Fig. 8: Machine learning optimization of (ky, kz) measurement points. | Nature Communications

Fig. 8: Machine learning optimization of (kykz) measurement points.

From: Imaging nodal knots in momentum space through topolectrical circuits

Fig. 8

a Initial suboptimal set of (kykz) sampling points for the drumhead region, subject to a relatively relaxed criterion of \(\mathrm{log}\,| {Z}_{{\rm{avg}}}-{Z}_{{\rm{SD}}}|\, > \, 5.2\), where ZSD is the standard deviation of the impedance subject to 1% tolerance in the capacitances and inductances with parasitic resistance RpL = 0.11 Ω, RpC = 0.03 Ω. While possessing higher impedance than points outside the drumhead region with Zavg < 4.8, these still suffer from significant uncertainty effects (motley of colors). b The Nearest-Neighbor algorithm sets an allowed region (light blue) for new (kykz) points, which are at most a distance 0.1 away from at least two existing good sampling points. c New randomly generated unfiltered sampling points in the allowed region. d Output consisting of new sampling points filtered according to more stringent criteria \(\mathrm{log}\,| {Z}_{{\rm{ideal}}}|\, > \, 5.7,\quad | ({Z}_{{\rm{avg}}}-{Z}_{{\rm{ideal}}})/{Z}_{{\rm{ideal}}}|\, <\, 0.2,\quad {Z}_{{\rm{SD}}}/{Z}_{{\rm{ideal}}}\,<\, 0.2\), which only need to be sieved out from the allowed region.

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