45 citations · 184 across the 46 of their papers we have counts for
6 papers · 2 filters
Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
Yiping Lu, Haoxuan Chen, Jianfeng Lu +2
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method…
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…
A semigroup method for high dimensional elliptic PDEs and eigenvalue problems based on neural networks
Haoya Li, Lexing Ying
In this paper, we propose a semigroup method for solving high-dimensional elliptic partial differential equations (PDEs) and the associated eigenvalue problems based on neural netw…
Operator Shifting for General Noisy Matrix Systems
Philip Etter, Lexing Ying
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy…
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…
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
Lukas Einkemmer, Jingwei Hu, Lexing Ying
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the…