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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs
HT-Net 分层变压器 多尺度 偏微分方程 算子学习模型
2023/5/6
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiscale finite element methods: ideas and challenges
多尺度 有限元方法 思路 挑战
2023/5/6
Multiscale phenomena significantly impact on the computation and modeling for scientific and engineering problems. Multiscale finite element methods are used to build reduced order computational model...
Near-Optimal Detection of Geometric Objects by Fast Multiscale Methods
Fast Multiscale Methods Geometric Objects
2015/8/21
We construct detectors for ‘geometric’ objects in noisy data. Examples include a detector
for presence of a line segment of unknown length, position, and orientation in two-dimensional
image data wi...
Adaptive Multiscale Detection of Filamentary Structures Embedded in a Background of Uniform Random Points
Multiscale Geometric Analysis Pattern Recognition
2015/8/21
We are given a set of n points that appears uniformly distributed in the unit square [0,1]2.
We wish to test whether the set actually is generated from a non-uniform distribution having
a small frac...
Multiscale Geometric Analysis for 3-D Catalogues
laments large scale structures galaxy distribution
2015/8/21
We have developed tools for analysis of 3-D volumetric data which allow sensitive characterizations of point
clouds containing ˉlamentary structures. Our approach involves multiscale X-ray transforms...
We describe a frameworkfor multiscale image analysis in which line
segments play a role analogous to the role played by points in wavelet analysis.
The frameworkhas 5 key components.
Multiscale Representations for Manifold-Valued Data
Symmetric Space Lie Group Two-Scale Refi nement Scheme
2015/8/21
We describe multiscale representations for data observed on equispaced grids and taking
values in manifolds such as: the sphere S2, the special orthogonal group SO(3), the positive
definite ma...
Detecting the Presence of Mixing with Multiscale Maximum Likelihood
Log-concave Mixture detection
2015/8/20
A test of homogeneity tries to decide whether observations come from a single distribution or from a mixture of several distributions.
A powerful theory has been developed for the case where the comp...
MULTISCALE MAXIMUM LIKELIHOOD ANALYSIS OF A SEMIPARAMETRIC MODEL, WITH APPLICATIONS
LIKELIHOOD ANALYSIS SEMIPARAMETRIC MODEL WITH APPLICATIONS
2015/8/20
A special semiparametric model for a univariate density is introduced
that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for t...
The Block Criterion for Multiscale Inference About a Density, With Applications to Other Multiscale Problems
Fast algorithm Local increase in a density Multiscale test.
2015/8/20
The use of multiscale statistics, that is, the simultaneous inference about various
stretches of data via multiple localized statistics, is a natural and popular method for
inference about, for exam...
FAST MULTISCALE GAUSSIAN WAVEPACKET TRANSFORMS AND MULTISCALE GAUSSIAN BEAMS FOR THE WAVE EQUATION
ast multiscale Gaussian wavepacket transforms multiscale Gaussian beams wave equations
2015/7/14
We introduce a new multiscale Gaussian beam method for the numerical solution of the wave equation with smooth variable coefficients. The first computational question addressed in this paper is how to...
A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation
Multiscale Gaussian beams Multiscale Gaussian wave packets Phase space transform Wave equations
2015/7/14
The Gaussian beam method is an asymptotic method for wave equations with highly oscillatory data. In a recent published paper by two of the authors, a multiscale Gaussian beam method was first propose...
A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTEGRAL OPERATORS
Fourier integral operators the butterfly algorithm hierarchical decomposition separated representation
2015/7/14
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(x,ξ)f (ξ)dξ, where Φ(x, ξ) is a phase funct...
New Multiscale Transforms, Minimum Total Variation Synthesis: Applications to Edge-Preserving Image Reconstruction
Ridgelets curvelets wavelets pseudo-polar FFT Slant Stack Radon transform trigonometric interpolation total-variation edges edge-preserving tomography/deconvolution thresholding
2015/6/17
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
Multiscale Chirplets and Near-Optimal Recovery of Chirps
Minimax Estimation Chirps Recursive Partitioning Time-Frequency Analysis Local Cosines Adaptive Estimation Oracle Inequalities
2015/6/17
This paper considers the model problem of recovering a signal f(t) from noisy sampled measurements. The objects we wish to recover are chirps which are neither smoothly varying nor stationary but rath...