Scaling and Benchmarking an Evolutionary Algorithm for Constructing Biophysical Neuronal Models

Abstract

Single neuron models are fundamental for computational modeling of the brain's neuronal networks, and understanding how ion channel dynamics mediate neural function. A challenge in defining such models is determining biophysically realistic channel distributions. Here, we present an efficient, highly parallel evolutionary algorithm for developing such models, named NeuroGPU-EA. NeuroGPU-EA uses CPUs and GPUs concurrently to simulate and evaluate neuron membrane potentials with respect to multiple stimuli. We demonstrate a logarithmic cost for scaling the stimuli used in the fitting procedure. NeuroGPU-EA outperforms the typically used CPU based evolutionary algorithm by a factor of 10 on a series of scaling benchmarks. We report observed performance bottlenecks and propose mitigation strategies. Finally, we also discuss the potential of this method for efficient simulation and evaluation of electrophysiological waveforms.

Keywords: biophysical neuron model; electrophysiology; evolutionary algorithms; high performance computing; non-convex optimization; strong scaling; weak scaling.

Figure 1

Stimuli and electrophysiological score functions used in algorithm: (A) Various stimuli used in the fitting procedure of EA. (B) Corresponding target voltages that are recorded from patch clamp experiments as a result of the stimuli in (A). (C) Demonstrates how electrophysiological score functions are computed on a single trace. These score functions are used to compare target and simulated firing traces.

Figure 2

(A) Sequential execution EA. (B) CPU-EA maps the simulation/evaluation of a model to a single core. (C) GPU-EA maps each stimuli to a GPU, then scores the simulation in parallel on each CPU core. (D) Timeline of NeuroGPU-EA for two generations. The algorithm starts new stimuli on GPUs while the CPUs are still completing the previous ones.

Figure 3

Simulation-evaluation scaling CPU vs. GPU: Experiments measuring the time it takes to run one simulation-evaluation step using NeuroGPU-EA, CoreNeuron-EA, and CPU-EA. (A) One compute node and population size increases, as in Table 1. (B) Increases compute nodes and population size is constant, as in Table 2. (C) Increasing compute nodes and population size, as in Table 3.

Figure 4

GPU bottleneck shifts to CPU as population per node increases: at large population sizes the CPU operation for score functions is the bottleneck—denoted by relatively taller bars for CPU Eval. At smaller population sizes in (B) the GPU simulation is the bottleneck for CoreNeuron-EA—denoted by relatively taller bars for simulation. CPU and GPU time are balanced at small population sizes for NeuroGPU-EA in (A).

Figure 5

Scaling stimuli and electrophysiological scoring functions: Panel (A) represents the observed run time as the number of stimuli used in the algorithm increases. We provide two lines for scaling reference $\mathcal{O}(\frac{log(n)}{2})$ and $\mathcal{O}(\frac{log(n)}{4})$. Panel (B) represents the observed run time as the number of score functions used in the algorithm increases. We provide two lines for reference, $\mathcal{O}\left(\frac{n}{3}\right)$ and $\mathcal{O}(\frac{log(n)}{4})$.

Figure 6

Best fitted model after 50 generations of EA using 8 stimuli and 20 score functions (red) plotted against experimental data (black). (A) Long square stimulus. (B) Short square stimulus. (C) Noisy stimulus. The remaining stimuli and scores are shown in Supplementary Figure 5 and Supplementary Table 1, respectively.

Figure 7

EA score and model fit both improve with larger population size: (A) Objective function optimization trajectory in EA with varying population sizes. Scores start around 2,500 but the y-axis is constrained to clearly show results. Lower scores indicate a closer fit to experimental data. The minima of the objective function are denoted by large circles and the lower the minima the more the best simulated response resembles the experimentally recorded waveform. Confidence intervals are computed using 10 random initializations. Panel (B) illustrates the neuron model responses corresponding to varying population sizes.