3 papers
math.NA2021
Solving and Learning Nonlinear PDEs with Gaussian Processes
Yifan Chen, Bamdad Hosseini, Houman Owhadi +1
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identificat…
math.NA2020
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data
Yifan Chen, Thomas Y. Hou
There is an intimate connection between numerical upscaling of multiscale PDEs and scattered data approximation of heterogeneous functions: the coarse variables selected for derivi…
math.ST2020
Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation
Yifan Chen, Houman Owhadi, Andrew M. Stuart
Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of a…