10 citations · 21 across the 5 of their papers we have counts for
5 papers · 1 filter
Multi-Level Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data
Zhihan Li, Yuwei Fan, Lexing Ying
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schrödinger equation). In this pape…
Solving Traveltime Tomography with Deep Learning
Yuwei Fan, Lexing Ying
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to…
Coarse-Proxy Reduced Basis Methods for Integral Equations
Philip A. Etter, Yuwei Fan, Lexing Ying
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodo…
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-…
A multiscale neural network based on hierarchical matrices
Yuwei Fan, Lin Lin, Lexing Ying +1
In this work we introduce a new multiscale artificial neural network based on the structure of -matrices. This network generalizes the latter to the nonlinear case by…