This script produces a balanced random network of scale*11250 neurons in which the excitatory-excitatory neurons exhibit STDP with multiplicative depression and power-law potentiation. A mutual equilibrium is obtained between the activity dynamics (low rate in asynchronous irregular regime) and the synaptic weight distribution (unimodal). The number of incoming connections per neuron is fixed and independent of network size (indegree=11250).

This is the standard network investigated in: Morrison et al (2007). Spike-timing-dependent plasticity in balanced random networks. Neural Comput 19(6):1437-67 Helias et al (2012). Supercomputers ready for use as discovery machines for neuroscience. Front. Neuroinform. 6:26 Kunkel et al (2014). Spiking network simulation code for petascale computers. Front. Neuroinform. 8:78

A note on scaling

This benchmark was originally developed for very large-scale simulations on supercomputers with more than 1 million neurons in the network and 11.250 incoming synapses per neuron. For such large networks, synaptic input to a single neuron will be little correlated across inputs and network activity will remain stable over long periods of time.

The original network size corresponds to a scale parameter of 100 or more. In order to make it possible to test this benchmark script on desktop computers, the scale parameter is set to 1 below, while the number of 11.250 incoming synapses per neuron is retained. In this limit, correlations in input to neurons are large and will lead to increasing synaptic weights. Over time, network dynamics will therefore become unstable and all neurons in the network will fire in synchrony, leading to extremely slow simulation speeds.

Therefore, the presimulation time is reduced to 50 ms below and the simulation time to 250 ms, while we usually use 100 ms presimulation and 1000 ms simulation time.

For meaningful use of this benchmark, you should use a scale > 10 and check that the firing rate reported at the end of the benchmark is below 10 spikes per second.

from __future__ import print_function  # for Python 2
import numpy as np
import os
import sys
import time

import nest
import nest.raster_plot

M_INFO = 10
M_ERROR = 30

Define all relevant parameters: changes should be made here

params = {
    'nvp': 1,               # total number of virtual processes
    'scale': 1.,            # scaling factor of the network size
                            # total network size = scale*11250 neurons
    'simtime': 250.,        # total simulation time in ms
    'presimtime': 50.,      # simulation time until reaching equilibrium
    'dt': 0.1,              # simulation step
    'record_spikes': True,  # switch to record spikes of excitatory
                            # neurons to file
    'path_name': '.',       # path where all files will have to be written
    'log_file': 'log',      # naming scheme for the log files

def convert_synapse_weight(tau_m, tau_syn, C_m):

Computes conversion factor for synapse weight from mV to pA

This function is specific to the leaky integrate-and-fire neuron model with alpha-shaped postsynaptic currents.

    # compute time to maximum of V_m after spike input
    # to neuron at rest
    a = tau_m / tau_syn
    b = 1.0 / tau_syn - 1.0 / tau_m
    t_rise = 1.0 / b * (-lambertwm1(-np.exp(-1.0 / a) / a).real - 1.0 / a)

    v_max = np.exp(1.0) / (tau_syn * C_m * b) * (
        (np.exp(-t_rise / tau_m) - np.exp(-t_rise / tau_syn)) /
        b - t_rise * np.exp(-t_rise / tau_syn))
    return 1. / v_max

tau_syn = 0.32582722403722841

brunel_params = {
    'NE': int(9000 * params['scale']),  # number of excitatory neurons
    'NI': int(2250 * params['scale']),  # number of inhibitory neurons

    'Nrec': 1000,  # number of neurons to record spikes from

    'model_params': {  # Set variables for iaf_psc_alpha
        'E_L': 0.0,  # Resting membrane potential(mV)
        'C_m': 250.0,  # Capacity of the membrane(pF)
        'tau_m': 10.0,  # Membrane time constant(ms)
        't_ref': 0.5,  # Duration of refractory period(ms)
        'V_th': 20.0,  # Threshold(mV)
        'V_reset': 0.0,  # Reset Potential(mV)
        # time const. postsynaptic excitatory currents(ms)
        'tau_syn_ex': tau_syn,
        # time const. postsynaptic inhibitory currents(ms)
        'tau_syn_in': tau_syn,
        'tau_minus': 30.0,  # time constant for STDP(depression)
        # V can be randomly initialized see below
        'V_m': 5.7  # mean value of membrane potential

    # Note that Kunkel et al. (2014) report different values. The values
    # in the paper were used for the benchmarks on K, the values given
    # here were used for the benchmark on JUQUEEN.
    'randomize_Vm': True,
    'mean_potential': 5.7,
    'sigma_potential': 7.2,

    'delay': 1.5,  # synaptic delay, all connections(ms)

