The problem of obtaining an optimal spline with free knots is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been acco...
In this work, we introduce Pontryagin Neural Networks (PoNNs) and employ them to learn the optimal control actions for unconstrained and constrained optimal intercept problems. PoNNs represent a particular family of Physics-Informed Neural Networks (...
Finding a simple root for a nonlinear equation
The National Meteorological Satellite Center/Korean Meteorological Administration (NMSC/KMA) receives data directly from low Earth orbit (LEO) satellites (including NOAA-18,19; MetOp-A,B; and Suomi-NPP), and generates Level 2 products (e.g., temperat...
Aerosol optical depth (AOD) is one of the basic characteristics of atmospheric aerosol. A global ground-based network of sun and sky photometers, the Aerosol Robotic Network (AERONET) provides AOD data with low uncertainty. However, AERONET observati...
The ensemble optimal interpolation method was used in this study to conduct an examination of the assimilations of significant wave height (SWH) data from HY-2A satellite altimeter based on the WAVEWATCH III global ocean wave model. The results sugge...
Mean dynamic topography (MDT) is crucial for research in oceanography and climatology. The optimal interpolation method (OIM) is applied to MDT modeling, where the error variance–covariance information of the observations is established. The global g...
Time-optimal trajectory planning is one of the most important ways to improve work efficiency and reduce cost and plays an important role in practical application scenarios of robots. Therefore, it is necessary to optimize the running time of the tra...
Thermal infrared remote sensing measurements have greatly improved in terms of spectral, spatial, and temporal resolution. These improvements are producing a clearer picture of the land surface and Earth atmospheric composition than ever before. Neve...
A nonlinear equation
To estimate the spatial and temporal distribution of aerosol optical depth (AOD), we used the optimal interpolation (OI). In OI, observational data and a model forecast are linearly combined according to their relative accuracies. Weight coefficients...
Spatial-temporal optimal interpolation (STOI) is a data assimilation method based on minimizing the error in an estimate. Error correlations can be modeled with analytical functions. We investigated the effect of the form of the error correlation fun...
The development of a snow depth product over North America is investigated by applying two-dimensional optimal interpolation to passive microwave satellite-derived and in-situ measured snow depth. At each snow-covered satellite footprint, the techniq...
A common approach to estimating the spatial–temporal distribution of atmospheric species properties is data assimilation. Data assimilation methods provide the best estimate of the required parameter by combining observations with appropriate p...
With the swift advancement of the geometric modeling industry and computer technology, traditional generalized Ball curves and surfaces are challenging to achieve the geometric modeling of various complex curves and surfaces. Constructing an interpol...
To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length...
In this work, a simple, efficient and accurate database in the form of a lookup table to use in reflectarray design and direct layout optimization is presented. The database uses N-linear interpolation internally to estimate the reflection coefficien...
The optimal tuning of high-order motion parameters has emerged as a promising strategy for actively controlling the kinematics/dynamics of high-speed cam mechanisms. However, accomplishing this task remains challenging with current low-order interpol...
In this paper, a simple and effective self-adaptive material interpolation scheme is proposed to solve the numerical instability problem, which may occur in topology optimization considering geometrical nonlinearity when using density-based method. T...
This paper presents an optimization algorithm for tuning the interpolation parameters of computer numerical control (CNC) controllers; it operates by considering multiple objective functions, namely, contour errors, the machining time (MT), and vibra...
Water quality monitoring demands the use of spatial interpolation techniques due to on-ground challenges. The implementation of various spatial interpolation methods results in significant variations from the true spatial distribution of water qualit...
Dynamic optimization problems (DOPs) are widely encountered in complex chemical engineering processes. However, due to the existence of highly constrained, nonlinear, and nonsmooth environment in chemical processes, which usually causes nonconvexity,...
Objectives: We devised a simple and practical method for optimizing intraocular lens (IOL) constants using linear interpolation, based on the IOL power calculation study protocol proposed by Hoffer et al., and evaluated its effectiveness. Methods: Th...
Cortisol is an important marker of hypothalamic-pituitary-adrenal function and follows robust circadian and diurnal rhythms. However, biomarker sampling protocols can be labor-intensive and cost-prohibitive. Objectives: Explore analytical approaches...
The high dimensionality of large datasets can severely impact the data mining process. Therefore, feature selection becomes an essential preprocessing stage, aimed at reducing the dimensionality of the dataset by selecting the most informative featur...
