The ensemble-mean output (mean over ten independently seeded copies of a trained…
PHYSICS · Multi-part · Fermi University Physics · Computational Physics · High-performance and data-driven computational physics · High-performance and data-driven computational physics
Scientific Computing for Physicists, Ch Neural networks on physical data: backpropagation, convolution and symmetry
Problem
The ensemble-mean output Pˉ (mean over ten independently seeded copies of a trained convolutional classifier, each giving 1 for the ordered phase and 0 for the disordered phase) is measured on independent Monte Carlo configurations of a square Ising lattice of size L=32 at several temperatures, reported as kBT/J: The mean outputs Pˉ at kBT/J=2.15,2.20,2.25,2.30,2.35,2.40 are 0.93,0.81,0.62,0.38,0.19,0.08 respectively.
((a)) Using linear interpolation between the two temperatures whose outputs bracket Pˉ=0.5, locate the half-crossing kBT×/J for L=32.
((b)) Compute the difference between kBT×/J and Onsager's exact value kBTc/J=2.269185.
((c)) State, in one sentence, what else would be needed before this single number could be reported as the network's estimate of Tc rather than only as its L=32 half-crossing.