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Efficient gradient computation for dynamical models.

B Sengupta1, K J Friston1, W D Penny1

  • 1Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.

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|April 29, 2014
PubMed
Summary
This summary is machine-generated.

This study compares gradient estimation techniques for neuroscience data assimilation. The adjoint method is most efficient for optimizing dynamical systems, especially with many parameters.

Keywords:
Adjoint methodsAugmented LagrangianDynamic causal modellingDynamical systemsModel fitting

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Systems Neuroscience

Background:

  • Data assimilation is crucial in neuroscience, from single neurons to fMRI.
  • It involves inverting generative models to explain and predict data.
  • Optimization typically uses gradient-based methods to extremize functionals.

Purpose of the Study:

  • Compare three gradient estimation techniques for time-dependent functionals.
  • Evaluate finite differences, forward sensitivities, and the adjoint method.
  • Determine the most efficient method for dynamical systems.

Main Methods:

  • Implemented and compared finite differences, forward sensitivities, and adjoint methods.
  • Analyzed computational efficiency based on system states and parameters.
  • Focused on gradient estimation for dynamical systems.

Main Results:

  • The adjoint method offers the most efficient gradient computation for dynamical systems.
  • This efficiency is pronounced in systems with more parameters than states.
  • Forward sensitivities are computationally expensive; finite differences are intermediate.

Conclusions:

  • The adjoint method is superior for optimizing complex dynamical models in neuroscience.
  • Adjoint-based inversion of dynamical causal models (DCMs) can scale to large neuroimaging models.
  • This facilitates the study of large-scale neural interactions and network dynamics.