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Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
Abstract The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in theExpand
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems
We propose an algorithm for extracting the diagonal of the inverse matrices arising from electronic structure calculation. The proposed algorithm uses a hierarchical decomposition of theExpand
Fast construction of hierarchical matrix representation from matrix-vector multiplication
TLDR
A hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices, is developed, which shows efficiency and accuracy of the proposed algorithm. Expand
Frozen Gaussian Approximation for General Linear Strictly Hyperbolic Systems: Formulation and Eulerian Methods
  • J. Lu, Xu Yang
  • Computer Science, Mathematics
  • Multiscale Model. Simul.
  • 10 October 2010
TLDR
Eulerian methods based on frozen Gaussian approximation are developed to overcome the divergence problem of Lagrangian methods and can also be used for the Herman–Kluk propagator in quantum mechanics. Expand
Deep Network Approximation for Smooth Functions
TLDR
It is established that optimal approximation error characterization of deep ReLU networks for smooth functions in terms of both width and depth simultaneously and is non-asymptotic in the sense that it is valid for arbitrary width anddepth specified by $N\in\mathbb{N}^+$ and $L\in-N^+$, respectively. Expand
Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods
Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuousExpand
Solving parametric PDE problems with artificial neural networks
TLDR
This work proposes using neural network to parameterise the physical quantity of interest as a function of input coefficients and demonstrates the simplicity and accuracy of the approach through notable examples of PDEs in engineering and physics. Expand
Stochastic modified equations for the asynchronous stochastic gradient descent
TLDR
An optimal mini-batching strategy for ASGD via solving the optimal control problem of the associated SME is proposed and the convergence of ASGD to the SME in the continuous time limit is shown. Expand
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
We describe an efficient implementation of an algorithm for computing selected elements of a general sparse symmetric matrix A that can be decomposed as A = LDLT, where L is lower triangular and D isExpand
Scaling Limit of the Stein Variational Gradient Descent: The Mean Field Regime
TLDR
It is proved that in the large particle limit the empirical measure of the particle system converges to a solution of a non-local and nonlinear PDE and global existence, uniqueness and regularity of the solution to the limiting PDE are proved. Expand
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