Grid Interpolation Research Articles

The VSPEC Collection: A suite of utilities to model spectroscopic phase curves of 3D exoplanet atmospheres in the presence of stellar variability

We present the Variable Star PhasE Curve (VSPEC) Collection, a set of Python packages for simulating combined-light spectroscopic observations of 3-dimensional exoplanet atmospheres in the presence of stellar variability and inhomogeneity. VSPEC uses the Planetary Spectrum Generator’s Global Emission Spectra (PSG/GlobES) application along with a custom-built multi-component time-variable stellar model based on a user-defined grid of stellar photosphere models to produce spectroscopic light curves of the planet-host system. VSPEC can be a useful tool for modeling observations of exoplanets in transiting geometries (primary transit, secondary eclipse) as well as orbital phase curve measurements, and is built in a modular and flexible configuration for easy adaptability to new stellar and planetary model inputs. We additionally present a set of codes developed alongside the core VSPEC modules, including the stellar surface model generator vspec-vsm, the stellar spectral grid interpolation code GridPolator, and a Python interface for PSG, libpypsg.

Advanced surrogate model for electron-scale turbulence in tokamak pedestals

We derive an advanced surrogate model for predicting turbulent transport at the edge of tokamaks driven by electron temperature gradient (ETG) modes. Our derivation is based on a recently developed sensitivity-driven sparse grid interpolation approach for uncertainty quantification and sensitivity analysis at scale, which informs the set of parameters that define the surrogate model as a scaling law. Our model reveals that ETG-driven electron heat flux is influenced by the safety factor $q$ , electron beta $\beta _e$ and normalized electron Debye length $\lambda _D$ , in addition to well-established parameters such as the electron temperature and density gradients. To assess the trustworthiness of our model's predictions beyond training, we compute prediction intervals using bootstrapping. The surrogate model's predictive power is tested across a wide range of parameter values, including within-distribution testing parameters (to verify our model) as well as out-of-bounds and out-of-distribution testing (to validate the proposed model). Overall, validation efforts show that our model competes well with, or can even outperform, existing scaling laws in predicting ETG-driven transport.

Verification and validation of a coupled CFD–FEM approach with overset structured grid through free decay and regular wave tests

This paper presents a comprehensive verification and validation study applied to the hydrodynamic analysis of a semi-submersible Floating Offshore Wind Turbine (FOWT) platform. The numerical simulation is conducted using a coupled Computational Fluid Dynamics-Finite Element Method (CFD–FEM) approach. The CFD program incorporates an overset grid interpolation method, facilitating a more systematic grid refinement in the estimation of discretization uncertainties. A mooring analysis program, based on the FEM scheme, is integrated with the CFD program to simulate the dynamic responses of mooring system. The necessity of the nonlinear mooring model is demonstrated by comparing solutions with a comparative test using a linear mooring model. The verification study, based on a least-squares-based extrapolation method, quantifies the spatial and temporal discretization errors of the numerical model. The numerical solutions based on the baseline model are further validated against the model test measurements. A pitch free decay model test and a regular wave model test conducted within the OC5 project are utilized for the verification and validation study. Results from both tests demonstrate the reliability and accuracy of the coupled method.

Yadism: yet another deep-inelastic scattering module

We present yadism, a library for the evaluation of both polarized and unpolarized deep-inelastic scattering (DIS) structure functions and cross sections up to N3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}LO in perturbative QCD. The package provides computations of observables in fixed-flavor and zero-mass variable flavor number schemes. The implementation of the general mass variable flavor number schemes is supported through the high virtuality limits for the heavy flavor coefficients. In addition, yadism provides a set of tools for the generation of interpolation grids in the PDF-independent PineAPPL format, allowing to test the PDF dependence on any DIS observable without needing to rerun the computation. This work is part of an ongoing effort to standardize the format of theory predictions in high-energy physics within the pineline framework. The code is open source, written in Python and documented to facilitate usage, integrations, and further extensions. Finally, the code has been benchmarked against the widely used APFEL++ and QCDNUM libraries.

