Fig. 5: Emergent PDE for a network of Hodgkin-Huxley like neurons in the pre-Bötzinger complex.
From: Learning emergent partial differential equations in a learned emergent space
a Trajectories of the ensemble and five snapshots (colored points) in the V, h plane of an ensemble of 1024 neurons. For better visability, only 64 trajectories are shown. b The two emergent coordinates ϕ1 and ϕ2. Through the color coding with the intrinsic heterogeneity \({I}_{{{{{{{{\rm{app}}}}}}}}}^{k}\), one can observe that \({I}_{{{{{{{{\rm{app}}}}}}}}}^{k}\) is a function of the emergent space coordinates. The rectangular grid indicates the space in which we chose to learn an effective PDE. c Snapshot of V at t = 10 obtained by fitting the simulation data on the grid shown in (b). d Snapshot of V at t = 10 predicted by the learned PDE model. e Space-time plot of the evolution of V at the cut ϕ1 = 0, as indicated in (c). f Predictions \(\hat{V}\) of the space-time evolution of V at ϕ1 = 0. The white lines indicate the borders of the boundary conditions.
