IA Scholar Query: Sketching Variational Hermite-RBF Implicits.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 03 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Surface Reconstruction from Point Clouds without Normals by Parametrizing the Gauss Formula
https://scholar.archive.org/work/f7gvwz4mfbhv3ktpbpvo6gj5qi
We propose Parametric Gauss Reconstruction (PGR) for surface reconstruction from point clouds without normals. Our insight builds on the Gauss formula in potential theory, which represents the indicator function of a region as an integral over its boundary. By viewing surface normals and surface element areas as unknown parameters, the Gauss formula interprets the indicator as a member of some parametric function spaces. We can solve for the unknown parameters using the Gauss formula and simultaneously obtain the indicator function. Our method bypasses the need for accurate input normals as required by most existing non-data-driven methods, while also exhibiting superiority over data-driven methods since no training is needed. Moreover, by modifying the Gauss formula and employing regularization, PGR also adapts to difficult cases such as noisy inputs, thin structures, sparse or nonuniform points, for which accurate normal estimation becomes quite difficult. Our code is publicly available at https://github.com/jsnln/ParametricGaussRecon.Siyou Lin, Dong Xiao, Zuoqiang Shi, Bin Wangwork_f7gvwz4mfbhv3ktpbpvo6gj5qiWed, 03 Aug 2022 00:00:00 GMTGaia Data Release 3. Apsis. III. Non-stellar content and source classification
https://scholar.archive.org/work/ca7cipejtrbyphij6o2tp6cuby
Context. As part of the third Gaia data release, we present the contributions of the non-stellar and classification modules from the eighth coordination unit (CU8) of the Data Processing and Analysis Consortium, which is responsible for the determination of source astrophysical parameters using Gaia data. This is the third in a series of three papers describing the work done within CU8 for this release. Aims. For each of the five relevant modules from CU8, we summarise their objectives, the methods they employ, their performance, and the results they produce for Gaia DR3. We further advise how to use these data products and highlight some limitations. Methods. The Discrete Source Classifier (DSC) module provides classification probabilities associated with five types of sources: quasars, galaxies, stars, white dwarfs, and physical binary stars. A subset of these sources are processed by the Outlier Analysis (OA) module, which performs an unsupervised clustering analysis, and then associates labels with the clusters to complement the DSC classification. The Quasi Stellar Object Classifier (QSOC) and the Unresolved Galaxy Classifier (UGC) determine the redshifts of the sources classified as quasar and galaxy by the DSC module. Finally, the Total Galactic Extinction (TGE) module uses the extinctions of individual stars determined by another CU8 module to determine the asymptotic extinction along all lines of sight for Galactic latitudes |b| > 5 deg. Results. Gaia DR3 includes 1591 million sources with DSC classifications; 56 million sources to which the OA clustering is applied; 1.4 million sources with redshift estimates from UGC; 6.4 million sources with QSOC redshift; and 3.1 million level 9 HEALPixes of size 0.013 squared degree, where the extinction is evaluated by TGE.L. Delchambre, C.A.L. Bailer-Jones, I. Bellas-Velidis, R. Drimmel, D. Garabato, R. Carballo, D. Hatzidimitriou, D.J. Marshall, R. Andrae, C. Dafonte, E. Livanou, M. Fouesneau, E. Licata, H.E.P. Lindstrom, M. Manteiga, C. Robin, A. Silvelo, et al.work_ca7cipejtrbyphij6o2tp6cubyMon, 13 Jun 2022 00:00:00 GMTGaussian Process Regression in the Flat Limit
https://scholar.archive.org/work/juz5k6kjznhebdavveupbzf2v4
Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused on a large-n asymptotics, characterising the behaviour of GP regression as the amount of data increases. Fixed-sample analysis is much more difficult outside of simple cases, such as locations on a regular grid. In this work we perform a fixed-sample analysis that was first studied in the context of approximation theory by Driscoll Fornberg (2002), called the "flat limit". In flat-limit asymptotics, the goal is to characterise kernel methods as the length-scale of the kernel function tends to infinity, so that kernels appear flat over the range of the data. Surprisingly, this limit is well-defined, and displays interesting behaviour: Driscoll Fornberg showed that radial basis interpolation converges in the flat limit to polynomial interpolation, if the kernel is Gaussian. Leveraging recent results on the spectral behaviour of kernel matrices in the flat limit, we study the flat limit of Gaussian process regression. Results show that Gaussian process regression tends in the flat limit to (multivariate) polynomial regression, or (polyharmonic) spline regression, depending on the kernel. Importantly, this holds for both the predictive mean and the predictive variance, so that the posterior predictive distributions become equivalent. Our results have practical consequences: for instance, they show that optimal GP predictions in the sense of leave-one-out loss may occur at very large length-scales, which would be invisible to current implementations because of numerical difficulties.Simon Barthelmé, Pierre-Olivier Amblard, Nicolas Tremblay, Konstantin Usevichwork_juz5k6kjznhebdavveupbzf2v4Mon, 10 Jan 2022 00:00:00 GMTSurrogate Modeling and Uncertainty Quantification for Radio Frequency and Optical Applications
https://scholar.archive.org/work/2eefy7x7pndope45htce77h2gm
This thesis addresses surrogate modeling and forward uncertainty propagation for parametric/stochastic versions of Maxwell's source and eigenproblem. Surrogate modeling is employed to reduce the computational complexity of sampling an underlying numerical solver. First, a rational kernel-based interpolation method is developed for the efficient approximation of frequency response functions. Next, the impact of uncertain shape and material parameters is considered, which originate, for instance, in manufacturing tolerances or measurement errors. To this end, several techniques for convergence acceleration of established spectral surrogate modeling techniques, as generalized polynomial chaos or stochastic collocation, are presented. In particular, transformed basis functions are constructed based on conformal maps that suitably transform the region of holomorphy. In addition, an adjoint representation of the stochastic error is employed for an efficient dimension-adaptive scheme as well as error correction. Several challenges arising in uncertainty quantification for radio frequency and optical components are addressed. A multifidelity scheme for an efficient and reliable yield estimation is presented which comprises sampling of a surrogate model as well as finite element models of different fidelity based on adjoint error estimation. To enable the application of spectral surrogate modeling techniques for Maxwell's eigenproblem with uncertain input data, a homotopy-based eigenvalue tracking method is proposed to ensure a consistent matching of eigenmodes. Quasi-periodic structures of finite size, subject to independent shape uncertainties, are tackled using a decoupled uncertainty propagation procedure on the unit cell level. The methods are numerically investigated using a number of benchmark problems that encompass academic and real-world models, and their efficiency is demonstrated. Finally, comprehensive uncertainty quantification and sensitivity studies are presented for the 9-cell TESLA cavities as well as di [...]Niklas Georgwork_2eefy7x7pndope45htce77h2gmScalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation
https://scholar.archive.org/work/3dnfpx3q4feahdr7ytpu6frxga
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Runge-Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokker-Planck-Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.Arno Solin, Ella Tamir, Prakhar Vermawork_3dnfpx3q4feahdr7ytpu6frxgaFri, 29 Oct 2021 00:00:00 GMT