Reconstructed Phase Spaces and LSTM Neural Network Ensemble Predictions

Abstract

We present a novel approach that combines the concept of reconstructed phase spaces with neural network time-series predictions. The presented methodology aims to reduce the parametrization problem of neural networks and improve autoregressive neural network time-series predictions. First, the idea is to interpolate a dataset based on its reconstructed phase space properties and then filter an ensemble prediction based on its phase space properties. The corresponding ensemble predictions are made using randomly parameterized LSTM (Long Short-Term Memory) neural networks. These neural networks then produce a multitude of auto-regressive predictions, which are then filtered to achieve a smooth reconstructed phase space trajectory. Thus, we can circumvent the problem of parameterizing the neural network for each dataset individually. Here, the interpolation and the ensemble prediction aim to produce a smooth trajectory in a reconstructed phase space. The best results are compared to a single hidden layer LSTM neural network and benchmark results from the literature. The results show that the baseline predictions are outperformed for all three discussed datasets, and one of the benchmark results from the literature is bested by the presented approach.