6 papers
Approximate inversion of discrete Fourier integral operators
Jordi Feliu-Fabà, Lexing Ying
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the…
Hierarchical Interpolative Factorization Preconditioner for Parabolic Equations
Jordi Feliu-Fabà, Lexing Ying
This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equati…
Meta-learning Pseudo-differential Operators with Deep Neural Networks
Jordi Feliu-Faba, Yuwei Fan, Lexing Ying
This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-…
Learning Twitter User Sentiments on Climate Change with Limited Labeled Data
Allison Koenecke, Jordi Feliu-Fabà
While it is well-documented that climate change accepters and deniers have become increasingly polarized in the United States over time, there has been no large-scale examination o…
A multiscale neural network based on hierarchical nested bases
Yuwei Fan, Jordi Feliu-Faba, Lin Lin +2
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear map…
Recursively Preconditioned Hierarchical Interpolative Factorization for Elliptic Partial Differential Equations
Jordi Feliu-Fabà, Kenneth L. Ho, Lexing Ying
The hierarchical interpolative factorization for elliptic partial differential equations is a fast algorithm for approximate sparse matrix inversion in linear or quasilinear time.…