Fig 1.
Model overview: Given a set of parameters θ, a network of point-neurons are simulated, from which the population spiking activities ν(t) are computed (top). With morphological neurons spatially extended in a column, the synaptic spiking activities from the point-neuron network can be ‘replayed’ on the morphological neurons, and the resulting local field potential ϕ(r, t) at 6 locations is computed (bottom). Note that only one excitatory and one inhibitory neuron is shown, in simulation there is one for each point-neuron. The power density spectra Pν(t) and Pϕ(r, t), of the population spiking activities and local field potential respectively, are also computed. The metamodel M directly models the power spectra given the parameter set, or the parameters given observed power spectra.
Table 1.
Description of point-neuron network following the guidelines of [33].
Table 2.
Point-neuron network parameters.
Table 3.
Description of multi-compartment neuron populations.
Table 4.
Multi-compartment neuron parameters.
Fig 2.
Each column shows, from top to bottom, a raster plot, population firing rates, the power spectrum of the population averaged firing rates, the LFP, and the power spectrum of the LFP. The raster plot and firing rates are taken from the excitatory population. A: Synchronous regular activity. B: Synchronous irregular activity. C: Asynchronous irregular activity.
Fig 3.
A: For two different parameter sets, the power spectrum of the population spiking activity from 10 simulations (black lines), and metamodels (blue and orange lines) are shown. The shaded area shows two standard deviations of the distribution given by the metamodels. B: Same as A, but for the LFP. Only the DGPR metamodel was trained on the LFP. C: Distribution over maximum (over frequencies) absolute errors for both metamodels, on the power spectrum of the population spiking activity. D: Same as for C, but for the LFP. E: Mean standard deviation of the metamodel outputs, evaluated at the parameters in the test data set. F: Same as E, but for the LFP.
Fig 4.
Mean (over test data set and training data set) of the maximum (over frequencies) errors, in absolute scale, as a function of the number of examples used to train the metamodels on the population spiking activities.
Fig 5.
In A, C and D, the left-hand and right-hand side show equivalent plots for the population spiking activities and LFPs respectively. The DGPR metamodel is used in both cases. A: 1D and 2D marginal posterior distributions over a subset of the parameters, for an example in the test data set. The red dots and bars show the parameter values corresponding to the simulation output the posterior distribution was computed for. B: Left: mean (across test data set) of standard deviation of the 1D marginal distributions for each parameter. Right: Absolute error of the parameter predictions based on the expectation. C: Metamodel predictions for the power spectra of excitatory population spiking activity (left) and the uppermost channel of the LFP (right) in orange. Black lines show 50 simulation outputs run with parameters drawn from the posterior distribution. D: Distribution of maximum distance between the ground-truth simulation output from which the posterior distribution was computed, and the simulation output from the posterior distributions (black lines in C). Left plot shows the errors from the population spiking activities, right plot shows the errors from the LFP. The black lines show the simulations from the posterior conditioned on the population spiking activities, the gray lines show the simulations from the posterior conditioned on the LFP.
Fig 6.
A: mean marginal standard deviations of the posterior distributions. B: mean marginal standard deviations of the posterior predictive distributions. C: mean distance between expectation of marginal posterior distribution and the parameters from the simulation the posterior distribution is conditioned on. D: Same as C, but for the posterior predictive distribution.
Fig 7.
Pearson correlation coefficients between samples from posterior distribution over parameters, averaged over the test data set.
Upper triangle shows the correlation coefficients for the posterior distributions from the simulated power spectra from the population spiking activities, while the lower triangle shows the same correlation coefficients from the LFP.