Interpolation Scheme Research Articles

A 4 km daily gridded meteorological dataset for China from 2000 to 2020.

Multi-variate gridded meteorological data with high spatial resolution play a key role in studies related to climate change. This study constructed a 4 km daily gridded meteorological dataset for mainland of China (China Daily Meteorological Dataset; CDMet) from 2000 to 2020. The dataset includes nine meteorological variables: 2-meter air temperature (maximum, minimum, and mean temperatures), total precipitation, skin temperature, 10-meter wind speed, relative humidity, surface pressure, and sunshine duration. CDMet was generated using an adaptive interpolation scheme, which employed thin-plate spline and random forest methods to construct the interpolation model. Six combinations of location and terrain information were designed and used as covariates in the model together with reanalysis data. Validation with independent observation stations and existing datasets showed that CDMet has acceptable accuracy, reasonable seasonal variability, and precise spatial distribution, and its accuracy is comparable to that of other datasets. Due to its comprehensive variables and high resolution, CDMet can be used as input data for hydrological, agricultural, and ecological models.

Airborne Multi-Channel Forward-Looking Radar Super-Resolution Imaging Using Improved Fast Iterative Interpolated Beamforming Algorithm

Radar forward-looking imaging is critical in many civil and military fields, such as aircraft landing, autonomous driving, and geological exploration. Although the super-resolution forward-looking imaging algorithm based on spectral estimation has the potential to discriminate multiple targets within the same beam, the estimation of the angle and magnitude of the targets are not accurate due to the influence of sidelobe leakage. This paper proposes a multi-channel super-resolution forward-looking imaging algorithm based on the improved Fast Iterative Interpolated Beamforming (FIIB) algorithm to solve the problem. First, the number of targets and the coarse estimates of angle and magnitude are obtained from the iterative adaptive approach (IAA). Then, the accurate estimates of angle and magnitude are achieved by the strategy of iterative interpolation and leakage subtraction in FIIB. Finally, a high-resolution forward-looking image is obtained through non-coherent accumulation. The simulation results of point targets and scenes show that the proposed algorithm can distinguish multiple targets in the same beam, effectively improve the azimuthal resolution of forward-looking imaging, and attain the accurate reconstruction of point targets and the contour reconstruction of extended targets.

Optimized Soil Moisture Mapping Strategies on the Tibetan Plateau Using Downscaled and Interpolated Maps as Mutual Covariates

Accurate high-resolution soil moisture maps are crucial for a better understanding of hydrological processes and energy cycles. Mapping strategies such as downscaling and interpolation have been developed to obtain high-resolution soil moisture maps from multi-source inputs. However, research on the optimization performance of integrating downscaling and interpolation, especially through the use of mutual covariates, remains unclear. In this study, we compared four methods—two standalone methods based on downscaling and interpolation strategies and two combined methods that utilize soil moisture maps as mutual covariates within each strategy—in a case study of daily soil moisture mapping at a 1 km resolution in the Tibetan Plateau. We assessed mapping performance in terms of prediction accuracy and differences in spatial coverage. The results indicated that introducing interpolated soil moisture maps into the downscaling strategy significantly improved prediction accuracy (RMSE: −5.94%, correlation coefficient: +14.02%) but was limited to localized spatial coverage (6.9% of grid cells) near in situ sites. Conversely, integrating downscaled soil moisture maps into the interpolation strategy resulted in only modest gains in prediction accuracy (RMSE: −1.07%, correlation coefficient: +1.04%), yet facilitated broader spatial coverage (40.4% of grid cells). This study highlights the critical differences between downscaling and interpolation strategies in terms of accuracy improvement and spatial coverage, providing a reference for optimizing soil moisture mapping over large areas.

A fractional-order improved FitzHugh-Nagumo neuron model

Abstract In this paper, we propose a fractional-order improved FitzHugh-Nagumo (FHN) neuron model in terms of a generalised Caputo fractional derivative. Following the existence of a unique solution for the proposed model, we derive the numerical solution using a recently proposed L1 predictor-corrector method. The given method is based on the L1-type discretization algorithm and the spline interpolation scheme. We perform the error and stability analyses for the given method. We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns, chaotic patterns, and quasi-periodic patterns. The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics, which are inherent to many biological systems.

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory.

