71 citations · 207 across the 22 of their papers we have counts for
4 papers · 1 filter
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…
VPNets: Volume-preserving neural networks for learning source-free dynamics
Aiqing Zhu, Beibei Zhu, Jiawei Zhang +2
We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two net…
Approximation capabilities of measure-preserving neural networks
Aiqing Zhu, Pengzhan Jin, Yifa Tang
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyses the approximati…
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
Pengzhan Jin, Zhen Zhang, Aiqing Zhu +2
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we def…