52 citations · 114 across the 9 of their papers we have counts for
4 papers · 1 filter
Neural Partial Differential Equations with Functional Convolution
Ziqian Wu, Xingzhe He, Yijun Li +4
We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of…
Nonseparable Symplectic Neural Networks
Shiying Xiong, Yunjin Tong, Xingzhe He +3
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on pr…
Sparse Symplectically Integrated Neural Networks
Daniel M. DiPietro, Shiying Xiong, Bo Zhu
We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic i…
Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems
Yunjin Tong, Shiying Xiong, Xingzhe He +2
We propose an effective and lightweight learning algorithm, Symplectic Taylor Neural Networks (Taylor-nets), to conduct continuous, long-term predictions of a complex Hamiltonian d…