The ultrasonic phased array total focusing method (TFM) has the advantages of full-range dynamic focusing and high imaging resolution, but the problem of long imaging time limits its practically industrial applications. To reduce the imaging calculat...
Topological structural optimization is a powerful computational tool that enhances the structural efficiency of mechanical components. It achieves this by reducing mass without significantly altering stiffness. This study combines the Natural-Neighbo...
Hyper-parameters play a critical role in neural networks; they significantly impact both training effectiveness and overall model performance. Proper hyper-parameter settings can accelerate model convergence and improve generalization. Among various...
Nearshore bathymetry changes on scales of hours to months in ways that strongly impact coastal processes. However, even at the best-monitored sites, surveys are typically not conducted with sufficient frequency to capture important changes such as sa...
Designing a high-strength node is significant for space structures. Topological optimization can optimally allocate the material distribution of components to meet performance requirements. Although the material distribution after topology optimizati...
We develop a novel Steffensen-type iterative solver to solve nonlinear scalar equations without requiring derivatives. A two-parameter one-step scheme without memory is first introduced and analyzed. Its optimal quadratic convergence is then establis...
Geostatistical Analyst is a set of advanced tools for analysing spatial data and generating surface models using statistical and deterministic methods available in ESRI ArcMap software. It enables interpolation models to be created on the basis of da...
In this paper, we consider a recently developed data assimilation method, the Generalized Kalman Filter (GKF), which is a generalization of the widely-used Ensemble Optimal Interpolation (EnOI) method. Both methods are applied for modeling the Atlant...
The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential...
This paper presents two algorithms used to derive Aerosol Optical Depth (AOD) from a synergy of satellite and ground-based observations, as well as aerosol transport model output. The Spinning Enhanced Visible Infrared Radiometer (SEVIRI) instrument...
Image interpolation is one of key contents in image processing. We present an interpolation algorithm based on a rational function model with constraint parameters. Firstly, based on the construction principle of the rational function, the detection...
In the projection-driven multi-modal 3D object detection task, the data projection process has extremely high computational complexity, which restricts the efficiency of the detection network. In addition, traditional projection interpolation methods...
Digital Elevation Models (DEMs) are commonly used for environment, engineering, and architecture-related studies. One of the most important factors for the accuracy of DEM generation is the process of spatial interpolation, which is used for estimati...
Optimization processes or methods play an essential role in the continuous improvement of various human activities, particularly in agriculture, given its vital role in food production. In precision agriculture, which utilizes technology to optimize...
Basis functions are key in constructing interpolation equations in hull surface modification based on radial basis functions (RBF) interpolation. However, few have studied the selection of basis functions in depth. By comparing several typical basis...
When using machine learning methods to make predictions, the problem of small sample sizes or highly noisy observation samples is common. Current mainstream sample expansion methods cannot handle the data noise problem well. We propose a multipath sa...
Several window functions are currently applied to improve the performance of the discrete Fourier transform (DFT) harmonic detection method. These window functions exhibit poor accuracy in measuring the harmonic contents of a signal with high-order a...
Automatic parking path optimization is a key point for automatic parking. However, it is difficult to obtain the smooth, accurate and optimal parking path by using traditional automatic parking optimization algorithms. So, based on the automatic park...
This paper is devoted to developing new derivative-free optimization (DFO) methods for solving optimization problems where derivative information is not available or cannot be calculated numerically. To overcome the computational difficulties arising...
A key issue in fishery forecasting is the collection of high-precision subsurface environmental data. A data assimilation method, named gradient-dependent optimal interpolation, was used to construct the near-real-time vertical temperature and salini...
The ever increasing geophysical data streams pouring from earth observation satellite missions and numerical simulations along with the development of dedicated big data infrastructure advocate for truly exploiting the potential of these datasets, th...
Thin-walled structures have problems such as low stiffness, large deflection, and vibration. The layout of rib reinforcement in thin-walled structures plays a vital role in providing structural strength and rigidity and reducing structural weight. A...
This paper presents an efficient and compact Matlab code for 2D and 3D topology optimization of multi-materials. We extend a classical 88-line-based educational code to the multi-material problem using the mapping-based interpolation function, with w...
Maritime UAV path planning is a key link in realizing the intelligence of maritime emergency transportation, providing key support for fast and flexible maritime accident disposal and emergency material supply. However, most of the current UAV path p...
We present a scheme aimed at estimating daily spatial snow water equivalent (SWE) maps in real time and at high spatial resolution from scarce in-situ SWE measurements from Internet of Things (IoT) devices at actual sensor locations and historical SW...
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