Quantum recurrent neural networks for filtering

Ahamed, Woakil Uddin

Computer science
February 2009

Thesis or dissertation

© 2009 Woakil Uddin Ahamed. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

The essence of stochastic filtering is to compute the time-varying probability densityfunction (pdf) for the measurements of the observed system. In this thesis, a filter isdesigned based on the principles of quantum mechanics where the schrodinger waveequation (SWE) plays the key part. This equation is transformed to fit into the neuralnetwork architecture. Each neuron in the network mediates a spatio-temporal field witha unified quantum activation function that aggregates the pdf information of theobserved signals. The activation function is the result of the solution of the SWE. Theincorporation of SWE into the field of neural network provides a framework which is socalled the quantum recurrent neural network (QRNN). A filter based on this approachis categorized as intelligent filter, as the underlying formulation is based on the analogyto real neuron.In a QRNN filter, the interaction between the observed signal and the wave dynamicsare governed by the SWE. A key issue, therefore, is achieving a solution of the SWEthat ensures the stability of the numerical scheme. Another important aspect indesigning this filter is in the way the wave function transforms the observed signalthrough the network. This research has shown that there are two different ways (anormal wave and a calm wave, Chapter-5) this transformation can be achieved and thesewave packets play a critical role in the evolution of the pdf. In this context, this thesishave investigated the following issues: existing filtering approach in the evolution of thepdf, architecture of the QRNN, the method of solving SWE, numerical stability of thesolution, and propagation of the waves in the well. The methods developed in this thesishave been tested with relevant simulations. The filter has also been tested with somebenchmark chaotic series along with applications to real world situation. Suggestionsare made for the scope of further developments.

Department of Computer Science, The University of Hull
Kambhampati, Chandra
Sponsor (Organisation)
University of Hull
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