Trischler Adam P, D'Eleuterio Gabriele M T
Maluuba Research, 2000 Peel Street, Montreal, Canada.
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, Canada.
Neural Netw. 2016 Aug;80:67-78. doi: 10.1016/j.neunet.2016.04.001. Epub 2016 Apr 20.
We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that guarantees the quality of the network approximation. We show that a feedforward neural network can be trained on the vector-field representation of a given dynamical system using backpropagation, then recast it as a recurrent network that replicates the original system's dynamics. After detailing this algorithm and its relation to earlier approaches, we present numerical examples that demonstrate its capabilities. One of the distinguishing features of our approach is that both the original dynamical systems and the recurrent networks that simulate them operate in continuous time.
我们回顾了几种训练递归神经网络以逼近动态系统的最广泛使用的技术，然后描述了一种针对此任务的新算法。该算法基于早期的理论结果，该结果保证了网络逼近的质量。我们表明，可以使用反向传播在给定动态系统的向量场表示上训练前馈神经网络，然后将其重塑为复制原始系统动态的递归网络。在详细介绍了该算法及其与早期方法的关系之后，我们给出了展示其能力的数值示例。我们方法的一个显著特点是，原始动态系统和模拟它们的递归网络都在连续时间内运行。