In-situ measurement of particle length distribution by FBRM with application to needle- or rod-shape crystallization processes

In this paper, an in-situ measurement method is proposed for detecting needle- or rod-shape particle length distribution (PLD) during a crystallization process, by using the instrument named focused beam reflectance measurement (FBRM). A data pretreatment strategy is firstly presented to modify the measured chord length distribution (CLD) of particles by FBRM for proper analysis, which could guarantee measurement accuracy when the particle length are smaller than 150 μm. Based on the pretreated CLD, a moment conversion algorithm is established for estimating the moments of particle population density, so as to further improve the measurement accuracy for particles possessing larger sizes. Correspondingly, the particle growth-nucleation model parameters are efficiently estimated by using the interior point method (IPM) in combination with the homotopy analysis method (HAM). Then the PLD is reconstructed based on these estimated low-order moments, through a modified cubic-spline interpolation algorithm with variable interpolation grids. Experimental results on the seeded cooling crystallization process of β form L-glutamic acid (LGA) well demonstrate the effectiveness of the proposed method for in-situ measurement.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

A Bayesian Structural Modal Updating Method Based on Sparse Grid and Ensemble Kalman Filter

This study presents a sparse grid interpolation and ensemble Kalman filter (EnKF)-based Markov Chain Monte Carlo (MCMC) method (SG-EnMCMC). Initiating with the formulation of a recursive equation for the state space vector, derived from the structural dynamic equation, this study adopts a dimensionality reduction strategy. This approach involves a separation of physical parameters and the state space vector. The acquisition of physical parameters is accomplished through sampling, utilizing sample moments to substitute population moments, thereby mitigating the need for computationally high-dimensional covariance matrix calculations. To further streamline the recursive equation of the state space vector, a sparse grid method is employed for interpolation. This step simplifies the process while ensuring superior accuracy compared to the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Subsequent to this, acceptance rates and the final parameter posterior distribution within the MCMC framework are derived. The efficiency of the proposed method is assessed through validation in two shaking table experiments.

Simultaneous monitoring of the limited area ionosphere with the use of GPS and ionosonde

The importance of this study lies in its contribution to the field of ionospheric science, particularly in the monitoring and prediction of ionospheric parameters. This study focuses on comparing two techniques for spatio-temporal kriging of critical ionospheric parameters, namely the F2 layer critical frequency (foF2) and Total Electron Content (TEC), under both quiet and disturbed ionospheric conditions. The first technique, Ordinary Kriging (OK), relies solely on foF2 data, while the second technique, Kriging with External Drift (KED), incorporates the dynamic relationship between foF2 and TEC data to improve the interpolation process. This study demonstrates how KED, which utilizes dynamic secondary information, offers advantages over OK. By simultaneously monitoring the ionosphere from a single ionosonde station and collecting data from visible GPS satellites, KED enhances the accuracy of spatial structural analysis, enabling more precise estimations of ionospheric characteristics across interpolation grid nodes. The research highlights that the non-uniform distribution of ionosonde stations, especially in regions with limited foF2 data, can benefit from KED's incorporation of TEC data. Additionally, the study reveals the potential for improving TEC maps by assimilating foF2 data located at the periphery of the observation area. Furthermore, the paper discusses the determination of semivariogram structures for both foF2 and TEC data, emphasizing the spatial correlations between data points. These findings contribute to a better understanding of ionospheric behavior and the potential for enhanced ionospheric modeling.

Leakage monitoring and diagnosis of LNG storage tanks with temperature sensing network integration and artificial intelligence algorithm

Temperature is the most important safety monitoring indicator for leakage diagnosis during the operation phase of liquefied natural gas (LNG) storage tanks. Timely monitoring and accurate identification of LNG leakage events are crucial for accident prevention, loss reduction, and facility safety maintenance. This study integrates artificial intelligence (AI) algorithms and temperature sensing data to achieve intelligent monitoring and diagnosis of leakage in LNG storage tanks. Firstly, a comprehensive temperature sensing network is constructed by combining numerical simulation of the temperature field and temperature sensing experiments using fiber Bragg grating sensors. Secondly, Python is used to perform linear grid interpolation and flattening on the sensing network, generating 2D temperature nephogram samples that are conducive to AI algorithm recognition. Finally, sample features are extracted using machine vision, and leakage location calculation, leakage diagnosis and leakage volume calculation are implemented with the help of machine learning algorithms, achieving satisfactory accuracy on the test set. In addition, the ConvLSTM framework is introduced for deep learning and recurrent neural network training, enabling spatiotemporal prediction of the leakage area.

