JACIII Vol.10 No.4 pp. 567-577
doi: 10.20965/jaciii.2006.p0567


Feed-Forward Neural Networks Based on the Eigenstates of the Quantum Harmonic Oscillator

Gerasimos Rigatos

Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece

September 1, 2005
January 30, 2006
July 20, 2006
feed-forward neural networks, quantum harmonic oscillator, Schrödinger’s diffusion equation, Gauss-Hermite expansion, Hermite polynomials

The paper introduces feed-forward neural networks where the hidden units employ orthogonal Hermite polynomials for their activation functions. The proposed neural networks have some interesting properties: (i) the basis functions are invariant under the Fourier transform, subject only to a change of scale, (ii) the basis functions are the eigenstates of the quantum harmonic oscillator, and stem from the solution of Schrödinger’s diffusion equation. The proposed feed-forward neural networks belong to the general category of nonparametric estimators and can be used for function approximation, system modelling and image processing.

Cite this article as:
Gerasimos Rigatos, “Feed-Forward Neural Networks Based on the Eigenstates of the Quantum Harmonic Oscillator,” J. Adv. Comput. Intell. Intell. Inform., Vol.10, No.4, pp. 567-577, 2006.
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