The finite-volume theory has shown to be numerically efficient and stable for topology optimization of continuum elastic structures. The significant features of this numerical technique are the local satisfaction of equilibrium equations and the employment of compatibility conditions along edges in a surface-averaged sense. These are essential properties to adequately mitigate some numerical instabilities in the gradient version of topology optimization algorithms, such as checkerboard, mesh dependence, and local minima issues. Several computational tools have been proposed for topology optimization employing analysis domains discretized with essential features for finite-element approaches. However, this is the first contribution to offer a platform to generate optimized topologies by employing a Matlab code based on the finite-volume theory for compliance minimization problems. The Top2DFVT provides a platform to perform 2D topology optimization of structures in Matlab, from domain initialization for structured meshes to data post-processing. This contribution represents a significant advancement over earlier publications on topology optimization based on the finite-volume theory, which needed more efficient computational tools. Moreover, the Top2DFVT algorithm incorporates SIMP and RAMP material interpolation schemes alongside sensitivity and density filtering techniques, culminating in a notably enhanced optimization tool. The application of this algorithm to various illustrative cases confirms its efficacy and underscores its potential for advancing the field of structural optimization.

Effect of Interpolation Artifacts on Perceived Stability of Nearby Sources in a Navigable Reverberant Virtual Environment

Convolution with spatial Room Impulse Responses can achieve realistic auralizations. When combined with interpolation between spatially distributed RIRs, this technique can be used to create navigable virtual environments. This study explores the impact of various interpolation parameters on the perceived auditory stability of a nearby static sound source with listener movements in a reverberant environment. The auditory scene was rendered via third-order Ambisonic RIR convolution combined with magnitude-least-squares binaural decoding using nonindividualized head-related transfer functions. First, the estimated direction of arrival as a function of the listener’s position within a 2D grid of RIRs under various configurations is examined as an objective metric. The perceived stability of the auditory source is then assessed through a perceptual experiment. Participants freely explored a virtual scene reproduced over headphones and a tracked head-mounted display. They were asked to rate the stability of a nonvisual source under various conditions of RIR grid density, interpolation panning method, and reverberation time. Results indicate no need to use an RIR grid size finer than 1m to optimize source stability when using a three-nearest-neighbor interpolation scheme.

Comparisons of experimentally and numerically determined statistics for predicting low-occurrence wind speeds around a 1:1:2 block model

Accurate prediction of low-occurrence wind speeds around urban structures is crucial for safe building design. Although Large-eddy simulation (LES) is commonly used as a high-fidelity model as compared with the Reynolds-Averaged Navier–Stokes (RANS) simulations, the present validation process relies on the comparison of fundamental statistics of the mean and standard deviations. The discrepancies in LESs and wind-tunnel experiments (WTEs) are unclear in terms of physical quantities characterizing the unsteadiness of the simulated turbulent flow such as probability density and power spectral densities, and low-occurrence winds speeds. Therefore, this study aims to evaluate the effectiveness of LES in predicting unsteady wind behavior around a 1:1:2 block model. The study identifies prominent differences to improve the accuracy of unsteady numerical simulations especially for the purpose of predicting low-occurrence wind speeds. Various advection schemes in LESs were investigated, including first-order upwind, second-order linear, and dynamic interpolation schemes. The results show significant discrepancies, particularly in higher-order statistics and low-occurrence wind speeds, with WTE consistently exhibiting higher energy levels across all frequencies. These findings highlight the need to refine advection schemes to enhance their predictive accuracy. LESs with minimal numerical errors from discretization schemes can substantially improve urban wind assessments and contribute to the design of safer structures.

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

Reconstruction of directional sources using physics-informed neural networks

In the context of augmented/virtual reality applications, replicating the directivity of sound sources is a critical step to ensure a high-quality immersive experience. However, accurate directivity measurements require complex experimental procedures involving a high number of microphones. In these scenarios, spatial interpolation allows to reconstruct the sound field with fewer sensors, which can be sparsely distributed around the source. The literature offers several interpolation schemes for sound field reconstruction, although they exhibit limited accuracy due to the lack of knowledge on the underlying physics. Recently, Physics-Informed Neural Networks (PINN) have been used to directly solve partial differential equations and thus better predict the evolution of dynamical systems. In this manuscript, we propose a spatial interpolation scheme based on PINN for the reconstruction of sound source directivity. PINN are used to solve the Helmholtz equation starting from acquisitions of the directivity over a limited set of sparsely distributed points. Results are compared with the outcomes of well-established methods based on Spherical Harmonics Decomposition (SH), Thin Plate Pseudo-Splines Interpolation (SPLI) and Piece-wise Linear Spherical Triangular Interpolation (TRI). PINN prove to provide better reconstruction of the directivity with respect to the proposed comparison methods, even when dealing with highly sparse sampling grids.

