all AI news
Learning elliptic partial differential equations with randomized linear algebra. (arXiv:2102.00491v2 [math.NA] UPDATED)
Jan. 24, 2022, 2:10 a.m. | Nicolas Boullé, Alex Townsend
cs.LG updates on arXiv.org arxiv.org
Given input-output pairs of an elliptic partial differential equation (PDE)
in three dimensions, we derive the first theoretically-rigorous scheme for
learning the associated Green's function $G$. By exploiting the hierarchical
low-rank structure of $G$, we show that one can construct an approximant to $G$
that converges almost surely and achieves a relative error of
$\mathcal{O}(\Gamma_\epsilon^{-1/2}\log^3(1/\epsilon)\epsilon)$ using at most
$\mathcal{O}(\epsilon^{-6}\log^4(1/\epsilon))$ input-output training pairs with
high probability, for any $0<\epsilon<1$. The quantity $0<\Gamma_\epsilon\leq
1$ characterizes the quality of the training dataset. Along …
More from arxiv.org / cs.LG updates on arXiv.org
Jobs in AI, ML, Big Data
Senior Machine Learning Engineer (MLOps)
@ Promaton | Remote, Europe
Research Associate (Data Science/Information Engineering/Applied Mathematics/Information Technology)
@ Nanyang Technological University | NTU Main Campus, Singapore
Associate Director of Data Science and Analytics
@ Penn State University | Penn State University Park
Student Worker- Data Scientist
@ TransUnion | Israel - Tel Aviv
Vice President - Customer Segment Analytics Data Science Lead
@ JPMorgan Chase & Co. | Bengaluru, Karnataka, India
Middle/Senior Data Engineer
@ Devexperts | Sofia, Bulgaria