52 citations · 114 across the 9 of their papers we have counts for
5 papers · 1 filter
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…
RoeNets: Predicting Discontinuity of Hyperbolic Systems from Continuous Data
Shiying Xiong, Xingzhe He, Yunjin Tong +2
We introduce Roe Neural Networks (RoeNets) that can predict the discontinuity of the hyperbolic conservation laws (HCLs) based on short-term discontinuous and even continuous train…
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…
Neural Vortex Method: from Finite Lagrangian Particles to Infinite Dimensional Eulerian Dynamics
Shiying Xiong, Xingzhe He, Yunjin Tong +2
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex par…
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…