论文标题
通过泊松神经网络学习泊松系统和自治系统的轨迹
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
论文作者
论文摘要
我们提出了泊松神经网络（PNN），以从数据中学习泊松系统和自主系统的轨迹。基于Darboux-lie定理，泊松系统的相流量可以写为（1）坐标转换的组成，（2）扩展的符号映射和（3）转换的倒数。在这项工作中，我们将此结果扩展到了自主系统的未结织轨迹。我们使用具有物理先验的结构化神经网络来近似上述图。我们通过几个模拟证明了PNN能够非常准确地处理几项具有挑战性的任务，包括粒子在电磁电位中的运动，非线性schr {Ö} dinger方程和两体问题的像素观察。
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 Poisson system can be written as the composition of (1) a coordinate transformation, (2) an extended symplectic map and (3) the inverse of the transformation. In this work, we extend this result to the unknotted trajectories of autonomous systems. We employ structured neural networks with physical priors to approximate the three aforementioned maps. We demonstrate through several simulations that PNNs are capable of handling very accurately several challenging tasks, including the motion of a particle in the electromagnetic potential, the nonlinear Schr{ö}dinger equation, and pixel observations of the two-body problem.