    # synaptic weight
    'JE': 0.14,  # peak of EPSP

    'sigma_w': 3.47,  # standard dev. of E->E synapses(pA)
    'g': -5.0,

    'stdp_params': {
        'delay': 1.5,
        'alpha': 0.0513,
        'lambda': 0.1,  # STDP step size
        'mu': 0.4,  # STDP weight dependence exponent(potentiation)
        'tau_plus': 15.0,  # time constant for potentiation

    'eta': 1.685,  # scaling of external stimulus
    'filestem': params['path_name']

def build_network(logger):

parameters, creation of neurons and connections

Requires an instance of Logger as argument

    tic = time.time()  # start timer on construction

    # unpack a few variables for convenience
    NE = brunel_params['NE']
    NI = brunel_params['NI']
    model_params = brunel_params['model_params']
    stdp_params = brunel_params['stdp_params']

    # set global kernel parameters
        'total_num_virtual_procs': params['nvp'],
        'resolution': params['dt'],
        'overwrite_files': True})

    nest.SetDefaults('iaf_psc_alpha', model_params)

    nest.message(M_INFO, 'build_network', 'Creating excitatory population.')
    E_neurons = nest.Create('iaf_psc_alpha', NE)

    nest.message(M_INFO, 'build_network', 'Creating inhibitory population.')
    I_neurons = nest.Create('iaf_psc_alpha', NI)

    if brunel_params['randomize_Vm']:
        nest.message(M_INFO, 'build_network',
                     'Randomzing membrane potentials.')

        seed = nest.GetKernelStatus(
            'rng_seeds')[-1] + 1 + nest.GetStatus([0], 'vp')[0]
        rng = np.random.RandomState(seed=seed)

        for node in get_local_nodes(E_neurons):
                           {'V_m': rng.normal(

        for node in get_local_nodes(I_neurons):
                           {'V_m': rng.normal(

    # number of incoming excitatory connections
    CE = int(1. * NE / params['scale'])
    # number of incomining inhibitory connections
    CI = int(1. * NI / params['scale'])

    nest.message(M_INFO, 'build_network',
                 'Creating excitatory stimulus generator.')

    # Convert synapse weight from mV to pA
    conversion_factor = convert_synapse_weight(
        model_params['tau_m'], model_params['tau_syn_ex'], model_params['C_m'])
    JE_pA = conversion_factor * brunel_params['JE']

    nu_thresh = model_params['V_th'] / (
        CE * model_params['tau_m'] / model_params['C_m'] *
        JE_pA * np.exp(1.) * tau_syn)
    nu_ext = nu_thresh * brunel_params['eta']

    E_stimulus = nest.Create('poisson_generator', 1, {
                             'rate': nu_ext * CE * 1000.})

    nest.message(M_INFO, 'build_network',
                 'Creating excitatory spike detector.')

    if params['record_spikes']:
        detector_label = os.path.join(
            'alpha_' + str(stdp_params['alpha']) + '_spikes')
        E_detector = nest.Create('spike_detector', 1, {
            'withtime': True, 'to_file': True, 'label': detector_label})

    BuildNodeTime = time.time() - tic

    logger.log(str(BuildNodeTime) + ' # build_time_nodes')
    logger.log(str(memory_thisjob()) + ' # virt_mem_after_nodes')

    tic = time.time()

    nest.SetDefaults('static_synapse_hpc', {'delay': brunel_params['delay']})
    nest.CopyModel('static_synapse_hpc', 'syn_std')
    nest.CopyModel('static_synapse_hpc', 'syn_ex',
                   {'weight': JE_pA})
    nest.CopyModel('static_synapse_hpc', 'syn_in',
                   {'weight': brunel_params['g'] * JE_pA})

    stdp_params['weight'] = JE_pA
    nest.SetDefaults('stdp_pl_synapse_hom_hpc', stdp_params)

    nest.message(M_INFO, 'build_network', 'Connecting stimulus generators.')

    # Connect Poisson generator to neuron

    nest.Connect(E_stimulus, E_neurons, {'rule': 'all_to_all'},
                 {'model': 'syn_ex'})
    nest.Connect(E_stimulus, I_neurons, {'rule': 'all_to_all'},
                 {'model': 'syn_ex'})

    nest.message(M_INFO, 'build_network',
                 'Connecting excitatory -> excitatory population.')

    nest.Connect(E_neurons, E_neurons,
                 {'rule': 'fixed_indegree', 'indegree': CE,
                     'autapses': False, 'multapses': True},
                 {'model': 'stdp_pl_synapse_hom_hpc'})

    nest.message(M_INFO, 'build_network',
                 'Connecting inhibitory -> excitatory population.')

