Synthesis of recurrent neural networks for dynamical system simulation
This work addresses the challenge of simulating continuous-time dynamical systems with neural networks, but it appears incremental as it builds on earlier theoretical results and existing training techniques.
The authors tackled the problem of training recurrent neural networks to approximate dynamical systems by developing a novel algorithm that converts a feedforward network trained on a vector field into a recurrent network, demonstrating its capabilities through numerical examples.
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, using matrix manipulations, 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.