axis toolpath that significantly reduces curvature extremes in the smoothed path, achieving reductions ranging from 36.28 % to 45.51 %. Additionally, the proposed method streamlines the interpolation process, resulting in time savings ranging from 5.68 % to 8.78 %, all the while adhering to the same geometric and kinematic constraints.

Optimized DM-RS Configuration for Improved 5G New Radio Network Capacity and Performance

Network load in mobile networks is continuously growing, putting pressure on mobile operators to deliver target network performance and user experience. This paper focuses on network capacity improvement through increased spectral efficiency, which can be achieved with overhead reduction by optimizing the demodulation reference signal (DM-RS) configuration, which is one of the channels/reference signals with the largest contribution to overhead. In a high-speed scenario, the Doppler effect noticeably influences the temporal nature of the channel such that a channel interpolation process is required within a slot. However, increasing the number of symbols used for DM-RS has a negative impact on capacity. The Doppler effect was analyzed for various 5G NR configurations of operating frequency and subcarrier spacing (SCS), and various use cases were considered using user equipment (UE) speed as the main parameter. For suitable use cases, the DM-RS configuration was optimized in networks with live traffic. The impact of the configuration change on 5G/NR spectral efficiency, user experience and link adaptation performance was assessed through a deep-dive analysis of active measurements, available performance Management (PM) counters and key performance indicators. An optimized DM-RS configuration is proposed, and it is demonstrated to achieve gains of 5–15%, depending on the metric used, use case analyzed, network load, traffic mix and other relevant network characteristics such as topology and clutter type.

A New Approach to Landscape Visual Quality Assessment from a Fine-Tuning Perspective

Various methods for evaluating the visual quality of landscapes have been continuously studied. In the era of the rapid development of big data, methods to obtain evaluation data efficiently and accurately have received attention. However, few studies have been conducted to optimize the evaluation methods for landscape visual quality. Here, we aim to develop an evaluation model that is model fine-tuned using Scenic Beauty Evaluation (SBE) results. In elucidating the methodology, it is imperative to delve into the intricacies of refining the evaluation process. First, fine-tuning the model can be initiated with a scoring test on a small population, serving as an efficient starting point. Second, determining the optimal hyperparameter settings necessitates establishing intervals within a threshold range tailored to the characteristics of the dataset. Third, from the pool of fine-tuned models, selecting the one exhibiting optimal performance is crucial for accurately predicting the visual quality of the landscape within the study population. Lastly, through the interpolation process, discernible differences in landscape aesthetics within the core monitoring area can be visually distinguished, thereby reinforcing the reliability and practicality of the new method. In order to demonstrate the efficiency and practicality of the new method, we chose the core section of the famous Beijing–Hangzhou Grand Canal in Wujiang District, China, as a case study. The results show the following: (1) Fine-tuning the model can start with a scoring test on a small population. (2) The optimal hyperparameter setting intervals of the model need to be set in a threshold range according to different dataset characteristics. (3) The model with optimal performance is selected among the four fine-tuning models for predicting the visual quality of the landscape in the study population. (4) After the interpolation process, the differences in landscape aesthetics within the core monitoring area can be visually distinguished. We believe that the new method is efficient, accurate, and practically applicable for improving landscape visual quality evaluation.

Three-Stage Interpolation Method for Demosaicking Monochrome Polarization DoFP Images.

The emergence of polarization image sensors presents both opportunities and challenges for real-time full-polarization reconstruction in scene imaging. This paper presents an innovative three-stage interpolation method specifically tailored for monochrome polarization image demosaicking, emphasizing both precision and processing speed. The method introduces a novel linear interpolation model based on polarization channel difference priors in the initial two stages. To enhance results through bidirectional interpolation, a continuous adaptive edge detection method based on variance differences is employed for weighted averaging. In the third stage, a total intensity map, derived from the previous two stages, is integrated into a residual interpolation process, thereby further elevating estimation precision. The proposed method undergoes validation using publicly available advanced datasets, showcasing superior performance in both global parameter evaluations and local visual details when compared with existing state-of-the-art techniques.

A multi-order candidates weighting framework for discontinuity capturing of hyperbolic conservation laws

Weighted compact nonlinear schemes (WCNSs) represent a popular family of high-order methods used for simulating compressible flows. Within these methods, the nonlinear interpolation process is crucial for the scheme's ability to capture shocks. In this study, we introduce a generalized weighting framework that utilizes candidates of varying orders, named multi-order candidates (MOC) weighting, to design nonlinear schemes capable of capturing discontinuities. Analyzing within the MOC framework reveals that the Z nonlinear weights are equivalent to the JS nonlinear weights, supplemented by an additional fifth-order candidate. The convergence accuracy of the MOC weighting is examined, indicating that higher-order candidates in the MOC weighting require smoothness indicators with higher-order leading terms for better accuracy. Based on this convergence analysis, consistently high-order smoothness indicators (CHOSI) are proposed for the MOC weighting, which are essential for achieving the designed high-order accuracy and high resolution. It is found that many existing nonlinear weighting methods can be integrated into the MOC framework. Three of these methods are analyzed and further improved within the MOC framework. Finally, the newly proposed schemes are tested across a range of benchmark problems to showcase their enhanced performance, also illustrating the MOC framework's capability in developing innovative schemes.