    nest.Connect(I_neurons, E_neurons,
                 {'rule': 'fixed_indegree', 'indegree': CI,
                     'autapses': False, 'multapses': True},
                 {'model': 'syn_in'})

    nest.message(M_INFO, 'build_network',
                 'Connecting excitatory -> inhibitory population.')

    nest.Connect(E_neurons, I_neurons,
                 {'rule': 'fixed_indegree', 'indegree': CE,
                     'autapses': False, 'multapses': True},
                 {'model': 'syn_ex'})

    nest.message(M_INFO, 'build_network',
                 'Connecting inhibitory -> inhibitory population.')

    nest.Connect(I_neurons, I_neurons,
                 {'rule': 'fixed_indegree', 'indegree': CI,
                     'autapses': False, 'multapses': True},
                 {'model': 'syn_in'})

    if params['record_spikes']:
        local_neurons = list(get_local_nodes(E_neurons))

        if len(local_neurons) < brunel_params['Nrec']:
                M_ERROR, 'build_network',
            number of local neurons is smaller than the number of neurons
            spikes should be recorded from. Aborting the simulation!''')

    nest.message(M_INFO, 'build_network', 'Connecting spike detectors.')
    nest.Connect(local_neurons[:brunel_params['Nrec']], E_detector,
                 'all_to_all', 'static_synapse_hpc')

# read out time used for building
BuildEdgeTime = time.time() - tic

logger.log(str(BuildEdgeTime) + ' # build_edge_time')
logger.log(str(memory_thisjob()) + ' # virt_mem_after_edges')

return E_detector if params['record_spikes'] else None

def run_simulation():

    # open log file
    with Logger(params['log_file']) as logger:


        logger.log(str(memory_thisjob()) + ' # virt_mem_0')

        sdet = build_network(logger)

        tic = time.time()


        PreparationTime = time.time() - tic

        logger.log(str(memory_thisjob()) + ' # virt_mem_after_presim')
        logger.log(str(PreparationTime) + ' # presim_time')

        tic = time.time()


        SimCPUTime = time.time() - tic

        logger.log(str(memory_thisjob()) + ' # virt_mem_after_sim')
        logger.log(str(SimCPUTime) + ' # sim_time')

        if params['record_spikes']:
            logger.log(str(compute_rate(sdet)) + ' # average rate')


def compute_rate(sdet):

This approximation is based on the number of local nodes, number of local spikes and total time. Since this also considers devices, the actual firing rate is usually underestimated.

    n_local_spikes = nest.GetStatus(sdet, 'n_events')[0]
    n_local_neurons = brunel_params['Nrec']
    simtime = params['simtime']
    return 1. * n_local_spikes / (n_local_neurons * simtime) * 1e3

def memory_thisjob():'memory_thisjob')
return nest.spp()

def lambertwm1(x):'{} LambertWm1'.format(x))
    return nest.spp()

def get_local_nodes(nodes):

Assumes nodes is a continous list of gids [1, 2, 3, ...], e.g., as returned by Create. Only works for nodes with proxies, i.e., regular neurons.

    nvp = nest.GetKernelStatus('total_num_virtual_procs')  # step size

    i = 0
    while i < len(nodes):
        if nest.GetStatus([nodes[i]], 'local')[0]:
            yield nodes[i]
            i += nvp
            i += 1

class Logger(object):

information from network simulations.

    def __init__(self, file_name):
        # copy output to cout for ranks 0..max_rank_cout-1
        self.max_rank_cout = 5
        # write to log files for ranks 0..max_rank_log-1
        self.max_rank_log = 30
        self.line_counter = 0
        self.file_name = file_name

    def __enter__(self):
        if nest.Rank() < self.max_rank_log:

            # convert rank to string, prepend 0 if necessary to make
            # numbers equally wide for all ranks
            rank = '{:0' + str(len(str(self.max_rank_log))) + '}'
            fn = '{fn}_{rank}.dat'.format(
                fn=self.file_name, rank=rank.format(nest.Rank()))

            self.f = open(fn, 'w')

            return self

    def log(self, value):
        if nest.Rank() < self.max_rank_log:
            line = '{lc} {rank} {value} \n'.format(
                lc=self.line_counter, rank=nest.Rank(), value=value)
            self.line_counter += 1

        if nest.Rank() < self.max_rank_cout:
            print(str(nest.Rank()) + ' ' + value + '\n', file=sys.stdout)
            print(str(nest.Rank()) + ' ' + value + '\n', file=sys.stderr)

    def __exit__(self, exc_type, exc_val, traceback):
        if nest.Rank() < self.max_rank_log:

if __name__ == '__main__':