论文标题
带有复发神经网络的随机动力学系统的通用时间均匀轨迹近似
Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks
论文作者
论文摘要
复发性神经网络在随机动力系统的近似轨迹上，具有随机输入，在非紧凑型域上以及无限或无限时间范围的近似轨迹。主要结果指出，在无限时间范围内的某些随机轨迹可以通过一类简单的反馈结构近似地近似于任何所需的准确性，即及时均匀地及时。这里的公式与有关该主题的相关文献形成鲜明对比，其中大部分仅限于紧凑的状态空间和有限的时间间隔。这里需要的模型条件是天然，温和且易于测试的，并且证明非常简单。
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that certain random trajectories over an infinite time horizon may be approximated to any desired accuracy, uniformly in time, by a certain class of deep recurrent neural networks, with simple feedback structures. The formulation here contrasts with related literature on this topic, much of which is restricted to compact state spaces and finite time intervals. The model conditions required here are natural, mild, and easy to test, and the proof is very simple.
