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math.NA2022★ 1 cited
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent
Yiping Lu, Jose Blanchet, Lexing Ying
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general cl…
math.NA2017★ 203 cited
PDE-Net: Learning PDEs from Data
Zichao Long, Yiping Lu, Xianzhong Ma +1
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed…