160 citations · 172 across the 10 of their papers we have counts for
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math.NA2021★ 11 cited
Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
Yiping Lu, Haoxuan Chen, Jianfeng Lu +2
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method…
cs.LG2021★ 160 cited
Physics-Informed Neural Operator for Learning Partial Differential Equations
Zongyi Li, Hongkai Zheng, Nikola Kovachki +5
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric…