Extended Data Fig. 4: Details on Particle Transport and Non- Euclidean Meshes.
From: Neuromorphic scaling advantages for energy-efficient random walk computations
(A) To avoid issues with random walks not ending exactly on the mesh, Δ𝑥 can be expressed as a function of both Δ𝑡𝑡 and ΔΩ (see Eq. SN3.14). The marker on this plot shows the selection for our simulations. (B) Average rounding distance in a single time step across all directions determined by the given value of ΔΩ. (C) The approximate solution to Eq. SN3.12 is calculated using Δ𝑡 = 0.01, Δ𝑥 = 1/15 and the given value of ΔΩ utilizing 1 million walkers per starting location. The absolute value of the difference of this average value and the average value calculated when ΔΩ = 1/15 is presented. In both panels, the blue circle indicates the value of ΔΩ used in the Loihi simulation. (D) Visualization of mesh structure for heat transport examples in the sphere. The center of each triangle represents a location in the mesh or an element of the state space. (E) Visualization of the mesh structure in the barbell. The center of each triangle or rectangle represents a location in the mesh.
