Random balanced network HPC benchmark

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 [1], [2], [3].

A note on connectivity

HPC Benchmark network architecture

Each neuron receives \(K_{in,{\\tau} E}\) excitatory connections randomly drawn from population E and \(K_{in,\\tau I}\) inhibitory connections from population I. Autapses are prohibited (denoted by the crossed out A next to the connections) while multapses are allowed (denoted by the M). Each neuron receives additional input from an external stimulation device. All delays are constant, all weights but excitatory onto excitatory are constant. Excitatory onto excitatory weights are time dependent. Figure taken from [4].

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.


import os
import sys
import time

import nest
import nest.raster_plot
import numpy as np
import scipy.special as sp

M_INFO = 10
M_ERROR = 30

Parameter section Define all relevant parameters: changes should be made here

params = {
    "num_threads": 1,  # total number of threads per process
    "scale": 1.0,  # scaling factor of the network size
    # total network size = scale*11250 neurons
    "simtime": 250.0,  # total simulation time in ms
    "presimtime": 50.0,  # 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 = (
        / (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 1.0 / v_max

For compatibility with earlier benchmarks, we require a rise time of t_rise = 1.700759 ms and we choose tau_syn to achieve this for given tau_m. This requires numerical inversion of the expression for t_rise in convert_synapse_weight. We computed this value once and hard-code it here.

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"],

Function Section

def build_network(logger):
    """Builds the network including setting of simulation and neuron
    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
    nest.local_num_threads = params["num_threads"]
    nest.resolution = params["dt"]
    nest.overwrite_files = True

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

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

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

        random_vm = nest.random.normal(brunel_params["mean_potential"], brunel_params["sigma_potential"])
        nest.GetLocalNodeCollection(E_neurons).V_m = random_vm
        nest.GetLocalNodeCollection(I_neurons).V_m = random_vm

    # number of incoming excitatory connections
    CE = int(1.0 * NE / params["scale"])
    # number of incomining inhibitory connections
    CI = int(1.0 * 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(1.0) * tau_syn
    nu_ext = nu_thresh * brunel_params["eta"]

    E_stimulus = nest.Create("poisson_generator", 1, {"rate": nu_ext * CE * 1000.0})

    nest.message(M_INFO, "build_network", "Creating excitatory spike recorder.")

    if params["record_spikes"]:
        recorder_label = os.path.join(brunel_params["filestem"], "alpha_" + str(stdp_params["alpha"]) + "_spikes")
        E_recorder = nest.Create("spike_recorder", params={"record_to": "ascii", "label": recorder_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_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"}, {"synapse_model": "syn_ex"})
    nest.Connect(E_stimulus, I_neurons, {"rule": "all_to_all"}, {"synapse_model": "syn_ex"})

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

        {"rule": "fixed_indegree", "indegree": CE, "allow_autapses": False, "allow_multapses": True},
        {"synapse_model": "stdp_pl_synapse_hom_hpc"},

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

        {"rule": "fixed_indegree", "indegree": CI, "allow_autapses": False, "allow_multapses": True},
        {"synapse_model": "syn_in"},

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

        {"rule": "fixed_indegree", "indegree": CE, "allow_autapses": False, "allow_multapses": True},
        {"synapse_model": "syn_ex"},

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

        {"rule": "fixed_indegree", "indegree": CI, "allow_autapses": False, "allow_multapses": True},
        {"synapse_model": "syn_in"},

    if params["record_spikes"]:
        if params["num_threads"] != 1:
            local_neurons = nest.GetLocalNodeCollection(E_neurons)
            # GetLocalNodeCollection returns a stepped composite NodeCollection, which
            # cannot be sliced. In order to allow slicing it later on, we're creating a
            # new regular NodeCollection from the plain node IDs.
            local_neurons = nest.NodeCollection(local_neurons.tolist())
            local_neurons = E_neurons

        if len(local_neurons) < brunel_params["Nrec"]:
                """Spikes can only be recorded from local neurons, but the
                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 recorders.")
        nest.Connect(local_neurons[: brunel_params["Nrec"]], E_recorder, "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_recorder if params["record_spikes"] else None

def run_simulation():
    """Performs a simulation, including network construction"""

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

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

        sr = 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(sr)) + " # average rate")


def compute_rate(sr):
    """Compute local approximation of average firing rate

    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 = sr.n_events
    n_local_neurons = brunel_params["Nrec"]
    simtime = params["simtime"]
    return 1.0 * n_local_spikes / (n_local_neurons * simtime) * 1e3

def memory_thisjob():
    """Wrapper to obtain current memory usage"""
    return nest.ll_api.spp()

def lambertwm1(x):
    """Wrapper for LambertWm1 function"""
    # Using scipy to mimic the gsl_sf_lambert_Wm1 function.
    return sp.lambertw(x, k=-1 if x < 0 else 0).real

class Logger:
    """Logger context manager used to properly log memory and timing
    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__":

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