Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes
In recent years, there has been widespread adoption of machine learning-based
approaches to automate the solving of partial differential equations (PDEs). Among these …
approaches to automate the solving of partial differential equations (PDEs). Among these …
Exponentially convergent multiscale methods for 2D high frequency heterogeneous Helmholtz equations
In this paper, we present a multiscale framework for solving the Helmholtz equation in
heterogeneous media without scale separation and in the high frequency regime where the …
heterogeneous media without scale separation and in the high frequency regime where the …
Multiscale elliptic PDE upscaling and function approximation via subsampled data
There is an intimate connection between numerical upscaling of multiscale PDEs and
scattered data approximation of heterogeneous functions: the coarse variables selected for …
scattered data approximation of heterogeneous functions: the coarse variables selected for …
[图书][B] On Multiscale and Statistical Numerical Methods for PDEs and Inverse Problems
Y Chen - 2023 - search.proquest.com
This thesis is about numerical methods for scientific computing and scientific machine
learning, with a focus on solving partial differential equations (PDEs) and inverse problems …
learning, with a focus on solving partial differential equations (PDEs) and inverse problems …