Peat depth mapping using grid interpolation from terrestrial peat drilling points data: A case study in Zamrud National Park

Zamrud National Park is the peak of the peat dome in the Kampar Peninsula. Peat depth data is needed as a baseline to maintain the balance of the water reservoir and carbon stock. Currently, available peat depth data is predictive photogrammetric data. Soil survey activities need to be carried out to provide accurate and up-to-date data. This research aims to map the peat depth using the best grid interpolation technique. Peat depth measurements were carried out terrestrially, while peat depth mapping used inverse distance weighted, kriging, and spline interpolation techniques. Drilling observation points are arranged based on a system of longitudinal transects and transverse transects in a northeast-southwest direction. The distance between longitudinal transects is 500 m and between transects is 1,000 m. The results showed that the Zamrud National Park area has diverse peat depths ranging from 5.3 to 16.7 m. The Kriging interpolation technique gives the best mapping accuracy results. The standard deviation value is 1.9 is smaller, the accuracy value is 98.82% higher, and the thickness of the dominating peat is 8.4-9.4 m for 7,093.47 ha (24.42% of the total park area).

Regional Sensitivity Analysis for Maximum Static Transfer Capability of Power Systems by Dimension-Adaptive Sparse Grid Interpolation

The maximum static transfer capability (MSTC) can be regarded as a measure of the power transmission ability of power systems in steady-state operation. These emerging uncertainty sources pose a difficult challenge for the efficient analysis and effective control of MSTC. To address this challenge, the dimension-adaptive sparse grid interpolation (DASGI) method is applied with modified boundaries of the collocation points to establish a surrogate model for the faster calculation of the MSTC based on AC optimal power flow (AC-OPF), thus accelerating its probabilistic analysis as well. Subsequently, the regional sensitivity analysis (RSA) is introduced in terms of contribution to the sample mean (CSM) and to the sample variance (CSV) to identify the critical regions of the uncertainty sources. Hence, an adjustment strategy is developed to increase the mean or decrease the variance of MSTC for secure and stable power transmission. Furthermore, the total CSM (TCSM) and total CSV (TCSV) are proposed as indicators to select the most influential random inputs as the preliminary step of RSA, which reduces the analytical burden. The effectiveness of this proposition is illustrated on the modified IEEE 118-bus system and the Polish 2383-bus power system, where the Monte Carlo simulation method, in combination with the AC-OPF-based MSTC model, provides an accuracy reference and a traditional sensitivity index provides the term for comparison.

Geometric Morphometrics Applied to Cartography

The morphological differences between two geographical maps can be highlighted by a polycentric distance cartogram resulting from a bidimensional regression. Beyond the communicational interest of the transformations thus produced, the method makes it possible to reveal the differences in structure and therefore constitutes a real research tool. However, bidimensional regression can only compare the shape of two maps. Since the 1990s, geometric morphometrics has revolutionized the morphological analysis of natural structures (and others). It has since been applied in many fields of research but not in cartography. This article describes the theoretical and methodological bases of a method combining bidimensional regression with a geometric morphometrics approach to compare the shape of several geographical maps. Geometric morphometrics and bidimensional regression indeed share common approaches of the statistical shape analysis like homologous landmarks and interpolation grids. However, there is no software in geometric morphometrics capable of directly reading geographical data, which would facilitate the work of cartographers accustomed to GIS software. That is why we present MapMorphy, a tool specifically developed for this task. An example on ancient maps illustrates the method.

Hierarchical Error Compensation Method for Two-Degree-of-Freedom Manipulator Positioning Error in Hybrid Robots

In this paper, taking a two-degree-of-freedom parallelogram serial manipulator of a hybrid robot as an example, a hierarchical error compensation method that combines geometric and non-geometric error compensation is proposed. First, we establish the geometric kinematic modeling and error model and use the Levenberg-Marquardt (L-M) method to identify the geometric error parameters. Then, we use the grid interpolation method to compensate for non-geometric errors, thereby improving the overall positioning accuracy of the manipulator. Finally, a simulation is presented to verify the correctness and effectiveness of the proposed method. The results show that the positioning accuracy is improved from 4.8568 mm to 0.0036 mm, and the attitude error is improved from 0.9437° to 0.0105°.

