Recurrent Neural Networks for Predicting ODE Dynamics
Brief Description
Recurrent Neural Networks (RNN) have shown to have remarkable capabilities when it comes to modeling sequential data and have been at the forefront of research in time-series forecasting problems in a variety of fields. First looking at RNNs with a mathematical focus, we saw whether claims of model stability from published and unpublished papers could be rigorously defended. We then investigate the practical abilities of RNNs through their implementation on certain systems of ordinary differential equations (ODE). We consider two approaches of Long Short-Term Memory (LSTM) Recurrent Neural Network architectures for predicting future time steps of solutions to first and second order ODEs as well as systems of coupled ODEs to use as a guide for more complicated systems in the future.
Contributors
Camille Renaud & Tan Bui-Thanh