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Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation

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Identifiers
DOI: 10.1137/15M1013870
OAI: oai:DiVA.org:liu-127236
Source
DiVA - Academic Archive On-line
Keywords
  • Model Reduction
  • Non-Negative Reduced Basis
  • Discrete Empirical Interpolation
  • Hodgkin-Huxley Equation
  • Summation By Parts Operators
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Abstract

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.

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