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Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis +1
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poiss…
Inverse modified differential equations for discovery of dynamics
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified…
Deep Hamiltonian networks based on symplectic integrators
Aiqing Zhu, Pengzhan Jin, Yifa Tang
HNets is a class of neural networks on grounds of physical prior for learning Hamiltonian systems. This paper explains the influences of different integrators as hyper-parameters o…
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…