An efficient and accurate solver for large, sparse neural networks
© Stolyarov et al. 2015
Published: 18 December 2015
The mammalian brain has about 1011 neurons and 1014 synapses, with each neuron presenting complex intra-cellular dynamics. The huge number of structures and interactions underlying nervous system function thus make modeling its behavior an extraordinary computational challenge. One strategy to reduce computation time in networks is to replace computationally expensive, stiff models for individual cells (such as the Hodgkin-Huxley equations and other conductance-based models) with integrate-and-fire models. Such models save time by not numerically resolving neural behavior during its action potential; instead, they simply detect the occurrence of an action potential, and propagate its effects to postsynaptic targets appropriately. Thus, a complicated system of continuous ordinary differential equations is replaced with a simpler, but discontinuous, differential equation.
However, accurate existing methods for integrating discontinuous ordinary differential equations (ODEs) scale poorly with problem size, requiring O(N2) time steps for a system with N variables. The underlying challenge is that discontinuities introduce O(dt) errors to conventional time integration schemes, thus requiring very small time steps in the vicinity of a discontinuity .
This work was supported by the SMU Hamilton Undergraduate Research Scholars Program (RS).
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