Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

Abstract

Contemporary modeling approaches to the dynamics of neural networks include two important classes of models: biologically grounded spiking neuron models and functionally inspired rate-based units. We present a unified simulation framework that supports the combination of the two for multi-scale modeling, enables the quantitative validation of mean-field approaches by spiking network simulations, and provides an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. In addition to the standard implementation we present an iterative approach based on waveform-relaxation techniques to reduce communication and increase performance for large-scale simulations of rate-based models with instantaneous interactions. Finally we demonstrate the broad applicability of the framework by considering various examples from the literature, ranging from random networks to neural-field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation.

Extremely Scalable Spiking Neuronal Network Simulation Code: From Laptops to Exascale Computers

“…Users can extend the range of available models by employing a domain-specific model description language (Plotnikov et al, 2016 ) or by providing an appropriate implementation in C++. The simulation kernel supports further biophysical mechanisms, for example neuromodulated plasticity (Potjans et al, 2010 ), structural plasticity (Diaz-Pier et al, 2016 ), coupling between neurons via gap junctions (Hahne et al, 2015 ), and non-spiking neurons with continuous interactions, such as rate-based models (Hahne et al, 2017 ).…”

A multi-scale layer-resolved spiking network model of resting-state dynamics in macaque visual cortical areas

“…The stationary firing rates ν i are then given by [ 84 ] which holds up to linear order in and where with ζ denoting the Riemann zeta function [ 85 ]. We solve this equation for our high-dimensional network by finding the fixed points of the first-order differential equation [ 86 ] for different initial conditions ν 0 using the continuous-time dynamics framework of NEST [ 87 ], which uses the exponential Euler algorithm, with step size h = 0.1, where s denotes a dimensionless pseudo-time. To investigate the local stability of the fixed point, we study the evolution of a small perturbation δν around the fixed point ν * to linear order, The perturbation decays to zero if the maximal real value of the eigenvalues of the effective connectivity matrix G , the Jacobian of Φ , is smaller than 1.…”

Efficient Communication in Distributed Simulations of Spiking Neuronal Networks With Gap Junctions

“…A hybrid programming model allows running a combination of MPI processes for distributed computation and threads for lightweight parallelization within compute nodes (Ippen et al, 2017). NEST scales well throughout an entire range of platforms -from laptops to supercomputers (Jordan et al, 2018), and it supports advanced model components, for example neuromodulated plasticity (Potjans et al, 2010), structural plasticity (Diaz-Pier et al, 2016), coupling between neurons via gap junctions (Hahne et al, 2015), and non-spiking neurons with continuous interactions such as rate-based models (Hahne et al, 2017). The simulation code used for the benchmarks is based on the NEST 2.14 release, with Git SHA ba8aa7e (4g) and 0f8d5b5 (5g), respectively.…”

“…This limits the practical use of the technology for large-scale simulations using several hundreds of compute nodes. The framework was later extended to support rate-based connections (Hahne et al, 2017), the scalability issues, however, remained. Technically gap junctions and rate-based connections require similar capabilities in a simulator: both lead to an instantaneous coupling between two neurons.…”