Search from over 60,000 research works

Advanced Search

Inverse problems in neural field theory

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Potthast, R. orcid id iconORCID: https://orcid.org/0000-0001-6794-2500 and Beim Graben, P. (2009) Inverse problems in neural field theory. SIAM Journal on Applied Dynamical Systems, 8 (4). pp. 1405-1433. ISSN 1536-0040 doi: 10.1137/080731220

Abstract/Summary

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Altmetric Badge

Item Type Article
URI https://reading-clone.eprints-hosting.org/id/eprint/29359
Item Type Article
Refereed Yes
Divisions Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher Society for Industrial and Applied Mathematics
Download/View statistics View download statistics for this item

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Search Google Scholar