# Runtime Construction of Large-Scale Spiking Neuronal Network Models on GPU Devices
## 2 Materials and Methods
### Models Used for Performance Evaluation  
This present work evaluates the performance of the proposed approach on two network models: a cortical microcircuit and a simple network model of two neuron populations. The models are depicted schematically in Figure 2. The microcircuit model of [PERSON] and [PERSON] [24] represents a 1 mm\({}^{2}\) patch of early sensory cortex at the biological plausible density of neurons and synapses. The full-scale model comprises four cortical layers (L2/3, L4, L5, and L6) and consists of about 77,000 current-based leaky integrate-and-fire model neurons, which are organized into one excitatory and one inhibitory population per layer. These eight neuron populations are recurrently connected by about 300 million synapses with exponentially decaying postsynaptic currents; the connection probabilities are derived from anatomical and electrophysiological measurements. The connection rule used is fixed_total_number with autapses and multapses allowed. The dynamics of the membrane potentials and synaptic currents are integrated using the exact integration method proposed by [PERSON] and [PERSON] [25], and the membrane potential of the neurons of every population are initialized from a normal distribution with mean and standard deviation optimized from the neuron population as in [26]. This approach avoids transients at the beginning of the simulation. Signals originating from outside of the local circuitry, i.e., from other cortical areas and the thalamus, can be approximated with Poisson-distributed spike input or DC current input. Tables 1-4 of [27] (see _fixed total number_ models) contain a detailed model description and report the values of the parameters. The model explains the experimentally observed cell-type and layer-specific firing statistics, and it has been used in the past both as a building block for larger models (e.g., [28]) and as a benchmark for several validation studies [9; 17; 26; 29; 30; 31; 32].  
Figure 2: Schematic representation of the networks used in this work. (**A**) Diagram of the cortical microcircuit model reproduced from [26]. (**B**) Scheme of the network of two populations of Izhikevich neurons.  
The second model is designed for testing the scaling performance of the network construction by changing the number of neurons and the number of connections in the network across biologically relevant ranges for different connection rules (see Section 2.1; autapses and multiapses allowed). The model consists of two equally sized neuron populations, which are recurrently connected to themselves and to each other in four nestgpu.Connect() calls. The total number of neurons in the network is \(N\) (i.e., \(N/2\) per population), and the target total number of connections is \(N\times K\) connections, where \(K\) is the target number of connections per neuron. Dependent on the connection rule used, the instantiated networks may exhibit small deviations from the following target values:  
* fixed_total_number: The total number of connections used in each connect call is set to \(\lfloor N\times K/4\rfloor\).
* fixed_indegree: The in-degree used in each connect call is set to \(\lfloor K/2\rfloor\).
* fixed_outdegree: The out-degree used in each connect call is set to \(\lfloor K/2\rfloor\).  
The network uses Izhikevich neurons [33], but the studied scaling behavior is independent of the neuron model as well as the neuron, connection, and simulation parameters. Indeed, the only parameters that have an impact on this scaling experiment are the total number of neurons and the number of connections per neuron (i.e., \(N\) and \(K\)).