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Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2016 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 2, B297-B326 p.Article in journal (Refereed) Published
Abstract [en]

The accurate and fast prediction of potential propagation in neuronal networks is of prime importance in neurosciences. This work develops a novel structure-preserving model reduction technique to address this problem based on Galerkin projection and nonnegative operator approximation. It is first shown that the corresponding reduced-order model is guaranteed to be energy stable, thanks to both the structure-preserving approach that constructs a distinct reduced-order basis for each cable in the network and the preservation of nonnegativity. Furthermore, a posteriori error estimates are provided, showing that the model reduction error can be bounded and controlled. Finally, the application to the model reduction of a large-scale neuronal network underlines the capability of the proposed approach to accurately predict the potential propagation in such networks while leading to important speedups.

Place, publisher, year, edition, pages
SIAM publishing , 2016. Vol. 38, no 2, B297-B326 p.
Keyword [en]
Model reduction, non-negative reduced basis, discrete empirical interpolation, Hodgkin-Huxley equation, Summation by parts operators
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-127236DOI: 10.1137/15M1013870ISI: 000375484800031OAI: diva2:920972
Available from: 2016-04-19 Created: 2016-04-19 Last updated: 2016-06-13Bibliographically approved

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