A fast noise filtering algorithm for time series prediction using recurrent neural networks

Recurrent neural networks (RNNs) due to their ability to process sequences of data have found applications in many fields of science, engineering and humanities, including speech, handwriting and human action recognition, automatic translation, robot control etc. One of the RNN application is time series prediction used in analysis of business and financial data, anomaly detection, weather forecast. A large number of different architectures were discussed recently and the flow of new modifications of standard RNN continues to increase and all these architectures share some common features inherited from the basic systems. Trajectory prediction based on incomplete or noisy data is one of the most amazing features of organism brains that allows living creatures to survive in complex and mostly unfriendly environment. A large number of mathematical algorithms developed for this purpose have many applications in multiple engineering field, e.g., development of guidance systems, self-driving vehicles, motor control etc. [1]. It was shown that when the input signal represents a chaotic dynamics (in discrete or discretized continuous setting) RNNs indeed predict chaotic attractor for some number of steps and then the predicted trajectories diverge from the actual ones [2-4]. This result seems natural as it reflects an important property of chaotic dynamics - extremely high sensitivity of chaotic systems to small perturbations in initial conditions. What does happen when a trajectory is perturbed by external noise of specific statistics, e.g., white noise?