Fast grid to grid interpolation for radio interferometric imaging

Backward and forward interpolations on a Fourier grid are computationally expensive operations for radio interferometric imaging algorithms. By merging these operations, we propose the Grid to Grid (G2G) method which aims to reduce the computational cost and memory footprint. We have also shown that the oversampling factor used for the convolution function in the G2G method strongly impacted the accuracy and computational speed. Acceleration on graphics processing units (GPU), well suited for this embarrassingly parallel algorithm, has been studied mainly for backward operation. Thus, we propose a GPU and CPU implementation of the G2G method on Nvidia A100 and Intel Ice Lake processors. Experiments have shown a GPU performance improvement with a Fourier-point throughput better than up to 37% regarding standard gridder and degridder.

Lagrangian motion magnification with double sparse optical flow decomposition

Microexpressions are fast and spatially small facial expressions that are difficult to detect. Therefore, motion magnification techniques, which aim at amplifying and hence revealing subtle motion in videos, appear useful for handling such expressions. There are basically two main approaches, namely, via Eulerian or Lagrangian techniques. While the first one magnifies motion implicitly by operating directly on image pixels, the Lagrangian approach uses optical flow (OF) techniques to extract and magnify pixel trajectories. In this study, we propose a novel approach for local Lagrangian motion magnification of facial micro-motions. Our contribution is 3-fold: first, we fine tune the recurrent all-pairs field transforms (RAFT) for OFs deep learning approach for faces by adding ground truth obtained from the variational dense inverse search (DIS) for the OF algorithm applied to the CASME II video set of facial micro expressions. This enables us to produce OFs of facial videos in an efficient and sufficiently accurate way. Second, since facial micro-motions are both local in space and time, we propose to approximate the OF field by sparse components both in space and time leading to a double sparse decomposition. Third, we use this decomposition to magnify micro-motions in specific areas of the face, where we introduce a new forward warping strategy using a triangular splitting of the image grid and barycentric interpolation of the RGB vectors at the corners of the transformed triangles. We demonstrate the feasibility of our approach by various examples.

Effect of interpolation kernels and grid refinement on two way-coupled point-particle simulations

The predictive capability of two way–coupled point-particle Euler–Lagrange model in accurately capturing particle-flow interactions under grid refinement, wherein the particle size can be comparable to the grid size, is systematically evaluated. Two situations are considered, (i) uniform flow over a stationary particle, and (ii) decaying isotropic turbulence laden with Kolmogorov-scale particles. Particle-fluid interactions are modeled using only the standard drag law, typical of large density-ratio systems. A zonal, advection-diffusion-reaction (Zonal-ADR) model is used to obtain the undisturbed fluid velocity needed in the drag closure. Two main types of interpolation kernels, grid-based and particle size–based, are employed. The effect of interpolation kernels on capturing the particle-fluid interactions, kinetic energy, dissipation rate, and particle acceleration statistics are evaluated in detail. It is shown that the interpolation kernels whose width scales with the particle size perform significantly better under grid refinement than kernels whose width scales with the grid size. Convergence with respect to spatial resolution is obtained with the particle size–based kernels with and without correcting for the self-disturbance effect. While the use of particle size–based interpolation kernels provide spatial convergence and perform better than kernels that scale based on grid size, small differences can still be seen in the converged results with and without correcting for the particle self-disturbance. Such differences indicate the need for self-disturbance correction to obtain the best results, especially when the particles are larger than the grid size.

Mean Seasonal Sea Surface Height Variations in and around the Makassar Strait

Seasonal variations are significant in currents in the Makassar Strait, 80% of the Indonesian Throughflow (ITF) from the Pacific to the Indian Ocean, and they are in phase with both the monsoon and the sea surface height anomaly (SSHA) difference between two oceans. However, dynamics are not well discussed since gridded SSHA products within the strait are less reliable because of both over-smoothing and contamination in coastal areas. In this study, therefore, 17 years of along-track Jason altimetry data with the ALES retracker are used without grid interpolation to investigate seasonal SSHA variations in and around the Makassar Strait. All SSHA variations are in phase from the southern Celebes Sea to the northern Java Sea through the Makassar Strait, but their amplitude decreases by the distance from the southern shallow area. These amplitude modulations produce the pressure gradient force, which is maximum to the north of 4°S reaching 1.5 × 10−6 ms−2, and that would be balanced with the bottom friction of the upper-layer ITF velocity, rather than the wind stress whose magnitude 5 × 10−8 ms−2 is too small. The SSHA difference between the two oceans is in phase but is isolated from the Makassar Strait by adjacent uncorrelated SSHA variations.