BundleMoCap++: Efficient, robust and smooth motion capture from sparse multiview videos

Producing smooth and accurate motions from sparse videos without requiring specialized equipment and markers is a long-standing problem in the research community. Most approaches typically involve complex processes such as temporal constraints, multiple stages combining data-driven regression and optimization techniques, and bundle solving over temporal windows. These increase the computational burden and introduce the challenge of hyperparameter tuning for the different objective terms. In contrast, BundleMoCap++ offers a simple yet effective approach to this problem. It solves the motion in a single stage, eliminating the need for temporal smoothness objectives while still delivering smooth motions without compromising accuracy. BundleMoCap++ outperforms the state-of-the-art without increasing complexity. Our approach is based on manifold interpolation between latent keyframes. By relying on a local manifold smoothness assumption and appropriate interpolation schemes, we efficiently solve a bundle of frames using two or more latent codes. Additionally, the method is implemented as a sliding window optimization and requires only the first frame to be properly initialized, reducing the overall computational burden. BundleMoCap++’s strength lies in achieving high-quality motion capture results with fewer computational resources. To do this efficiently, we propose a novel human pose prior that focuses on the geometric aspect of the latent space, modeling it as a hypersphere, allowing for the introduction of sophisticated interpolation techniques. We also propose an algorithm for optimizing the latent variables directly on the learned manifold, improving convergence and performance. Finally, we introduce high-order interpolation techniques adapted for the hypersphere, allowing us to increase the solving temporal window, enhancing performance and efficiency.

Structural and Dynamical Quality Assessment of Gap‐Filled Sea Surface Temperature Products

AbstractPrevious studies that intercompared global Level‐4 (L4) sea surface temperature (SST) analyses were centered on the assessment of the accuracy and bias of SST by comparing them with independent near‐surface Argo profile temperature data. This type of assessment is centered on the absolute value of SST rather than on SST spatial properties (gradients), which is more relevant to the study of oceanographic features (e.g., fronts, eddies, etc.) and ocean dynamics. Here, we use, for the first time, the spectrum of singularity exponents to assess the structural and dynamical quality of different L4 gap‐filled products based on the multifractal theory of turbulence. Singularity exponents represent the geometrical projection of the turbulence cascade, and its singular spectrum can be related to the probability density function of the singularity exponents normalized by the scale. Our results reveal that the different schemes used to produce the L4 SST products generate different singularity spectra, which are then used to identify a potential loss of dynamical information or structural coherence. This new diagnostic constitutes a valuable tool to assess the structural quality of SST products and can support data satellite SST producers efforts to improve the interpolation schemes used to generate gap‐filled SST products.

Meshless Error Recovery Parametric Investigation in Incompressible Elastic Finite Element Analysis

The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and global), convergence rates, and adaptive mesh improvement for triangular/quadrilateral discretization schemes. It uses meshless moving least squares (MLS) interpolation with rectangular and circular support regions and solves benchmark plate and cylinder problems. It is observed that a circular influence region, a cubic spline weight function, and regular mesh patterns yield a better performance of than an MLS-based error recovery method. The study also concludes that lower dilation index values with rectangular influence regions are preferable for regular meshes, while higher dilation index values with radial influence regions are suitable for preferable meshes to enhance MLS error recovery.

Stress-constrained concurrent multiscale topological design of porous composites based on discrete material optimisation

Porous composites have attracted increasing attention in recent decades. This study develops a concurrent multiscale topology optimisation (CMTO) method under a prescribed stress constraint for designing porous composites with multi-domain microstructures. First, to address the difficulty of predicting local stress due to varying of microstructural type throughout the optimisation process, a continuous and differentiable stress measure is proposed to effectively approximate the local stress. Second, an inverse homogenisation method based on isogeometric analysis (IGA) is developed to improve the accuracy of stress prediction, and then it is integrated into a CMTO which is developed based on the discrete material optimisation (DMO) interpolation scheme. Third, a stress constraint which is differentiable with respect to both macro and micro design variables is proposed to enable the stress-constrained concurrent optimisation of the macrostructural configuration, microstructural configuration and distribution. Fourth, a novel post-processing approach is established to achieve smooth while volume preserving contour of unit cells with layouts. Finally, two benchmark design examples, namely l-bracket and Crack problems, are implemented using the presented CMTO under a global stress constraint to demonstrate the effectiveness of the proposed method. The result indicates that the proposed method can effectively decrease the stress concentration via three design manners, i.e., the macrostructural configuration, microstructural configuration and distribution. Also, an “interface-enlarging” phenomenon was interestingly but reasonably found in those cases when subjected to stress-constraint considerations.

