3.4k citations · 3.4k across the 19 of their papers we have counts for
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math.SG2019★ 3 cited
Unit triangular factorization of the matrix symplectic group
Pengzhan Jin, Yifa Tang, Aiqing Zhu
In this work, we prove that any symplectic matrix can be factored into no more than 9 unit triangular symplectic matrices. This structure-preserving factorization of the symplectic…
cs.LG2019★ 3.4k cited
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, George Em Karniadakis
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a sin…
stat.ML2019★ 15 cited
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
Pengzhan Jin, Lu Lu, Yifa Tang +1
The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and gene…