Voronoi Natural Neighbours Tessellation: An interpolation and grid agnostic approach to forensic soil provenancing

Recently there has been an increase of work dedicated to developing a more objective soil provenancing capability. Notwithstanding the significant progress made, the presented provenancing techniques have predominately been based upon interpolation grids, generated from often arbitrary decisions of the user (e.g., grid cell size, grid placement, interpolation model, etc.). To address the acknowledged reproducibility issues, this paper introduces a spatial modelling technique based upon Voronoi Tessellations that is free from arbitrary user decisions. Termed herein as Voronoi Natural Neighbours Tessellation (VNNT), the proposed approach segments the survey area into many “honeycomb-like” polygons. Of which, the exact number, shape, location, and orientation of polygons are inherently dependent upon the original density of input sampling points from the survey, not a user’s subjective decision.Utilising compositional geochemistry data from a fit-for-purpose topsoil survey and eleven “blind” soil samples from Canberra, Australia, we compare this proposed VNNT approach against a simpler Voronoi Tessellation, and a previously presented 500 m × 500 m grid following a modified and upscaled Natural Neighbour interpolation. Aside from also being computationally less intensive, our results indicated the proposed VNNT approach regularly yielded at least equal, or often more accurate provenance predictions than that of the gridded Natural Neighbour interpolation. Importantly, the delineation of individual polygons is fundamentally dependent upon the survey’s real sampling design, and most truthfully reflects the underlying sampling density, and associated uncertainties. Consequently, the VNNT approach is significantly less susceptible to expert bias as a result of subjective decision-making and “fine-tuning” of interpolation parameters.

Low-rank Green's function representations applied to dynamical mean-field theory

Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In particular, the intermediate representation with sparse sampling and the discrete Lehmann representation (DLR) make use of low rank compression techniques to obtain optimal approximations with controllable accuracy. We consider the use of the DLR in dynamical mean-field theory (DMFT) calculations, and in particular show that the standard full Matsubara frequency grid can be replaced by the compact grid of DLR Matsubara frequency nodes. We test the performance of the method for a DMFT calculation of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ at temperature $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ using a continuous-time quantum Monte Carlo impurity solver, and demonstrate that Matsubara frequency quantities can be represented on a grid of only 36 nodes with no reduction in accuracy, or increase in the number of self-consistent iterations, despite the presence of significant Monte Carlo noise.

A Gridded Monthly Precipitation Merged Rain Gauge and Satellite Analysis Dataset for the Tian Shan Range between 1981 and 2019

Abstract An accurate and reliable precipitation product on regular grids is essential for understanding trends and variability within climate studies, for weather forecasting, and in hydrology and agrometeorology applications. However, the construction of high-resolution spatiotemporal precipitation grid products is challenging for complex terrain with sparse rain gauge networks and when only coarse spatial resolutions of satellite data are available. The objective of this study was to consequently provide a practical method to create a grid precipitation product by merging accurate quantitative observations from weather stations with continuous spatial information and from a satellite-based estimate product. The new gridded precipitation product exhibits a monthly temporal resolution and a spatial resolution of 0.01° for the Tian Shan range, extending back to 1981. To overcome the limitation of low densities and sparse distributions of meteorological stations in the complex terrain of the Tian Shan, a suitable interpolation of Australian National University Spline (ANUSPLIN) was used to interpolate grid precipitation based on in situ data. The interpolation grid precipitation was then merged with the satellite precipitation product developed by the U.S. Geological Survey and the Climate Hazards Group. After evaluation and validation using withheld stations and comparison to reference datasets, the result indicated that the merged product exhibits considerable promise for application in complex terrain. The method can be widely applied and is expected to construct precipitation products with high spatial and temporal resolution by merging multiple precipitation data sources. Significance Statement The purpose of this study is to construct a gridded precipitation dataset by merging the interpolation precipitation based on in situ observation and a satellite precipitation product in arid mountain regions. This is important because gridded precipitations are essential to the evaluation of climate model output and detection of trends in mean climate and climate extremes. Our results present a guide on merging frameworks to construct precipitation datasets used multisource data sources for regions with complex topography, precipitation scarcity, and ungauged and sparse collection.