Cubic q-Bézier Triangular Patch for Scattered Data Interpolation and Its Algorithm

This paper presents an approach to scattered data interpolation using q-Bézier triangular patches via an efficient algorithm. While existing studies have formed q-Bézier triangular patches through convex combination, their application to scattered data interpolation has not been previously explored. Therefore, this study aims to extend the use of q-Bézier triangular patches to scattered data interpolation by achieving C1 continuity throughout the data points. We test the proposed scheme using both established data points and real-life engineering problems. We compared the performance of the proposed interpolation scheme with a well-known existing scheme by varying the q parameter. The comparison was based on visualization and error analysis. Numerical and graphical results were generated using MATLAB. The findings indicate that the proposed scheme outperforms the existing scheme, demonstrating a higher coefficient of determination (R2), smaller root mean square error (RMSE), and faster central processing unit (CPU) time. These results highlight the potential of the proposed q-Bézier triangular patches scheme for more accurate and reliable scattered data interpolation via the proposed algorithm.

Three-Dimensional Probe Mispositioning Errors Compensation: A Feasibility Study in the Non-Redundant Helicoidal Near to Far-Field Transformation Case

A feasibility study on the compensation of 3D mispositioning errors of the probe occurring in the characterization of a long antenna, via a non-redundant (NR) near to far-field (NTFF) transformation with helicoidal scan, is conducted in this article. Such types of errors can result from imperfections in the rail driving the linear motion of the probe and from an imprecise synchronization of the linear and rotational movements of the probe and the antenna when drawing the scan helix. To correct them, an approach, which proceeds through two steps, is proposed. The former step uses a technique called cylindo rical wave (CW) correction for compensating the phase of the near-field (NF) samples, which, owing to the rail imperfections, result in not being acquired over the measurement cylinder surface. The latter exploits an iterative scheme to restore the samples at the sampling points required by the adopted NR representation along the scan helix from those obtained by applying the CW correction technique and impaired by 2D mispositioning errors. The so compensated NF samples are then effectively recovered via a 2D optimal sampling interpolation (OSI) scheme to accurately obtain the input data required to carry out the standard cylindrical NTFF transformation. The OSI representation is determined here by assuming a long antenna under test as enclosed in a prolate ellipsoid or cylinder ending into two hemispheres (cigar) in order to make, depending on the particular geometry of the considered antenna, the representation effectively non-redundant. The reported numerical simulation results show the capability of the proposed approach to compensate even severe 3D mispositioning errors, thus enabling its usage in a real measurement scenario.

AHKASH: a new Hybrid particle-in-cell code for simulations of astrophysical collisionless plasma.

We introduce Astrophysical Hybrid-Kinetic simulations with the flash code ([Formula: see text]) - a new Hybrid particle-in-cell (PIC) code developed within the framework of the multiphysics code flash. The new code uses a second-order accurate Boris integrator and a predictor-predictor-corrector algorithm for advancing the Hybrid-kinetic equations, using the constraint transport method to ensure that magnetic fields are divergence-free. The code supports various interpolation schemes between the particles and grid cells, with post-interpolation smoothing to reduce finite particle noise. We further implement a [Formula: see text] method to study instabilities in weakly collisional plasmas. The new code is tested on standard physical problems such as the motion of charged particles in uniform and spatially varying magnetic fields, the propagation of Alfvén and whistler waves, and Landau damping of ion acoustic waves. We test different interpolation kernels and demonstrate the necessity of performing post-interpolation smoothing. We couple the turbgen turbulence driving module to the new Hybrid PIC code, allowing us to test the code on the highly complex physical problem of the turbulent dynamo. To investigate steady-state turbulence with a fixed sonic Mach number, it is important to maintain isothermal plasma conditions. Therefore, we introduce a novel cooling method for Hybrid PIC codes and provide tests and calibrations of this method to keep the plasma isothermal. We describe and test the 'hybrid precision' method, which significantly reduces (by a factor [Formula: see text]) the computational cost, without compromising the accuracy of the numerical solutions. Finally, we test the parallel scalability of the new code, showing excellent scaling up to 10,000 cores.

