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math.NA2021★ 1 cited
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations
Yifan Chen, Thomas Y. Hou, Yixuan Wang
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 waven…
math.NA2021★ 21 cited
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…