## Search

Now showing items 1-10 of 27

#### Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks

Deep networks, especially Convolutional Neural Networks (CNNs), have been
successfully applied in various areas of machine learning as well as to
challenging problems in other scientific and engineering fields. ...

#### Numerical methods for stochastic differential equations based on Gaussian mixture

We develop in this work a numerical method for stochastic differential
equations (SDEs) with weak second order accuracy based on Gaussian mixture.
Unlike the conventional higher order schemes for SDEs based on It\^o-Tayl...

#### A convergent method for linear half-space kinetic equations

(2017-04-23)

We give a unified proof for the well-posedness of a class of linear half-space equations
with general incoming data and construct a Galerkin method to numerically resolve
this type of equations in a systematic way. Our main ...

#### Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

(2017-04-23)

We develop a surface hopping algorithm based on frozen Gaussian approximation for
semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches
surface hopping method. The algorithm is asymptotically ...

#### Randomized sampling for basis functions construction in generalized finite element methods

(2018-02-14)

In the context of generalized finite element methods for elliptic equations with rough
coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically
on the use of appropriate basis functions. This ...

#### Detecting localized eigenstates of linear operators

(2017-11-30)

We describe a way of detecting the location of localized eigenvectors of a linear
system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large.
We define the family of functions $f_{\alpha}: \left\{1.2. ...

#### A quasinonlocal coupling method for nonlocal and local diffusion models

(2017-04-23)

In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal
diffusion model directly with the classical local diffusion in one dimensional space.
This new coupling framework removes interfacial ...

#### An asymptotic preserving method for transport equations with oscillatory scattering coefficients

(2017-04-26)

We design a numerical scheme for transport equations with oscillatory periodic scattering
coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen
number goes to zero. It also captures ...

#### Solving parametric PDE problems with artificial neural networks

(2017-11-30)

The curse of dimensionality is commonly encountered in numerical partial differential
equations (PDE), especially when uncertainties have to be modeled into the equations
as random coefficients. However, very often ...

#### Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

(2017-04-23)

We present a new cubic scaling algorithm for the calculation of the RPA correlation
energy. Our scheme splits up the dependence between the occupied and virtual orbitals
in $\chi^0$ by use of Cauchy's integral formula. This ...