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Inverse problems in neural field theory

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Potthast, R. 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

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To link to this article 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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:29359
Publisher:Society for Industrial and Applied Mathematics

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