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math.NA2022★ 1 cited
Tensor Neural Network and Its Numerical Integration
Yifan Wang, Pengzhan Jin, Hehu Xie
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polyno…
cs.LG2022★ 12 cited
On Numerical Integration in Neural Ordinary Differential Equations
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. Howe…
cs.LG2022★ 3 cited
MIONet: Learning multiple-input operators via tensor product
Pengzhan Jin, Shuai Meng, Lu Lu
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several…