A robust compact finite difference framework for simulations of compressible turbulent flows

A robust high-order compact finite difference framework is proposed for simulations of compressible turbulent flows with high spectral resolution using a fully collocated variable storage paradigm. Both inviscid and viscous fluxes are assembled at the edge-staggered grid locations. Nonlinear robustness is attained as a consequence of the intrinsic reduction of aliasing errors in the inviscid fluxes due to the spectral behavior of the compact interpolation schemes. Additional robustness is provided by enhancing the spectral resolution of the viscous flux and its divergence at small scales using purely staggered numerical differentiation. Demonstrative simulations have shown numerical stability of the compact finite difference discretization without any type of solution filtering on both Cartesian and curvilinear meshes. For simulations on a curvilinear mesh, a general metric evaluation approach that satisfies the geometric conservation law is proposed. Additional approaches to combining the proposed scheme with approximate Riemann solvers and artificial diffusivities for shock-capturing are also discussed. Along with theoretical analysis, rigorous evaluation and validation of the methodology on canonical tests, including classic two-dimensional simulations, direct numerical simulations, and large-eddy simulations, are used to confirm robustness and accuracy.

Estimating the Ebro river discharge at 1 km/daily resolution using indirect satellite observations

Estimating river discharge Q at global scale from satellite observations is not yet fully satisfactory in part because of limited space/time resolution. Furthermore, on highly anthropized basins, it is essential to anchor the analysis to reliable Q measurements. Gauge networks are however very sparse and limited in time, and SWOT (Surface Water Ocean Topography) river discharge estimates at global scale are not yet available. The method proposed here is able to obtain continuous daily Q estimates at 1 km/daily resolution, using indirect satellite data and ground-based estimates. We focus here on the Ebro. Over such an anthropized basin (e.g. change of land use, irrigation), the exploitation of 205 available gauges at their nominal resolution (i.e., daily point measurements) is a necessity. The hydrological Continuum model is used to help interpolate spatially and temporally the observations into our optimal interpolation scheme. The proposed Q-mapping is similar to an assimilation scheme were Earth observations (precipitation, evapotranspiration and total water storage change) and model simulations are constrained by in situ gauge measurements. The Q estimates are evaluated using a rigorous leave-one-out experiment, showing a good agreement with the in situ data: a correlation of 0.72 (median), and a 75th percentile of Nash-Sutcliffe Efficiency up to 0.62. Our spatio-temporal continuous Q estimates at high spatial/temporal resolution can describe complex continental water dynamics, including extreme events. SWOT estimates will soon be available, at the global scale but with irregular space/time sampling: our method should help exploit them to obtain a regular space-temporal description of the water cycle at high resolution.

Bifurcation analysis of piecewise-smooth engineering systems with delays through numeric continuation of periodic orbits

This paper presents a numeric continuation framework for periodic orbits of piecewise-smooth and hybrid dynamical systems with fixed point delays. For the numeric solution of the corresponding infinite dimensional multi-point boundary value problem, a novel discretization and interpolation scheme is developed employing Chebyshev polynomial based spectral collocation techniques. The same approach is employed for the formulation of the corresponding monodromy matrix enabling stability analysis on the found periodic orbits. Special care is attributed to the accurate detection of discontinuity induced bifurcations such as grazing and sliding, and the implemented pseudo-arclength framework is adapted to allow two parameter continuation of these critical points. The capabilities of the developed algorithms are demonstrated on a set of delayed piecewise-smooth and hybrid dynamical systems, showcasing potential engineering applications from the fields of control theory, traffic dynamics modelling, and machine tool vibrations. Finally, a detailed tutorial is attached in the appendix to accompany the open-source release of the developed codebase.

Scalable interpolation of satellite altimetry data with probabilistic machine learning

We present GPSat; an open-source Python programming library for performing efficient interpolation of non-stationary satellite altimetry data, using scalable Gaussian process techniques. We use GPSat to generate complete maps of daily 50 km-gridded Arctic sea ice radar freeboard, and find that, relative to a previous interpolation scheme, GPSat offers a 504 × computational speedup, with less than 4 mm difference on the derived freeboards on average. We then demonstrate the scalability of GPSat through freeboard interpolation at 5 km resolution, and Sea-Level Anomalies (SLA) at the resolution of the altimeter footprint. Interpolated 5 km radar freeboards show strong agreement with airborne data (linear correlation of 0.66). Footprint-level SLA interpolation also shows improvements in predictive skill over linear regression. In this work, we suggest that GPSat could overcome the computational bottlenecks faced in many altimetry-based interpolation routines, and hence advance critical understanding of ocean and sea ice variability over short spatio-temporal scales.