Topic
Collocation (remote sensing)
About: Collocation (remote sensing) is a research topic. Over the lifetime, 679 publications have been published within this topic receiving 8538 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: A comprehensive review of the literature on physics-informed neural networks can be found in this article , where the primary goal of the study was to characterize these networks and their related advantages and disadvantages, as well as incorporate publications on a broader range of collocation-based physics informed neural networks.
Abstract: Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.
1,223 citations
TL;DR: Experimental results for low NDVI values show a large sensitivity to soil moisture and a relatively good Pearson correlation coefficient, and as the vegetation cover increases (NDVI increases) the reflectivity, the sensitivity to soils moisture and the Pearson correlation coefficients decreases, but it is still significant.
Abstract: Global navigation satellite systems-reflectometry (GNSS-R) is an emerging remote sensing technique that makes use of navigation signals as signals of opportunity in a multistatic radar configuration, with as many transmitters as navigation satellites are in view. GNSS-R sensitivity to soil moisture has already been proven from ground-based and airborne experiments, but studies using space-borne data are still preliminary due to the limited amount of data, collocation, footprint heterogeneity, etc. This study presents a sensitivity study of TechDemoSat-1 GNSS-R data to soil moisture over different types of surfaces (i.e., vegetation covers) and for a wide range of soil moisture and normalized difference vegetation index (NDVI) values. Despite the scattering in the data, which can be largely attributed to the delay-Doppler maps peak variance, the temporal and spatial (footprint size) collocation mismatch with the SMOS soil moisture, and MODIS NDVI vegetation data, and land use data, experimental results for low NDVI values show a large sensitivity to soil moisture and a relatively good Pearson correlation coefficient. As the vegetation cover increases (NDVI increases) the reflectivity, the sensitivity to soil moisture and the Pearson correlation coefficient decreases, but it is still significant.
282 citations
1 Mar 1981
TL;DR: In this article, the authors present some numerical methods for estimating spherical harmonic coefficients from data sampled on the sphere, where the data may be given in the form of area means or of point values, and it may be free from errors or affected by measurement noise.
Abstract: : This report presents some numerical methods for estimating spherical harmonic coefficients from data sampled on the sphere. The data may be given in the form of area means or of point values, and it may be free from errors or affected by measurement 'noise'. The case discussed to greatest length is that of complete, global data sets on regular grids (i.e., lines of latitude and longitude, the latter, at least, separated by constant interval); the case where data are sparsely and irregularly distributed is also considered in some detail. The first section presents some basic properties of spherical harmonics, stressing their relationship to two-dimensional Fourier series. Algorithms for the evaluation of the harmonic coefficients by numerical quadratures are given here, and it is shown that the number of operations is the order of N cubed for equal angular grids, where N is the number of lines of latitude, or 'Nyquist frequency', of the grid. The second section introduces a quadratic measure for the error in the estimation of the coefficients by linear techniques. This is the error measure of least squares collocation, which is a method that can be used for harmonic analysis. Efficient algorithms for implementing collocation on the whole sphere are described. a formal relationship between collocation and least squares adjustment is used to obtain an alternative form of the collocation algorithm that is likely to be stable with dense data sets and, with a minor modification, can be used to implement least squares adjustment as well. The basic principle is that for regular grids the variance-convariance matrix of the data consists of Toeplitz-circulant blocks, so it can be both set up and inverted very efficiently.
230 citations
TL;DR: This study is the first to apply triple collocation (TC) to obtain a robust global-scale cross-assessment of SMAP, SMOS and ASCAT soil moisture retrieval accuracy in terms of anomaly temporal correlation.
219 citations
TL;DR: In this article, a new approach to the solution of optimal control problems for mechanical systems is proposed, based on a direct discretization of the Lagrange-d'Alembert principle for the system (as opposed to using collocation or multiple shooting to enforce the equations of motion as constraints).
214 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 255 |
| 2024 | 449 |
| 2023 | 625 |
| 2022 | 926 |
| 2021 | 84 |