.png){kind=icon}
返回
Elliptic PDE learning is provably data-efficient
.png){kind=icon}
OA
AI
DOI：10.1073/pnas.2303904120.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Partial differential equations (PDE) learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data. While deep learning models traditionally require copious amounts of training data, recent PDE learning techniques achieve spectacular results with limited data availability. Still, these results are empirical. Our work provides theoretical guarantees on the number of input-output training pairs required in PDE learning. Specifically, we exploit randomized numerical linear algebra and PDE theory to derive a provably data efficient algorithm that recovers solution operators of three-dimensional uniformly elliptic PDEs from input-output data and achieves an exponential convergence rate of the error with respect to the size of the training dataset with an exceptionally high probability of success.
Keyword:
deep learning
inverse problems
sample complexity
neural operators
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
P
IF:
9.1
论文数:
10.8W
被引数:
73.5W
机构
引用论文
分享收藏Cu-Ni Thin Films Electrodeposited on Si: Composition and Current Efficiency电沉积在Si上的cu-ni薄膜: 组成和电流效率
PREAI
分享收藏The biology and conservation of the giant gippsland earthworm MEGASCOLIDES AUSTRALIS mccoy, 1878
PREAI
分享收藏Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators基于算子通用逼近定理的DeepONet非线性算子学习OAAI
OAAI分享收藏Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions.png)
SIAM REVIEW
OAAI
SIAM REVIEWIF6.1
OAAI分享收藏
查看更多内容