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math.NA2024
Robustness of data-driven approaches in limited angle tomography
Yiran Wang, Yimin Zhong
The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stab…
math.NA2023
An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions
Yiran Wang, Suchuan Dong
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation pro…
math.NA2022
Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media
Yiran Wang, Eric Chung, Shuyu Sun
In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and…